tag:blogger.com,1999:blog-58537456213008418362024-03-06T01:39:40.332+07:00Mathematics's HouseThis blog consist of many mathematics problem and also many fact of mathematics. If you interest with MATHEMATICS, check this out !!!Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.comBlogger30125tag:blogger.com,1999:blog-5853745621300841836.post-76244363683905992522014-01-23T16:06:00.000+07:002014-01-23T16:06:27.012+07:00Persegi dalam LingkaranDiketahui sebuah lingkarang dengan tepat didalamnya terdapat sebuah persegi dengan panjang rusuk 14cm, berapakah luas lingkaran tersebut?Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-26083500119611604102014-01-23T15:57:00.003+07:002014-01-23T15:58:07.237+07:00Sisa Pembagian FaktorialTentukanlah sisa pembagian 1! + 2! + . . . + 2014! oleh 7 !Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-33163196958526714082013-11-25T15:01:00.000+07:002013-11-25T15:01:11.295+07:00Is This Your Card?<div style="background-color: white; color: #333333; font-family: 'Century Schoolbook', Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin-bottom: 25px;">
A magician randomly draws one card from a standard <span class="latexprocessor-inline latexprocessor-f9714ea999b36764e6fa455dc076e16ad115c3d849ad4acdd69f957a3c0224be" style="font-size: 20px;"><path d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z" id="MJMAIN-35-b291887027ca11e3bb5c40400601ade9039bdf28ec484fd0b50208acd725c000" stroke-width="0"></path><path d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z" id="MJMAIN-32-b291887027ca11e3bb5c40400601ade9039bdf28ec484fd0b50208acd725c000" stroke-width="0"></path></span>card deck. The probability that the card drawn is a heart or a diamond can be written as <span class="latexprocessor-inline latexprocessor-1bc0591dbd99ca179a11c1909b71787db0a39f4d71c1c79a7bfa97836d205313" style="font-size: 20px;"><path d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z" id="MJMATHI-61-7bc27ed4261311e3937340400601ade9c604315556b1479a8127549eca12f2a4" stroke-width="0"></path><path d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z" id="MJMATHI-62-7bc27ed4261311e3937340400601ade9c604315556b1479a8127549eca12f2a4" stroke-width="0"></path></span>, where <span class="latexprocessor-inline latexprocessor-5220707bcc6c973ee9df3f1b1089b126fb52d0bc063424a5729e57e706693e67" style="font-size: 20px;"><path d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z" id="MJMATHI-61-41fb76b0261311e3937340400601ade9d897724fee1845a297ca1dfdb6429de6" stroke-width="0"></path></span> and <span class="latexprocessor-inline latexprocessor-4e92c15aec5458acc79f9fc4ff17ace1109bfee735e8b1587bce5d86347ed81a" style="font-size: 20px;"><path d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z" id="MJMATHI-62-4597348a261311e3937340400601ade90f90f01c82214651a386291ff17b69fc" stroke-width="0"></path></span> are positive, coprime integers. What is the value of <span class="latexprocessor-inline latexprocessor-56901c3709b31f9b86b9ba24fb1eb337a5e5051ae951e1635e6c6a896f4a26d5" style="font-size: 20px;"><path d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z" id="MJMATHI-61-47267d9c261311e3937340400601ade9ab59cabb732541fcad2e709503607083" stroke-width="0"></path><path d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z" id="MJMAIN-2B-47267d9c261311e3937340400601ade9ab59cabb732541fcad2e709503607083" stroke-width="0"></path><path d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z" id="MJMATHI-62-47267d9c261311e3937340400601ade9ab59cabb732541fcad2e709503607083" stroke-width="0"></path></span>?</div>
<div class="assumptions" style="background-color: white; clear: left; color: #333333; float: left; font-family: 'Century Schoolbook', Georgia, 'Times New Roman', Times, serif; font-size: 0.75em; line-height: 30.9375px; margin-bottom: 15px; width: 580px;">
<h3 style="color: inherit; font-family: inherit; font-size: 1.05em; line-height: 27px; margin: 0px; text-rendering: optimizelegibility;">
Details and assumptions</h3>
<div style="line-height: 1.4em; margin-bottom: 15px;">
A standard deck of cards consists of 52 cards, formed by 13 ranks (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q and K) of 4 suits (clubs, diamonds, hearts and spades).</div>
</div>
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-16148587144547311772013-11-25T14:45:00.002+07:002013-11-25T14:45:42.996+07:00Point of Discontinuity<span style="background-color: white; color: #333333; font-family: 'Century Schoolbook', Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;">f is a function defined on the positive reals such that </span><span class="latexprocessor-inline latexprocessor-3782389b4292a54986f63587de9e62b8345db54c5d6a4ba67d942aa6056d3931" style="background-color: white; color: #333333; font-family: 'Century Schoolbook', Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 30.9375px;"><svg style="height: 3.222ex; margin-bottom: 1px; margin-left: 0px; margin-right: 0px; margin-top: 1px; vertical-align: -1.222ex; width: 20.111ex;" viewbox="0 -907.0915167844012 8678.559159102155 1380.5245811019809" 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71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z" id="MJMATHI-78-622ea0a4545a11e38dd940400601ade968c1a524de704473a5f94ece622f2cac" stroke-width="0"></path><path d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z" id="MJMAIN-2B-622ea0a4545a11e38dd940400601ade968c1a524de704473a5f94ece622f2cac" stroke-width="0"></path><path d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z" id="MJMAIN-36-622ea0a4545a11e38dd940400601ade968c1a524de704473a5f94ece622f2cac" stroke-width="0"></path><path d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z" id="MJMAIN-30-622ea0a4545a11e38dd940400601ade968c1a524de704473a5f94ece622f2cac" stroke-width="0"></path><path d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z" id="MJMATHI-78-622ea0a4545a11e38dd940400601ade968c1a524de704473a5f94ece622f2cac" stroke-width="0"></path><path d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z" 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For what value of </span><span class="latexprocessor-inline latexprocessor-b5eb933c119f6667524ce50ea2589d75a032624cfcafa90609d0cc5610963b14" style="background-color: white; color: #333333; font-family: 'Century Schoolbook', Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 30.9375px;"><svg style="height: 1.111ex; margin-bottom: 1px; margin-left: 0px; margin-right: 0px; margin-top: 1px; vertical-align: -0.222ex; width: 1.333ex;" viewbox="0 -462.9033013280564 572 494.80660265611283" xmlns:xlink="http://www.w3.org/1999/xlink"><defs id="MathJax_SVG_glyphs-538bb548261311e3937340400601ade92b36ddfabd924414a2f2919facbf4bf4"><path d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z" id="MJMATHI-78-538bb548261311e3937340400601ade92b36ddfabd924414a2f2919facbf4bf4" stroke-width="0"></path></defs><g fill="black" stroke-width="0" stroke="black" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-78-538bb548261311e3937340400601ade92b36ddfabd924414a2f2919facbf4bf4"></use></g></svg></span><span style="background-color: white; color: #333333; font-family: 'Century Schoolbook', Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"> is </span><span class="latexprocessor-inline latexprocessor-87c09674dfb7478bedaf03e3ed79ecfe96a6f711639fc70d4ca50c5f2e77f438" style="background-color: white; color: #333333; font-family: 'Century Schoolbook', Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 30.9375px;"><svg style="height: 2.444ex; margin-bottom: 1px; margin-left: 0px; margin-right: 0px; margin-top: 1px; vertical-align: -0.778ex; width: 4.444ex;" viewbox="0 -770.9033013280564 1900 1041.8066026561128" xmlns:xlink="http://www.w3.org/1999/xlink"><defs id="MathJax_SVG_glyphs-44509620261311e3937340400601ade9e875228c964d4366b3e3bd08f7171395"><path d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z" id="MJMATHI-66-44509620261311e3937340400601ade9e875228c964d4366b3e3bd08f7171395" stroke-width="0"></path><path d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z" id="MJMAIN-28-44509620261311e3937340400601ade9e875228c964d4366b3e3bd08f7171395" stroke-width="0"></path><path d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z" id="MJMATHI-78-44509620261311e3937340400601ade9e875228c964d4366b3e3bd08f7171395" stroke-width="0"></path><path d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z" id="MJMAIN-29-44509620261311e3937340400601ade9e875228c964d4366b3e3bd08f7171395" stroke-width="0"></path></defs><g fill="black" stroke-width="0" stroke="black" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-66-44509620261311e3937340400601ade9e875228c964d4366b3e3bd08f7171395"></use><use x="550" xlink:href="#MJMAIN-28-44509620261311e3937340400601ade9e875228c964d4366b3e3bd08f7171395" y="0"></use><use x="939" xlink:href="#MJMATHI-78-44509620261311e3937340400601ade9e875228c964d4366b3e3bd08f7171395" y="0"></use><use x="1511" xlink:href="#MJMAIN-29-44509620261311e3937340400601ade9e875228c964d4366b3e3bd08f7171395" y="0"></use></g></svg></span><span style="background-color: white; color: #333333; font-family: 'Century Schoolbook', Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"> undefined?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-27193540379652113192013-11-25T14:35:00.004+07:002013-11-25T14:36:05.613+07:00The Curve of "Love"<br />
<div style="text-align: justify;">
<span style="color: red; font-family: Georgia, 'Times New Roman', serif;">If we talk about love, we know that love is one of abstract things in this world. Like Mathematics, love just can feel with mind, heart, and sense. We know the symbol of love, isn't right? With mathematics, we can draw the symbol of love in Cartesian Coordinate. Its so amazing right? Mathematics like a magic, all things that we think can't happen, but in mathematics, it can be happen.</span></div>
<span style="font-family: Georgia, Times New Roman, serif;"><div style="text-align: justify;">
<span style="background-color: white; color: magenta;">This is the equation of "Love" :</span></div>
<span style="background-color: white; color: magenta;"><div style="text-align: justify;">
x⁶ + 3x⁴ y² - 3x⁴ + 3x² y⁴ - x² y³ - 6x² y² + 3x² + y⁶ - 3y⁴ + 3y² = 1</div>
<div style="text-align: justify;">
And if we draw the equation in Cartesian Coordinate (I use GeoGebra) we get:</div>
</span></span><br />
<br />
<div style="text-align: justify;">
<span style="color: magenta; font-family: Georgia, 'Times New Roman', serif;"><br /></span></div>
<span style="font-family: Georgia, Times New Roman, serif;"><div style="text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5ANIWkTHuuVucq8AD0BWme8jeypyZcuAotInz0tis7Mq9rNnVtRSGnLVEQRlYkg3_HJCAKw8VgErmzBf-HA8T0e9ozn4LntGZd2-W2iOPgLqAQhJ6oSQUqhDShcUj1JiPw-Rd4g1HJdE/s1600/love.png" imageanchor="1" style="color: magenta; margin-left: 1em; margin-right: 1em;"><img border="0" height="306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5ANIWkTHuuVucq8AD0BWme8jeypyZcuAotInz0tis7Mq9rNnVtRSGnLVEQRlYkg3_HJCAKw8VgErmzBf-HA8T0e9ozn4LntGZd2-W2iOPgLqAQhJ6oSQUqhDShcUj1JiPw-Rd4g1HJdE/s400/love.png" width="400" /></a></div>
<div style="text-align: justify;">
<br /></div>
<span style="background-color: white; color: lime;"><div style="text-align: justify;">
Believe it !!! It so amazing, with Mathematics we can do anything, so please loving mathematics !!!</div>
</span></span><br />
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-38765329492555873342013-07-30T16:44:00.003+07:002013-07-30T16:45:52.381+07:00Slope through two points<span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">Find the slope of a line that passes through the points </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.488em;"><span style="border: 0px; clip: rect(1.284em 1000em 2.542em -0.294em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mo" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">(</span><span class="mn" id="MathJax-Span-4" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-5" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mo" id="MathJax-Span-6" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">−</span><span class="mn" id="MathJax-Span-7" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">26</span><span class="mo" id="MathJax-Span-8" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">)</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.26em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.34em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">and </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-9" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.713em;"><span style="border: 0px; clip: rect(1.284em 1000em 2.542em -0.294em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-10" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mo" id="MathJax-Span-11" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">(</span><span class="mn" id="MathJax-Span-12" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">8</span><span class="mo" id="MathJax-Span-13" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-14" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">19</span><span class="mo" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">)</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.26em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.34em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">.</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-55979446065788064072013-07-30T16:44:00.001+07:002013-07-30T16:45:52.384+07:00X-intercept of a line<span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">What is the </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.56em;"><span style="border: 0px; clip: rect(1.592em 1000em 2.303em -0.353em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">x</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.625em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.063em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">-intercept of the line </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-4" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 5.125em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.497em -0.367em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-5" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-6" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">y<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.006em;"></span></span><span class="mo" id="MathJax-Span-7" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-8" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">2</span><span class="mi" id="MathJax-Span-9" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">x</span><span class="mo" id="MathJax-Span-10" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">−</span><span class="mn" id="MathJax-Span-11" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">96</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.11em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.288em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-46955718282496069172013-07-30T16:43:00.001+07:002013-07-30T16:45:52.382+07:00The y-intercept<span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">What is the </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.517em;"><span style="border: 0px; clip: rect(1.592em 1000em 2.497em -0.367em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">y<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.006em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.85em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.288em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">-intercept of the line with slope </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-4" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.67em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.303em -0.367em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-5" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-6" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">m</span><span class="mo" id="MathJax-Span-7" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-8" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">1</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.885em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.063em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;"> that passes through the point </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-3-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-9" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.488em;"><span style="border: 0px; clip: rect(1.284em 1000em 2.542em -0.294em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-10" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mo" id="MathJax-Span-11" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">(</span><span class="mn" id="MathJax-Span-12" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">19</span><span class="mo" id="MathJax-Span-13" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mtext" id="MathJax-Span-14" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;"> </span><span class="mn" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">33</span><span class="mo" id="MathJax-Span-16" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">)</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.26em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.34em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-84334658506811514272013-07-30T16:40:00.003+07:002013-07-30T16:42:07.703+07:00Minimario's diagonal<div style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin-bottom: 25px;">
Let <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.108em;"><span style="border: 0px; clip: rect(1.346em 1000em 2.32em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-4" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mi" id="MathJax-Span-5" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span><span class="mi" id="MathJax-Span-6" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">D</span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.939em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span> be a square with side length <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-7" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.512em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.338em -0.304em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-8" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-9" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">2</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.856em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span> and let <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-3-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-10" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.866em;"><span style="border: 0px; clip: rect(1.379em 1000em 2.298em -0.328em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-11" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-12" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">X<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.024em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.876em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span> be a point outside the square such that <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-4-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-13" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 7.161em;"><span style="border: 0px; clip: rect(1.237em 1000em 2.482em -0.328em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-14" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">X<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.024em;"></span></span><span class="mi" id="MathJax-Span-16" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mo" id="MathJax-Span-17" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="mi" id="MathJax-Span-18" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">X<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.024em;"></span></span><span class="mi" id="MathJax-Span-19" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mo" id="MathJax-Span-20" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="msqrt" id="MathJax-Span-21" style="border: 0px; display: inline; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.338em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.338em -0.304em); left: 0.826em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-22" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-23" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">2</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.882em 1000em 1.178em -0.354em); left: 0.826em; margin: 0px; padding: 0px; position: absolute; top: -1.865em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.512em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.082em 1000em 4.318em -0.282em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -4.056em; vertical-align: 0px;"><span style="border: 0px; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">√</span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.251em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.211em; width: 0px;"></span></span></nobr></span>. The length of the longest diagonal in pentagon <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-5-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-24" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.935em;"><span style="border: 0px; clip: rect(1.346em 1000em 2.32em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-25" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-26" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-27" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">X<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.024em;"></span></span><span class="mi" id="MathJax-Span-28" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mi" id="MathJax-Span-29" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span><span class="mi" id="MathJax-Span-30" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">D</span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.939em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span> can be expressed as <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-6-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-31" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.377em;"><span style="border: 0px; clip: rect(3.136em 1000em 4.38em -0.282em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -4em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-32" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="msqrt" id="MathJax-Span-33" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.377em;"><span style="border: 0px; clip: rect(1.62em 1000em 2.309em -0.319em); left: 0.826em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-34" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-35" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">x</span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.882em 1000em 1.178em -0.354em); left: 0.826em; margin: 0px; padding: 0px; position: absolute; top: -1.746em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.551em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.082em 1000em 4.318em -0.282em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -3.938em; vertical-align: 0px;"><span style="border: 0px; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">√</span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.25em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.347em; width: 0px;"></span></span></nobr></span>. What is the value of <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-7-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-36" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.551em;"><span style="border: 0px; clip: rect(1.62em 1000em 2.309em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-37" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-38" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">x</span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.611em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.058em; width: 0px;"></span></span></nobr></span>?</div>
<div style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin-bottom: 25px;">
</div>
<div class="solvable-image center" style="background-color: white; clear: left; color: #333333; float: left; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin: 20px 0px; width: 580px;">
<img src="https://brilliant1.r.worldssl.net/user_media/solvable/images/3675_diag.png" style="border: 0px; margin: 0px auto; max-width: 100%; vertical-align: middle;" /></div>
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-32793956190624362502013-07-30T16:39:00.002+07:002013-07-30T16:39:58.155+07:00Maximizing Rectangle Area<div style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin-bottom: 25px;">
A rectangle has perimeter equal to <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.023em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.36em -0.304em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">28</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.882em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span>. What is the maximum possible area of this rectangle?</div>
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-76808946243238090562013-07-30T16:36:00.003+07:002013-07-30T16:38:23.062+07:00Area of Inscribed Isosceles Triangle<div style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin-bottom: 25px;">
<span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.282em;"><span style="border: 0px; clip: rect(1.346em 1000em 2.32em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-4" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mi" id="MathJax-Span-5" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.939em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span> is an isosceles triangle with <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-6" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 4.328em;"><span style="border: 0px; clip: rect(1.386em 1000em 2.36em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-7" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-8" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-9" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mo" id="MathJax-Span-10" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="mi" id="MathJax-Span-11" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">B</span><span class="mi" id="MathJax-Span-12" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.939em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span>. The circumcircle of <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-3-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-13" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.282em;"><span style="border: 0px; clip: rect(1.346em 1000em 2.32em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-14" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-16" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mi" id="MathJax-Span-17" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.939em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span> has radius <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-4-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-18" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.512em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.36em -0.311em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-19" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-20" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">8</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.882em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span>. Given that <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-5-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-21" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.535em;"><span style="border: 0px; clip: rect(1.346em 1000em 2.32em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-22" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-23" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-24" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.939em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span> is a diameter of the circumcircle, what is the area of triangle <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-6-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-25" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.282em;"><span style="border: 0px; clip: rect(1.346em 1000em 2.32em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-26" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-27" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-28" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mi" id="MathJax-Span-29" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.939em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span>?</div>
<div class="assumptions" style="background-color: white; clear: left; color: #333333; float: left; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 0.75em; line-height: 30.9375px; margin-bottom: 15px; width: 580px;">
<h3 style="color: inherit; font-family: inherit; font-size: 1.05em; line-height: 27px; margin: 0px; text-rendering: optimizelegibility;">
Details and assumptions</h3>
<div style="line-height: 1.4em; margin-bottom: 15px;">
The <strong>circumcircle</strong> of a triangle <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-7-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 17px; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-30" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 19px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.315em;"><span style="border: 0px; clip: rect(1.361em 1000em 2.422em -0.45em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.238em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-31" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-32" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-33" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mi" id="MathJax-Span-34" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.238em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.947em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.085em; width: 0px;"></span></span></nobr></span> passes through <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-8-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 17px; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-35" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 19px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.177em;"><span style="border: 0px; clip: rect(1.415em 1000em 2.648em -0.45em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.292em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-36" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-37" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mo" id="MathJax-Span-38" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mi" id="MathJax-Span-39" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">B</span><span class="mo" id="MathJax-Span-40" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mi" id="MathJax-Span-41" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.292em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.14em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.278em; width: 0px;"></span></span></nobr></span>.</div>
</div>
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-63148548281378916472013-07-30T16:34:00.003+07:002013-07-30T16:35:28.440+07:00Angles in a Acute Triangle<div style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin-bottom: 25px;">
In acute triangle <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.148em;"><span style="border: 0px; clip: rect(1.386em 1000em 2.36em -0.295em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">△</span><span class="mi" id="MathJax-Span-4" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-5" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mi" id="MathJax-Span-6" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.939em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span>, <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-7" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 5.745em;"><span style="border: 0px; clip: rect(1.384em 1000em 2.36em -0.299em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-8" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-9" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">∠</span><span class="mi" id="MathJax-Span-10" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span><span class="mi" id="MathJax-Span-11" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-12" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mo" id="MathJax-Span-13" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="msubsup" id="MathJax-Span-14" style="border: 0px; display: inline; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.452em;"><span style="border: 0px; clip: rect(1.425em 1000em 2.36em -0.312em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">34</span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 1.023em; margin: 0px; padding: 0px; position: absolute; top: -2.584em; vertical-align: 0px;"><span class="mo" id="MathJax-Span-16" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 18px; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">∘</span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.941em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span> and <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-3-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-17" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.748em;"><span style="border: 0px; clip: rect(1.382em 1000em 2.298em -0.323em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-18" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-19" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">E<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.026em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.872em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span> is the foot of the perpendicular from <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-4-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-20" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.748em;"><span style="border: 0px; clip: rect(1.379em 1000em 2.298em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-21" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-22" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.876em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span> to <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-5-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-23" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.535em;"><span style="border: 0px; clip: rect(1.346em 1000em 2.32em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-24" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-25" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-26" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.045em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.939em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span>. A point <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-6-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-27" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.905em;"><span style="border: 0px; clip: rect(1.379em 1000em 2.298em -0.323em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-28" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-29" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">H<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.057em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.876em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span> on line segment <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-7-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-30" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.495em;"><span style="border: 0px; clip: rect(1.379em 1000em 2.298em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-31" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-32" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span><span class="mi" id="MathJax-Span-33" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">E<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.026em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.876em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span> is chosen, and <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-8-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-34" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.866em;"><span style="border: 0px; clip: rect(1.379em 1000em 2.298em -0.328em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-35" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-36" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">X<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.024em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.876em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span> is the foot of the perpendicular from <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-9-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-37" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.905em;"><span style="border: 0px; clip: rect(1.379em 1000em 2.298em -0.323em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-38" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-39" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">H<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.057em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.876em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span> to <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-10-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-40" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.495em;"><span style="border: 0px; clip: rect(1.346em 1000em 2.298em -0.319em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-41" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-42" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">A</span><span class="mi" id="MathJax-Span-43" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">B</span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.914em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span>. What is the measure (in degrees) of <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-11-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-44" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.187em;"><span style="border: 0px; clip: rect(1.408em 1000em 2.338em -0.299em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-45" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-46" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">∠</span><span class="mi" id="MathJax-Span-47" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">E<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.026em;"></span></span><span class="mi" id="MathJax-Span-48" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">H<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.057em;"></span></span><span class="mi" id="MathJax-Span-49" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">X<span style="border: 0px; display: inline-block; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.024em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.889em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span>?</div>
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<div class="solvable-image center" style="background-color: white; clear: left; color: #333333; float: left; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin: 20px 0px; width: 580px;">
<img src="https://brilliant1.r.worldssl.net/user_media/solvable/images/1358_diag.png" style="border: 0px; margin: 0px auto; max-width: 100%; vertical-align: middle;" /></div>
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-75431416146120093192013-07-30T16:30:00.005+07:002013-07-30T16:32:08.774+07:00Calvin the Cat man<span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;">Calvin has 3 cats. The oldest cat Heathcliff is 16 years old. The mean age of the cats is 10. The median age of the cats is 8. What is the age of the youngest cat?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-89824823481542810882013-07-30T16:30:00.004+07:002013-07-30T16:31:59.796+07:00Possible Test Scores for a grade of B<span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;">You are taking a Math class, where your grade is determined by your performance in 5 tests. The maximum score on each test is 100. Your first </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.512em;"><span style="border: 0px; clip: rect(1.425em 1000em 2.338em -0.326em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">4</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.869em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.045em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"> test scores have been </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-4" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.935em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.532em -0.312em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-5" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-6" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">63</span><span class="mo" id="MathJax-Span-7" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-8" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">80</span><span class="mo" id="MathJax-Span-9" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-10" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">90</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.079em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.268em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"> and </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-3-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-11" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.023em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.36em -0.311em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-12" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-13" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">85</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.882em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;">. To receive a B in the class, the average of the five test scores must be greater than or equal to </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-4-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-14" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.023em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.36em -0.311em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-15" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-16" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">80</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.882em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"> and strictly smaller than </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-5-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-17" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.023em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.36em -0.312em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-18" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-19" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">90</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.882em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;">. If only integer test scores are allowed, how many different test scores could you receive for the last test and get a grade of B?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-53621979687562279382013-07-30T16:25:00.002+07:002013-07-30T16:29:46.546+07:00Trip Expenses<span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;">A group of friends are planning a road trip. If they all contribute $24, then they would be $6 short of the total cost of the trip. If they all contribute $25, then they would have $3 more than the total cost of the trip. What is the total cost of the trip?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-59527054519671501332013-07-30T16:24:00.001+07:002013-07-30T16:25:17.629+07:00Pity the frog<span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;">A frog is stuck at the bottom of a man-made well which is 21 feet deep. Each day, the frog is able to climb up 5 feet. However, each night, the frog slides down 3 feet. On which day would the frog be able to escape this well?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-23184010779614272712013-07-30T16:21:00.001+07:002013-07-30T16:22:46.516+07:00Find that remainder!<span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;">What is the remainder when </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.046em;"><span style="border: 0px; clip: rect(1.425em 1000em 2.36em -0.326em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">4321</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.894em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"> is divided by </span><span class="MathJax_Preview" style="background-color: white; color: #888888; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="background-color: white; border: 0px; color: #333333; direction: ltr; display: inline; float: none; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; margin: 0px; padding: 0px; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-4" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.535em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.36em -0.312em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-5" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-6" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">321</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.882em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.071em; width: 0px;"></span></span></nobr></span><span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px;">?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-12906171409165275282013-07-30T16:16:00.003+07:002013-07-30T16:22:46.515+07:00Reciprocal Sum Equality<div style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin-bottom: 25px;">
If <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.512em;"><span style="border: 0px; clip: rect(1.621em 1000em 2.308em -0.321em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">a</span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.609em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.057em; width: 0px;"></span></span></nobr></span> and <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-4" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.433em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.309em -0.314em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.18em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-5" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-6" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">b</span></span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.901em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.058em; width: 0px;"></span></span></nobr></span> are coprime positive integers such that</div>
<div style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin-bottom: 25px;">
<span class="MathJax_Preview" style="color: #888888;"></span></div>
<div aria-readonly="true" class="MathJax_Display" role="textbox" style="margin: 1em 0em; position: relative; text-align: center; width: 580px;">
<span class="MathJax" id="MathJax-Element-3-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 22px; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-7" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 9.522em;"><span style="border: 0px; clip: rect(0.759em 1000em 3.046em -0.234em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-8" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-9" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.632em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.338em -0.271em); left: 8.015625px; margin: 0px 0px 0px -0.256em; padding: 0px; position: absolute; top: -2.896em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-10" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.436em 1000em 2.338em -0.304em); left: 8.015625px; margin: 0px 0px 0px -0.256em; padding: 0px; position: absolute; top: -1.534em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-11" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">2</span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.882em 1000em 1.178em -0.354em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.28em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.632em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-12" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mfrac" id="MathJax-Span-13" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em 0px 0.342em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.632em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.338em -0.271em); left: 8.015625px; margin: 0px 0px 0px -0.256em; padding: 0px; position: absolute; top: -2.896em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-14" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.437em 1000em 2.36em -0.312em); left: 8.015625px; margin: 0px 0px 0px -0.256em; padding: 0px; position: absolute; top: -1.534em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">3</span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.882em 1000em 1.178em -0.354em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.28em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.632em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-16" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mfrac" id="MathJax-Span-17" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em 0px 0.342em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.632em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.338em -0.271em); left: 8.015625px; margin: 0px 0px 0px -0.256em; padding: 0px; position: absolute; top: -2.896em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-18" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.425em 1000em 2.338em -0.326em); left: 8.015625px; margin: 0px 0px 0px -0.256em; padding: 0px; position: absolute; top: -1.534em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-19" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">4</span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.882em 1000em 1.178em -0.354em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.28em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.632em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-20" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mfrac" id="MathJax-Span-21" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em 0px 0.342em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.632em;"><span style="border: 0px; clip: rect(1.436em 1000em 2.338em -0.271em); left: 8.015625px; margin: 0px 0px 0px -0.256em; padding: 0px; position: absolute; top: -2.896em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-22" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.436em 1000em 2.36em -0.304em); left: 8.015625px; margin: 0px 0px 0px -0.256em; padding: 0px; position: absolute; top: -1.534em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-23" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">5</span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.882em 1000em 1.178em -0.354em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.28em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.632em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-24" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="mfrac" id="MathJax-Span-25" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em 0px 0.398em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.632em;"><span style="border: 0px; clip: rect(1.621em 1000em 2.308em -0.321em); left: 8.015625px; margin: 0px 0px 0px -0.256em; padding: 0px; position: absolute; top: -2.857em; vertical-align: 0px;"><span class="mi" id="MathJax-Span-26" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">a</span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.368em 1000em 2.309em -0.314em); left: 8.015625px; margin: 0px 0px 0px -0.216em; padding: 0px; position: absolute; top: -1.494em; vertical-align: 0px;"><span class="mi" id="MathJax-Span-27" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">b</span><span style="border: 0px; display: inline-block; height: 2.18em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.882em 1000em 1.178em -0.354em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.28em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.632em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-28" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">,</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 2.449em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.859em; width: 0px;"></span></span></nobr></span></div>
<br />
<div style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 22px; line-height: 30.9375px; margin-bottom: 25px;">
what is the value of <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-4-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-29" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 25px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.085em;"><span style="border: 0px; clip: rect(1.408em 1000em 2.42em -0.321em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.22em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-30" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-31" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">a</span><span class="mo" id="MathJax-Span-32" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mi" id="MathJax-Span-33" style="border: 0px; display: inline; font-family: MathJax_Math; font-style: italic; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">b</span></span><span style="border: 0px; display: inline-block; height: 2.22em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.983em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.14em; width: 0px;"></span></span></nobr></span>?</div>
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-50557760352127886152013-07-23T19:44:00.002+07:002013-07-30T15:38:57.966+07:00Nancy's Closet Staff discount<span style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 20px; line-height: 32.03125px;">With the holiday approaching, Nancy's Closet is having a sale, where all their clothes are 40% off. Mary, who works there, can get a further staff discount of 40% off the sale price. What is the total percent discount that Mary gets?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-72031260627189275622013-07-23T19:33:00.001+07:002013-07-30T15:40:38.127+07:00Sequences<h3 style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 1.4em; font-weight: normal; line-height: 27px; margin: 0px 0px 50px; text-rendering: optimizelegibility;">
<div style="font-size: 1.1em; line-height: 1.6em; margin-bottom: 9px;">
What is the <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 20px; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.238em;"><span style="border: 0px; clip: rect(2.987em 1000em 4.151em -0.346em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -4em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-3" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.238em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.314em -0.346em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-4" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">6</span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.517em; margin: 0px; padding: 0px; position: absolute; top: -2.556em; vertical-align: 0px;"><span class="texatom" id="MathJax-Span-5" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-6" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-7" style="border: 0px; display: inline; font-family: MathJax_Math; font-size: 16px; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">t</span><span class="mi" id="MathJax-Span-8" style="border: 0px; display: inline; font-family: MathJax_Math; font-size: 16px; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">h</span></span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.151em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.075em; width: 0px;"></span></span></nobr></span> term in the following sequence:</div>
<div style="font-size: 1.1em; line-height: 1.6em; margin-bottom: 9px;">
<span class="MathJax_Preview" style="color: #888888;"></span></div>
<div aria-readonly="true" class="MathJax_Display" role="textbox" style="margin: 1em 0em; position: relative; text-align: center; width: 588px;">
<span class="MathJax" id="MathJax-Element-2-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 20px; line-height: normal; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-9" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 8.097em;"><span style="border: 0px; clip: rect(0.691em 1000em 3em -0.305em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-10" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-11" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">12</span><span class="mo" id="MathJax-Span-12" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-13" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">6</span><span class="mo" id="MathJax-Span-14" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">4</span><span class="mo" id="MathJax-Span-16" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-17" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-18" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-19" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">2</span><span class="mfrac" id="MathJax-Span-20" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em 0px 0.287em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.637em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.292em -0.338em); left: 7.390625px; margin: 0px 0px 0px -0.258em; padding: 0px; position: absolute; top: -2.839em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-21" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">2</span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.368em 1000em 2.314em -0.338em); left: 7.390625px; margin: 0px 0px 0px -0.258em; padding: 0px; position: absolute; top: -1.477em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-22" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">5</span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.871em 1000em 1.189em -0.388em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.28em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.637em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-23" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;">,</span><span class="munderover" id="MathJax-Span-24" style="border: 0px; display: inline; margin: 0px; padding: 0px 0px 0px 0.167em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.653em;"><span style="border: 0px; clip: rect(3.871em 1000em 4.129em -0.388em); left: 0.012em; margin: 0px; padding: 0px; position: absolute; top: -4em; vertical-align: 0px;"><span class="mspace" id="MathJax-Span-25" style="border: 0px; display: inline-block; height: 0em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 1.628em;"></span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.764em 1000em 2.162em -0.388em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.713em; vertical-align: 0px;"><span class="mo" id="MathJax-Span-26" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.653em;"><span style="border: 0px; font-family: MathJax_Main; left: -0.084em; margin: 0px; padding: 0px; position: absolute; top: -4em; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 0.959em; margin: 0px; padding: 0px; position: absolute; top: -4em; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 0.425em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-27" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">.</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 2.478em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.871em; width: 0px;"></span></span></nobr></span></div>
</h3>
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-87097704294836471242013-07-23T19:30:00.001+07:002013-07-30T15:38:57.976+07:00Ages of Students<h3 style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 1.4em; font-weight: normal; line-height: 27px; margin: 0px 0px 50px; text-rendering: optimizelegibility;">
<div style="font-size: 1.1em; line-height: 1.6em; margin-bottom: 9px;">
Calvin is looking at the ages of 4 Brilliant students. He decides to add them up 3 at a time, and obtains the values 51, 57, 61 and 65. What is the sum of the ages of all 4 of these students?</div>
</h3>
<div class="assumptions" style="background-color: white; clear: left; color: #333333; float: left; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 13px; line-height: 18px; margin: 0px 0px 30px; width: 588px;">
<h3 style="color: inherit; font-family: inherit; font-size: 1.4em; line-height: 27px; margin: 0px; text-rendering: optimizelegibility;">
Details and assumptions</h3>
<div style="font-size: 1.4em; line-height: 1.6em; margin-bottom: 9px;">
If the ages of the students are 1, 2, 3 and 4, then adding them up 3 at a time will yield <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-5-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-37" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 21px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 5.687em;"><span style="border: 0px; clip: rect(1.443em 1000em 2.48em -0.351em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.253em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-38" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-39" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span class="mo" id="MathJax-Span-40" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-41" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-42" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-43" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-44" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-45" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">6</span></span><span style="border: 0px; display: inline-block; height: 2.253em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.963em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.148em; width: 0px;"></span></span></nobr></span>, <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-6-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-46" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 21px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 5.687em;"><span style="border: 0px; clip: rect(1.432em 1000em 2.48em -0.351em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.253em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-47" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-48" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span class="mo" id="MathJax-Span-49" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-50" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-51" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-52" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">4</span><span class="mo" id="MathJax-Span-53" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-54" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">7</span></span><span style="border: 0px; display: inline-block; height: 2.253em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.975em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.148em; width: 0px;"></span></span></nobr></span>, <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-7-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-55" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 21px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 5.687em;"><span style="border: 0px; clip: rect(1.432em 1000em 2.48em -0.351em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.253em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-56" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-57" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span class="mo" id="MathJax-Span-58" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-59" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-60" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-61" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">4</span><span class="mo" id="MathJax-Span-62" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-63" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">8</span></span><span style="border: 0px; display: inline-block; height: 2.253em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.975em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.148em; width: 0px;"></span></span></nobr></span>, <span class="MathJax_Preview" style="color: #888888;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-8-Frame" role="textbox" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; padding: 0px; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-64" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 21px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 5.687em;"><span style="border: 0px; clip: rect(1.432em 1000em 2.48em -0.384em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.253em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-65" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-66" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-67" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-68" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-69" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mn" id="MathJax-Span-70" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">4</span><span class="mo" id="MathJax-Span-71" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-72" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.278em; position: static; vertical-align: 0px;">9</span></span><span style="border: 0px; display: inline-block; height: 2.253em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 0.975em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.148em; width: 0px;"></span></span></nobr></span>.</div>
</div>
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-79211044839694971422013-07-23T19:26:00.001+07:002013-07-30T15:38:57.973+07:00Indices and Surds<h3 style="background-color: white; color: #333333; font-size: 1.4em; font-weight: normal; line-height: 27px; margin: 0px 0px 50px; text-rendering: optimizelegibility;">
<div style="font-family: Palatino, Georgia, 'Times New Roman', Times, serif;">
</div>
</h3>
<h3 style="background-color: white; color: #333333; font-family: Palatino, Georgia, 'Times New Roman', Times, serif; font-size: 1.4em; font-weight: normal; line-height: 27px; margin: 0px 0px 50px; text-rendering: optimizelegibility;">
<div style="font-size: 1.1em; line-height: 1.6em; margin-bottom: 9px;">
What is the value of</div>
<div style="font-size: 1.1em; line-height: 1.6em; margin-bottom: 9px;">
<span class="MathJax_Preview" style="color: #888888;"></span></div>
<div aria-readonly="true" class="MathJax_Display" role="textbox" style="margin: 1em 0em; position: relative; text-align: center; width: 588px;">
<span class="MathJax" id="MathJax-Element-1-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-size: 20px; line-height: normal; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-size: 23px; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 19.94em;"><span style="border: 0px; clip: rect(0.691em 1000em 3.261em -0.268em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-3" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.996em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.292em -0.305em); left: 46.390625px; margin: 0px 0px 0px -0.258em; padding: 0px; position: absolute; top: -2.839em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-4" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.172em 1000em 2.451em -0.316em); left: 46.390625px; margin: 0px 0px 0px -1.938em; padding: 0px; position: absolute; top: -1.353em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-5" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="msqrt" id="MathJax-Span-6" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.335em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.292em -0.305em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-7" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-8" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.871em 1000em 1.189em -0.388em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -1.862em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.517em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.071em 1000em 4.329em -0.316em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -4.053em; vertical-align: 0px;"><span style="border: 0px; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">√</span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-9" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="msqrt" id="MathJax-Span-10" style="border: 0px; display: inline; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.335em;"><span style="border: 0px; clip: rect(1.369em 1000em 2.314em -0.346em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-11" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-12" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">3</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.871em 1000em 1.189em -0.388em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -1.85em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.517em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.071em 1000em 4.329em -0.316em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -4.041em; vertical-align: 0px;"><span style="border: 0px; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">√</span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.871em 1000em 1.189em -0.388em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.28em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 3.996em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-13" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mfrac" id="MathJax-Span-14" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em 0px 0.342em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 3.996em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.292em -0.305em); left: 46.390625px; margin: 0px 0px 0px -0.258em; padding: 0px; position: absolute; top: -2.839em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.183em 1000em 2.451em -0.316em); left: 46.390625px; margin: 0px 0px 0px -1.938em; padding: 0px; position: absolute; top: -1.364em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-16" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="msqrt" id="MathJax-Span-17" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.335em;"><span style="border: 0px; clip: rect(1.369em 1000em 2.314em -0.346em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-18" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-19" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">3</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.871em 1000em 1.189em -0.388em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -1.85em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.517em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.071em 1000em 4.329em -0.316em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -4.041em; vertical-align: 0px;"><span style="border: 0px; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">√</span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-20" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="msqrt" id="MathJax-Span-21" style="border: 0px; display: inline; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.335em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.314em -0.338em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-22" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-23" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">5</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.871em 1000em 1.189em -0.388em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -1.851em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.517em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.071em 1000em 4.329em -0.316em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -4.042em; vertical-align: 0px;"><span style="border: 0px; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">√</span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.871em 1000em 1.189em -0.388em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.28em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 3.996em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-24" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mo" id="MathJax-Span-25" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">…</span><span class="mo" id="MathJax-Span-26" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mfrac" id="MathJax-Span-27" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em 0px 0.342em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 6.149em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.292em -0.305em); left: 71.390625px; margin: 0px 0px 0px -0.258em; padding: 0px; position: absolute; top: -2.839em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-28" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(1.183em 1000em 2.45em -0.316em); left: 71.390625px; margin: 0px 0px 0px -3.015em; padding: 0px; position: absolute; top: -1.364em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-29" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="msqrt" id="MathJax-Span-30" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.394em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.314em -0.346em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-31" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-32" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">359</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.601em 1000em 3.999em -0.388em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -4.581em; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.575em;"><span style="border: 0px; font-family: MathJax_Main; left: -0.084em; margin: 0px; padding: 0px; position: absolute; top: -4em; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 0.881em; margin: 0px; padding: 0px; position: absolute; top: -4em; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 0.386em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.071em 1000em 4.329em -0.316em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -4.042em; vertical-align: 0px;"><span style="border: 0px; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">√</span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-33" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="msqrt" id="MathJax-Span-34" style="border: 0px; display: inline; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.394em;"><span style="border: 0px; clip: rect(1.368em 1000em 2.314em -0.346em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-35" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mn" id="MathJax-Span-36" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">361</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.601em 1000em 3.999em -0.388em); left: 0.818em; margin: 0px; padding: 0px; position: absolute; top: -4.581em; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.575em;"><span style="border: 0px; font-family: MathJax_Main; left: -0.084em; margin: 0px; padding: 0px; position: absolute; top: -4em; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 0.881em; margin: 0px; padding: 0px; position: absolute; top: -4em; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 0.386em; margin: 0px; padding: 0px; position: absolute; top: -2.163em; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.071em 1000em 4.329em -0.316em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -4.042em; vertical-align: 0px;"><span style="border: 0px; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">√</span><span style="border: 0px; display: inline-block; height: 4em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.871em 1000em 1.189em -0.388em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -1.28em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 6.149em; display: inline-block; height: 0.06em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 1.06em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-37" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">?</span></span><span style="border: 0px; display: inline-block; height: 2.163em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 2.781em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -1.173em; width: 0px;"></span></span></nobr></span></div>
</h3>
Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-51146879790654331082012-12-14T20:37:00.004+07:002013-07-30T15:43:05.337+07:00Inilah Keunikan Matematika<b><span style="font-family: Georgia, Times New Roman, serif;">1 x 8 + 1 = 9</span></b><br />
<div class="MsoNormal">
<b><span style="font-family: Georgia, Times New Roman, serif;">
12 x 8 + 2 = 98<br />
123 x 8 + 3 = 987<br />
1234 x 8 + 4 = 9876<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-family: Georgia, Times New Roman, serif;">12345 x 8 + 5
= 98765<br />
123456 x 8 + 6 = 987654<br />
1234567 x 8 + 7 = 9876543<br />
12345678 x 8 + 8 = 98765432<br />
123456789 x 8 + 9 = 987654321<br />
1 x 9 + 2 = 11<br />
12 x 9 + 3 = 111<br />
123 x 9 + 4 = 1111<br />
1234 x 9 + 5 = 11111<br />
12345 x 9 + 6 = 111111<br />
123456 x 9 + 7 = 1111111<br />
1234567 x 9 + 8 = 11111111<br />
12345678 x 9 + 9 = 111111111<br />
123456789 x 9 + 10 = 1111111111<br />
9 x 9 + 7 = 88<br />
98 x 9 + 6 = 888<br />
987 x 9 + 5 = 8888<br />
9876 x 9 + 4 = 88888<br />
98765 x 9 + 3 = 888888<br />
987654x 9 + 2 = 8888888<br />
9876543 x 9 + 1 = 88888888<br />
98765432 x 9 + 0 = 888888888<br />
Hebatkan?<br />
Coba lihat simetri ini :<br />
1 x 1 = 1<br />
11 x 11 = 121<br />
111 x 111 = 12321<br />
1111 x 1111 = 1234321<br />
11111 x 11111 = 123454321<br />
111111 x 111111 = 12345654321<br />
1111111 x 1111111 = 1234567654321<br />
11111111 x 11111111 = 123456787654321<br />
111111111 x 111111111 = 12345678987654321<br />
kurang hebat,,,,<br />
Sekarang lihat ini<br />
Jika 101% dilihat dari sudut pandangan Matematika,<br />
apakah ia sama dengan 100%, atau ia LEBIH dari<br />
100%?<br />
Kita selalu mendengar orang berkata dia bisa<br />
memberi lebih dari 100%, atau kita selalu dalam<br />
situasi dimana seseorang ingin kita memberi 100%<br />
sepenuhnya.<br />
Bagaimana bila ingin mencapai 101%?<br />
Apakah nilai 100% dalam hidup?<br />
Mungkin sedikit formula matematika dibawah ini<br />
dapat membantu memberi<br />
jawabannya.<br />
Jika ABCDEFGHIJKLMNOPQRSTUVWXYZ<br />
Disamakan sebagai 1 2 3 4 5 6 7 8 9 10 11 12 13 14<br />
15 16 17 18 19 20 21 22 23 24 25 26<br />
Maka, kata KERJA KERAS bernilai :<br />
11 + 5 + 18 + 10 + 1 + 11 + 5 + 18 + 19 + 1 = 99%<br />
H-A-R-D-W-O-R-K<br />
8 + 1 + 18 + 4 + 23 + !5 + 18 + 11 = 99%<br />
K-N-O-W-L-E-D-G-E<br />
11 + 14 + 15 + 23 + 12 + 5 + 4 + 7 + 5 = 96%<br />
A-T-T-I-T-U-D-E<br />
1 + 20 + 20 + 9 + 20 + 21 + 4 + 5 = 100%<br />
Sikap diri atau ATTITUDE adalah perkara utama<br />
untuk mencapai 100% dalam hidup kita. Jika kita<br />
kerja keras sekalipun tapi tidak ada ATTITUDE yang<br />
positif didalam diri, kita masih belum mencapai<br />
100%.<br />
Tapi, LOVE OF GOD<br />
12 + 15 + 22 + 5 + 15 + 6 + 7 + 15 + 4 = 101%<br />
atau, SAYANG ALLAH<br />
19 + 1 + 25 + 1 + 14 + 7 + 1 + 12 + 12 + 1 + 8 = 101%<o:p></o:p></span></b></div>
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Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com2tag:blogger.com,1999:blog-5853745621300841836.post-79088492863911572562012-12-14T20:29:00.002+07:002013-07-30T15:38:57.971+07:00Kuis Perbandingan<span style="color: red; font-family: Georgia, Times New Roman, serif;">Di sekolah Harapan Bangsa sedang dilaksanakan kerja bakti. 5 orang siswa sedang mengecat tembok kelas mereka, jika mereka melakukan bersama akan selesai dalam 12 hari, padahal jika dilakukan oleh seorang tukang cat, pekerjaan itu akan selesai dalam 10 hari. Jika pekerjaan itu dilakukan oleh seorang tukang cat dan 6 orang siswa, dalam berapa hari pekerjaan tersebut akan selesai?</span>Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0tag:blogger.com,1999:blog-5853745621300841836.post-31542990381326067382012-12-14T20:22:00.001+07:002013-07-30T15:40:38.125+07:00Kuis Sudut<div class="separator" style="clear: both; text-align: center;">
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Tentukan besar sudut ABC !Anonymoushttp://www.blogger.com/profile/08624034496860162129noreply@blogger.com0