CASO ONCE

CALCULAR EL O LOS VALORES DE "X" Y DE "Y"

ECUACIONES

DATOS A ESTUDIANTES :

N° A B C D E F1 152 146 390.8774663593290000 154 295 573.121290471004000002 147 153 282.3847248404400000 145 303 407.066645472262000003 150 144 387.7909269916170000 152 291 575.076407725226000004 145 151 369.3115778538260000 143 299 540.728645604599000005 148 142 392.0264036255340000 150 287 586.508623845376000006 143 149 435.0838753892320000 141 295 638.533580744838000007 146 140 333.2986126374160000 148 283 514.960943359284000008 141 147 380.7991568833690000 139 291 568.554296735585000009 144 138 433.6624838136380000 146 279 650.8855543379550000010 139 145 355.1984827451580000 137 287 540.6014400792630000011 142 136 427.4632602516380000 144 275 645.1516762504110000012 137 143 393.5003120163480000 135 283 593.3789807322230000013 140 134 403.3144435995770000 142 271 615.9570019303070000014 135 141 424.4380344917020000 133 279 636.1707517178320000015 138 132 419.1826158634380000 140 267 638.4710146493530000016 133 139 445.6912266236650000 131 275 665.9338537146270000017 136 130 394.5471277862230000 138 263 608.9191430041710000018 131 137 439.0725081706610000 129 271 658.6564899025530000019 134 128 419.2467006994340000 136 259 641.3544779230980000020 129 135 436.2255883206950000 127 267 656.1059031710200000021 132 126 446.4559677612850000 134 255 677.3361189395760000022 127 133 406.8713373468170000 125 263 620.10505946962400000

)2(

)1(

FYLogEXLogD

CYLogBXLogA

23 130 124 412.9024670459910000 132 251 634.9484603193760000024 125 131 449.4126920865090000 123 259 674.4863592286860000025 128 122 395.5978841031000000 130 247 614.0266838658830000026 123 129 442.1460625395580000 121 255 665.4478314185140000027 126 120 409.4722651427150000 128 243 631.2974739414380000028 121 127 425.2834276914080000 119 251 644.2730602780330000029 124 118 415.9890964032800000 126 239 639.4004111846420000030 119 125 430.1969476116730000 117 247 650.3826428017770000031 122 116 431.4533159993280000 124 235 658.7665095347550000032 117 123 413.3029119684110000 115 243 629.2063205790700000033 120 114 423.5860358854710000 122 231 648.4258919199030000034 115 121 423.2529831216580000 113 239 641.0950718496830000035 118 112 418.1727857735190000 120 227 641.1133504642100000036 113 119 436.5517684031780000 111 235 657.3014391420300000037 116 110 396.4273239821090000 118 223 613.4805126669290000038 111 117 412.8330367556730000 109 231 626.9851885556430000039 114 108 420.0241670955980000 116 219 642.1648622561690000040 109 115 399.6759411725570000 107 227 610.1198382594150000041 112 106 411.9308592468130000 114 215 631.1150921712650000042 107 113 404.2240600002540000 105 223 614.6686021975700000043 110 104 392.9943018437660000 112 211 606.5516060570100000044 105 111 404.9566529719920000 103 219 614.5127571374750000045 108 102 397.5783024658110000 110 207 611.1630858448080000046 103 109 411.7788885759740000 101 215 621.8577768214040000047 106 100 383.1972580009900000 108 203 592.2124705641830000048 101 107 403.6848208039570000 99 211 610.6141140940550000049 104 98 386.7223275074750000 106 199 595.3024490016490000050 99 105 397.2043588069540000 97 207 601.3193448994600000051 102 96 393.0158513745660000 104 195 601.9383500718570000052 97 103 380.3791492515590000 95 203 579.3680317547520000053 100 94 373.6073710858300000 102 191 576.3683400516900000054 95 101 392.6737411776890000 93 199 592.9485512839490000055 98 92 361.6991601696430000 100 187 560.26846828769300000

56 93 99 384.3897127882150000 91 195 581.2036334486400000057 96 90 372.0389736372630000 98 183 571.4988996601510000058 91 97 369.0158481237100000 89 191 560.7811870707120000059 94 88 359.4218626348850000 96 179 554.2702472334460000060 89 95 369.0737582413970000 87 187 559.1418212664200000061 92 86 361.4582036342470000 94 175 555.2121633816840000062 87 93 356.7132223874640000 85 183 542.3530405760620000063 90 84 352.9349790032730000 92 171 542.9530180923050000064 85 91 356.0815995377310000 83 179 539.7340011275340000065 88 82 345.5725444111870000 90 167 532.1047275590180000066 83 89 357.5294581089130000 81 175 539.6902602378420000067 86 80 330.9209216051880000 88 163 512.2455507693530000068 81 87 341.5693493301890000 79 171 518.2867847554830000069 84 78 336.9167151790960000 86 159 517.8412635414010000070 79 85 330.8134643836520000 77 167 503.2993090946090000071 82 76 317.5409691877980000 84 155 492.0275048038230000072 77 83 334.7789544866350000 75 163 506.0319468717260000073 80 74 314.5615336986110000 82 151 486.3911176751250000074 75 81 323.3934288861220000 73 159 490.1212650980760000075 78 72 311.8720892841800000 80 147 481.1086636380650000076 73 79 321.9097813992460000 71 155 486.2122394014600000077 76 70 300.3430244431350000 78 143 464.8935730906510000078 71 77 313.2551403176520000 69 151 473.5344960850510000079 74 68 297.1561812044130000 76 139 458.9153063630910000080 69 75 305.3896776370280000 67 147 461.7888776216470000081 72 66 295.5079934837790000 74 135 454.8697590134090000082 67 73 292.6770208721330000 65 143 444.1858070216470000083 70 64 281.3539003522220000 72 131 435.2492449690510000084 65 71 293.7452776421340000 63 139 443.1612638462720000085 68 62 279.9114727025590000 70 127 431.3760710940950000086 63 69 277.8447888321160000 61 135 421.6377488539740000087 66 60 271.0424136126330000 68 123 418.2512201947490000088 61 67 272.8370047123720000 59 131 413.18317464978900000

89 64 58 260.1821617574020000 66 119 402.6396516982190000090 59 65 268.0284235806360000 57 127 404.9513572391030000091 62 56 256.3627353280320000 64 115 395.7347595165180000092 57 63 257.3723395174100000 55 123 389.6741931620350000093 60 54 247.4342113543110000 62 111 382.4579369018910000094 55 61 252.1848751263800000 53 119 380.9162366278320000095 58 52 239.0666763633810000 60 107 369.8562692241810000096 53 59 248.0197632124460000 51 115 373.3887201112060000097 56 50 227.3148691317440000 58 103 353.0553245591290000098 51 57 235.5936471910870000 49 111 355.8755883342210000099 54 48 221.1993903292200000 56 99 343.18162261338000000

100 49 55 231.4797739937940000 47 107 348.33433395201000000101 52 46 211.2264112521010000 54 95 328.53641712243100000102 47 53 222.4980132604570000 45 103 334.91232881432500000103 50 44 204.8196790143740000 52 91 318.25590052336600000104 45 51 212.2507157034730000 43 99 319.95948290144900000105 48 42 198.5270244669210000 50 87 308.10876476526900000106 43 49 206.4877734599590000 41 95 310.35147902139600000107 46 40 188.2353877550820000 48 83 292.98829439588100000108 41 47 197.4512197618140000 39 91 296.79744849298800000109 44 38 181.6395367204770000 46 79 282.42344023572000000110 39 45 188.7661772358700000 37 87 283.64472490283400000111 42 36 175.6941479525200000 44 75 272.67290534908100000112 37 43 178.0219004548620000 35 83 268.03514409797300000113 40 34 163.1740267168430000 42 71 254.70172066410600000114 35 41 170.6947229955250000 33 79 256.44664055260200000115 38 32 158.2402717862210000 40 67 246.16566142774600000116 33 39 161.0587981404580000 31 75 242.11804055676100000117 36 30 149.0415178822070000 38 63 232.29277341113200000118 31 37 153.4960969626060000 29 71 230.20209976020200000119 34 28 139.0456966598940000 36 59 217.40583284251000000120 29 35 145.9532380362860000 27 67 218.28966222221700000121 32 26 131.8735304832100000 34 55 206.04119518882300000

122 27 33 136.1253244402750000 25 63 203.67169044675300000123 30 24 122.6297477059750000 32 51 192.06020475117300000124 25 31 128.3332234098370000 23 59 191.41791023667700000125 28 22 113.6002409401090000 30 47 178.33297860775700000126 23 29 120.8272594677130000 21 55 179.48238271530300000127 26 20 105.6485148403960000 28 43 165.95613061276100000128 21 27 109.8507411994020000 19 51 163.46894660553000000129 24 18 95.1254985871403000 26 39 150.30591801117000000130 19 25 102.7306115381070000 17 47 151.92339552436300000131 22 16 85.5682395470147000 24 35 135.86412074854400000132 17 23 93.4349460490530000 15 43 137.82980062084000000133 20 14 77.1297315441399000 22 31 122.82197960148700000134 15 21 83.7905558454123000 13 39 123.32369343935500000135 18 12 68.6390809591125000 20 27 109.71013860513500000136 13 19 75.3714873181452000 11 35 110.20020555009000000137 16 10 58.9898419062600000 18 23 95.09942153300720000138 11 17 66.0333071995441000 9 31 96.00877991128700000139 14 8 50.2883452655824000 16 19 81.70008757132930000140 9 15 56.7749005256349000 7 27 81.89202288664970000141 12 6 41.2506455139958000 14 15 67.86069406249460000142 7 13 47.8311341548929000 5 23 68.09720458939790000143 10 4 31.5522091455454000 12 11 53.12951856162800000144 5 11 38.1150420859414000 3 19 53.45818374395580000145 8 2 22.8528272539540000 10 7 39.74538334450300000146 3 9 28.7387394250665000 1 15 39.18199125260480000147 6 0 13.3826935282696000 8 3 25.30500649745780000148 1 7 19.5412459073581000 -1 11 25.04693667759580000149 4 -2 3.8666172052073600 6 -1 10.77136866077420000150 -1 5 10.2148668778885000 -3 7 10.73619490166210000

CASO DOCE

CALCULAR EL O LOS VALORES DE "X" Y DE "Y"

ECUACIONES :

DATOS A ESTUDIANTES :

N° A B C D1 22 312 918713.8210585280 1.7920740543002300002 24 306 1554307.3490554000 1.7139308045812000003 26 316 1966556.6357871400 1.7351854875947700004 28 302 2857549.3082112300 1.6888503301187700005 30 320 3723565.2631951000 1.6858007811238600006 32 298 4489510.7533075000 1.6786295927422100007 34 324 7253564.6379471200 1.6099387715187200008 36 294 8800178.3306532900 1.5892593117504300009 38 328 9529475.0920966700 1.61836257849452000010 40 290 14921024.2484126000 1.53052038162615000011 42 332 15157086.8787863000 1.56573012606119000012 44 286 21203980.8833363000 1.50004677587762000013 46 336 24620107.3548142000 1.50398166653999000014 48 282 28294649.7848079000 1.47241183015986000015 50 340 33583500.3691123000 1.47029976122546000016 52 278 36337132.2785830000 1.44382585805271000017 54 344 51426014.6934145000 1.41449921495641000018 56 274 51563305.4239057000 1.39602449353157000019 58 348 63619945.3601658000 1.386650681651530000

)2(

YLogXLog

)1(

YLogXLog

D)B()B(

C)A()A(

20 60 270 70009247.4281149000 1.35313222122975000021 62 352 71444345.9986003000 1.36552791735510000022 64 266 106407052.1930980000 1.29903016973920000023 66 356 112991815.4458970000 1.30411906661657000024 68 262 106042958.1568690000 1.28383683213991000025 70 360 156973573.8066670000 1.25917088261152000026 72 258 139668157.1795630000 1.24181353888661000027 74 364 183609251.7665130000 1.22752198311035000028 76 254 194952214.8035010000 1.19775281268834000029 78 368 216115318.6523940000 1.19366118352443000030 80 250 227588642.6536410000 1.16507644221654000031 82 372 226996994.7030320000 1.16386717017772000032 84 246 310872736.7044030000 1.12617696777272000033 86 376 286820142.3956420000 1.12463173362471000034 88 242 337810538.5593400000 1.09603213824201000035 90 380 350063391.5531870000 1.08767182350749000036 92 238 333972969.4260270000 1.06634372765764000037 94 384 492698389.6623140000 1.04981036583011000038 96 234 495108323.7137100000 1.03084100452733000039 98 388 433611218.6689750000 1.01770640088661000040 100 230 639128961.0000000000 1.00000000000000000041 102 392 529968877.4653840000 0.98268832734549000042 104 226 685342487.3543580000 0.97008070082559700043 106 396 735218592.1680150000 0.95080881903913200044 108 222 746572965.8508070000 0.94011817395161300045 110 400 755692816.9536560000 0.91664635902153200046 112 218 720854288.3183460000 0.90775793487026800047 114 404 983488567.3525830000 0.88791577666997400048 116 214 862497515.5045790000 0.88009460709944000049 118 408 996082430.0966940000 0.85361903029885900050 120 210 997939187.5948410000 0.85289541991158100051 122 412 912560482.6430350000 0.81478604726937300052 124 206 1360252794.2356400000 0.832960800838717000

53 126 416 1321634071.0686100000 0.79498860883842600054 128 202 1102539219.3546900000 0.79395575914898900055 130 420 1645450639.4604500000 0.77109774229719200056 132 198 1294751944.8140800000 0.77036204695411500057 134 424 1359182967.7171000000 0.72739136572130200058 136 194 1756434469.9965900000 0.75541364576514700059 138 428 1736546911.1091200000 0.70715684672936500060 140 190 1712138365.5726700000 0.72507269237988000061 142 432 1581325308.8025400000 0.66811471309607500062 144 186 2175604496.4629100000 0.70990032950935900063 146 436 1833170764.3650700000 0.64446304631905400064 148 182 2098380382.4432600000 0.68002491001945000065 150 440 2052346441.5628200000 0.61973738569402200066 152 178 1814377578.2247600000 0.64317344592762100067 154 444 2761739850.3183200000 0.60889252442000100068 156 174 2615616186.8641000000 0.63992607355026900069 158 448 2091922911.1078300000 0.55843729478925200070 160 170 3192539998.5209500000 0.62727604316587100071 162 452 3310793286.5452100000 0.56223783250855600072 164 166 2477290685.6995100000 0.58463895299421800073 166 456 3226925210.6827600000 0.53154864232112700074 168 162 3124147207.0956100000 0.57626508052993000075 170 460 3016293525.5157000000 0.49814640381230100076 172 158 2708737907.9008200000 0.54183421670584900077 174 464 3789040901.6110700000 0.48839169559318200078 176 154 3075994237.6112900000 0.52779122630802500079 178 468 3510533446.1828800000 0.45580429802606000080 180 150 3364708742.6075200000 0.51186657080881600081 182 472 2881536117.1288700000 0.41417983716344300082 184 146 4520422272.6522500000 0.51232529593644500083 186 476 4185168704.2488800000 0.41894117010102000084 188 142 3208716167.3969700000 0.46506564597815600085 190 480 3280099781.3231500000 0.375353956085165000

86 192 138 5179040312.1771800000 0.48152180330093000087 194 484 3690610831.6514100000 0.36150289686501300088 196 134 4879003447.3896800000 0.45740359202719000089 198 488 4634445705.9668900000 0.35713409101557800090 200 130 4388709009.9242400000 0.43030186860458000091 202 492 3831975784.8938100000 0.32066486268721800092 204 126 5494344177.2537200000 0.42957947204396400093 206 496 4288567234.1770900000 0.30881094894958600094 208 122 4900742438.9712000000 0.40323726739582400095 210 500 4606072977.5660500000 0.29450805500443700096 212 118 3812730378.8184800000 0.36700852630828900097 214 504 6232738326.6720200000 0.29841540196467000098 216 114 5639684081.8971700000 0.38132609207768100099 218 508 5720716416.1774900000 0.273537414391020000

100 220 110 4168186749.7221900000 0.342747788626827000101 222 512 6876602425.5693700000 0.269519313198606000102 224 106 4633167495.0042400000 0.336320099159566000103 226 516 6264341808.3548900000 0.245824913884545000104 228 102 5834556485.5361200000 0.339967455305403000105 230 520 5414238003.0155400000 0.219708214644954000106 232 98 4579643637.9133000000 0.308570445920532000107 234 524 6801154181.2935400000 0.220218687742401000108 236 94 5069731159.5783400000 0.303733813924050000109 238 528 5824855055.7435900000 0.195430822961392000110 240 90 5358249374.6908700000 0.296069162390784000111 242 532 4258115593.0614600000 0.162710913443123000112 244 86 7369762333.3376300000 0.308308521323006000113 246 536 7412451477.9393500000 0.184163979279376000114 248 82 6522567430.3713600000 0.288800486787676000115 250 540 4475781234.3207300000 0.142232669812208000116 252 78 7850754804.6093600000 0.292297892071654000117 254 544 4928643674.5699700000 0.136757379029928000118 256 74 6889507020.3420700000 0.273719150525832000

119 258 548 6271952639.3982800000 0.139393368341956000120 260 70 5682017821.3292800000 0.251909891636198000121 262 552 4616849974.1636500000 0.113830974554120000122 264 66 7215309084.4618100000 0.260747681194413000123 266 556 5067327690.9961100000 0.109440646279493000124 268 62 5884353238.2166500000 0.239946855986423000125 270 560 5270584551.7137800000 0.102851469380677000126 272 58 3965499513.2342500000 0.208430503612739000127 274 564 3917850685.0385300000 0.082674076067606000128 276 54 7420593046.6987300000 0.244059947408896000129 278 568 6314161340.3566600000 0.095218501634663600130 280 50 3987229898.9280200000 0.199973095585708000131 282 572 7657282508.1087000000 0.096123396969054600132 284 46 4357503201.7052500000 0.202354180112053000133 286 576 6411442880.9864600000 0.081844529761483700134 288 42 5664268802.0584400000 0.216516649311612000135 290 580 4968553972.6037300000 0.066506804404809000136 292 38 3811809891.6518400000 0.191588781648509000137 294 584 6446707069.2405400000 0.069877193471409000138 296 34 4154331324.3849600000 0.197417231638087000139 298 588 4917177508.4231200000 0.055900679285154400140 300 30 4240806792.4345300000 0.201221804193130000141 302 592 4143194909.8991200000 0.046694564863607800142 304 26 2846425147.1532800000 0.183206184188134000143 306 596 6184517996.9091000000 0.053471231635922100144 308 22 5013332415.8766900000 0.224869204402323000145 310 600 2777617807.6169700000 0.030796168152981700146 312 18 6183513772.1593900000 0.251815702142867000147 314 604 3016008101.5411500000 0.029553229761796900148 316 14 4838405162.9672000000 0.259009759713930000149 318 608 4084651483.1841200000 0.032548986480259100150 320 10 3406656474.0563200000 0.276315789473684000

CASO TRECE

HALLAR EL VALOR DE LAS VARIABLES p, k, t :

FÓRMULAS :

PARÁMETROS : j = 0.20m = 4

DATOS :N° A B C D n1 4458.49565826593000 2293 6455.205686802090000 3331 35.492 2349.23868857447000 2442 3330.315416572850000 3480 38.473 4550.26107126601000 2361 6531.118079365390000 3399 36.854 2418.85253293582000 2430 3434.290144549940000 3468 38.235 4380.11416257502000 2279 6353.111083594480000 3317 35.216 2588.48756886602000 2408 3685.916182355560000 3446 37.797 4439.64234711937000 2317 6407.695360316810000 3355 35.978 2765.09297361709000 2386 3949.054470186220000 3424 37.359 4432.28891487973000 2325 6390.443897067360000 3363 36.13

10 2064.34984717934000 2454 2920.343163474800000 3492 38.7111 4344.36584451048000 2293 6289.411352035670000 3331 35.4912 2411.37318076868000 2412 3430.835535632470000 3450 37.8713 4399.21126555433000 2331 6337.713618559100000 3369 36.2514 2103.21230741243000 2440 2980.394664098290000 3478 38.43

1m/j1

m/j11m/j1m/j1BA

p

m

tmkm

p

m

1m/j1

m/j11m/j1DC

p

m

tmkm

tkn

15 4421.70673307913000 2359 6347.638543430100000 3397 36.8116 3542.77025458627000 2298 5121.604272620080000 3336 35.5917 4411.50892462249000 2367 6326.612884544670000 3405 36.9718 3055.11859846224000 2336 4392.322563754120000 3374 36.3519 4412.33644795001000 2385 6313.688912986930000 3423 37.3320 2115.98820799140000 2424 3004.136660541730000 3462 38.1121 4333.42730472660000 2343 6233.090782184810000 3381 36.4922 2182.32789873583000 2412 3103.221015311860000 3450 37.8723 4119.85287968895000 2261 5988.713193821060000 3299 34.8524 2346.76605636523000 2390 3347.138276555190000 3428 37.4325 4199.32816444186000 2299 6073.931551163170000 3337 35.6126 2518.06833483291000 2368 3602.403266477500000 3406 36.9927 4195.66848102080000 2307 6062.282514593270000 3345 35.7728 1829.08135834040000 2436 2590.821409752080000 3474 38.3529 4090.23220664213000 2275 5934.355729561420000 3313 35.1330 2167.14396298640000 2394 3088.038920406830000 3432 37.5131 4164.72040819551000 2313 6012.722002605010000 3351 35.8932 1863.21711141727000 2422 2643.731511804220000 3460 38.0733 4200.97273618008000 2341 6043.489893042570000 3379 36.4534 3273.34593359062000 2280 4741.626615750600000 3318 35.2335 4194.26820490653000 2349 6027.702584353090000 3387 36.6136 2792.48693740990000 2318 4022.114660114000000 3356 35.9937 4203.41129936785000 2367 6027.258252524370000 3405 36.9738 3448.34838755936000 2256 5012.287016052240000 3294 34.7539 4103.14600098841000 2325 5914.354598393590000 3363 36.1340 1932.66105109469000 2394 2751.887979048290000 3432 37.5141 3845.00166385889000 2243 5601.303781273860000 3281 34.4942 2091.66581297882000 2372 2987.652632758640000 3410 37.0743 3944.92195175268000 2281 5718.188617069060000 3319 35.2544 2257.43086258858000 2350 3234.599235926190000 3388 36.6345 3945.06253228760000 2289 5712.354205876800000 3327 35.4146 1580.86506857402000 2418 2241.388288596990000 3456 37.9947 3821.67533826543000 2257 5556.635058833920000 3295 34.77

48 1909.53100154195000 2376 2724.516740331710000 3414 37.1549 3916.31845390204000 2295 5666.108049801220000 3333 35.5350 1610.10186857205000 2404 2286.833863133490000 3442 37.7151 3966.72746759361000 2323 5718.499512654960000 3361 36.0952 2989.40772318012000 2262 4338.716443164570000 3300 34.8753 3963.62919791639000 2331 5708.165791072090000 3369 36.2554 2515.68906660658000 2300 3629.663548589240000 3338 35.6355 3981.35287058698000 2349 5720.702057601140000 3387 36.6156 3156.61078938834000 2238 4597.455825498190000 3276 34.3957 4029.12194778760000 2387 5762.276294046920000 3425 37.3758 1669.53530159507000 2376 2379.674434094900000 3414 37.1559 3555.31148969788000 2225 5190.313820125130000 3263 34.1360 1822.87771490216000 2354 2606.846019261960000 3392 36.7161 3676.14044037440000 2263 5339.865638286270000 3301 34.8962 1982.88033891790000 2332 2845.034292680280000 3370 36.2763 3680.18204480941000 2271 5340.053283330860000 3309 35.0564 1319.37920899461000 2400 1871.426449185310000 3438 37.6365 3538.43380951010000 2239 5155.668467998000000 3277 34.4166 1638.22551818146000 2358 2339.656478508290000 3396 36.7967 3653.71277970710000 2277 5297.263321015020000 3315 35.1768 1343.54946341941000 2386 1909.085912383680000 3424 37.3569 3718.66062755464000 2305 5372.046037678800000 3343 35.7370 2690.70663168146000 2244 3912.307522183810000 3282 34.5171 3719.27750797981000 2313 5367.378656896930000 3351 35.8972 2224.45303508129000 2282 3214.382893407390000 3320 35.2773 3745.83820073513000 2331 5393.391930281160000 3369 36.2574 2849.89016479399000 2220 4158.642287488470000 3258 34.0375 3812.13575045897000 2369 5463.040125984150000 3407 37.0176 2055.22377757550000 2288 2965.902343895920000 3326 35.3977 3250.55841293361000 2207 4755.200759696180000 3245 33.7778 1540.10523887734000 2336 2204.114055518060000 3374 36.3579 3392.71993263483000 2245 4938.380160639050000 3283 34.5380 1694.13109157803000 2314 2433.111868745610000 3352 35.91

81 3400.75654466052000 2253 4944.791068226280000 3291 34.6982 1044.31144039452000 2382 1480.323166316320000 3420 37.2783 3240.26927040822000 2221 4730.898631811880000 3259 34.0584 1352.93128558153000 2340 1932.854415059430000 3378 36.4385 3376.62862094607000 2259 4905.595407105220000 3297 34.8186 1063.25336318006000 2368 1509.878015865350000 3406 36.9987 3456.47642898420000 2287 5003.519439068190000 3325 35.3788 2377.01773558956000 2226 3461.858685512570000 3264 34.1589 3460.91239263613000 2295 5004.727482394120000 3333 35.5390 1918.52676616700000 2264 2775.705378214800000 3302 34.9191 3496.55610621721000 2313 5044.707054083930000 3351 35.8992 2527.98498649028000 2202 3695.329802368940000 3240 33.6793 3581.93056136502000 2351 5143.488128984340000 3389 36.6594 1748.33433729414000 2270 2525.543299291500000 3308 35.0395 3528.76730411992000 2339 5074.510096626890000 3377 36.4196 1243.06685447362000 2318 1778.864531410740000 3356 35.9997 3094.41925775627000 2227 4513.172486137070000 3265 34.1798 1390.91453227954000 2296 1998.250482424730000 3334 35.5599 3106.53697254755000 2235 4526.000025397180000 3273 34.33

100 755.36145384454900 2364 1067.473901157140000 3402 36.91101 2926.96971262734000 2203 4281.796591065730000 3241 33.69102 1053.36712564310000 2322 1503.519098024360000 3360 36.07103 3084.81187288306000 2241 4490.531956401480000 3279 34.45104 768.92033895096300 2350 1088.610446954170000 3388 36.63105 3179.89609704855000 2269 4612.324541822160000 3307 35.01106 2048.14351981145000 2208 2986.858784153500000 3246 33.79107 3188.24918298397000 2277 4619.612103124300000 3315 35.17108 1597.68105739359000 2246 2313.087059712400000 3284 34.55109 3233.20942731727000 2295 4674.037293545430000 3333 35.53110 2190.72467005402000 2184 3207.037072827830000 3222 33.31111 3338.18790219977000 2333 4802.996220354340000 3371 36.29112 1426.55167139391000 2252 2061.294124720440000 3290 34.67113 3278.28191478176000 2321 4723.636884615880000 3359 36.05

114 2224.92135562790000 2170 3263.867874780600000 3208 33.03115 2781.02298072637000 2209 4063.710400765810000 3247 33.81116 1072.98211912932000 2278 1539.887973166410000 3316 35.19117 2797.29879478127000 2217 4083.138321473710000 3255 33.97118 452.24671578056600 2346 632.290442018739000 3384 36.55119 2598.35300783887000 2185 3807.867057113710000 3223 33.33120 739.27035182366800 2304 1051.076229245740000 3342 35.71121 2778.03213413657000 2223 4051.525116506940000 3261 34.09122 460.27639124439100 2332 644.701829704412000 3370 36.27123 2888.66058805387000 2251 4197.884912912420000 3289 34.65124 1703.91754103849000 2190 2486.832196201950000 3228 33.43125 2901.02191752667000 2259 4211.449634119930000 3297 34.81126 1261.71297414651000 2228 1826.012364192490000 3266 34.19127 2955.51747541193000 2277 4280.786626356050000 3315 35.17128 1837.97352939979000 2166 2693.324138013620000 3204 32.95129 3080.60152194404000 2315 4440.948548912650000 3353 35.93130 1089.67006295833000 2234 1572.636590487350000 3272 34.31131 3013.78293907229000 2303 4350.864696580570000 3341 35.69132 1866.12892170004000 2152 2740.345840389410000 3190 32.67133 2902.67508294831000 2281 4201.653168773700000 3319 35.25134 740.10948994249900 2260 1057.487505919930000 3298 34.83135 2472.84538138592000 2199 3615.694847495820000 3237 33.61136 134.76486917657800 2328 174.291074016059000 3366 36.19137 2254.27074972682000 2167 3308.654253583460000 3205 32.97138 410.40566686019000 2286 574.981551023375000 3324 35.35139 2456.08601247254000 2205 3588.056430534540000 3243 33.73140 137.13032667078400 2314 177.681201516110000 3352 35.91141 2582.53354533109000 2233 3759.647152968250000 3271 34.29142 1344.20853951731000 2172 1961.345090159240000 3210 33.07143 2598.98620659182000 2241 3779.678605322070000 3279 34.45144 910.45009318927500 2210 1314.000411501890000 3248 33.83145 2663.21869653550000 2259 3864.376938410380000 3297 34.81146 1469.63516780037000 2148 2153.799158255500000 3186 32.59

147 2808.87967252729000 2297 4056.740643831460000 3335 35.57148 737.51470313815500 2216 1059.087735149770000 3254 33.95149 2734.98775795409000 2285 3955.596618445430000 3323 35.33150 1491.70145420250000 2134 2190.810678950650000 3172 32.31

CASO CATORCE

ENCONTRAR EL O LOS VALORES DE " X " :

ECUACIÓN :

DATOS A ESTUDIANTES

N° A B C D1 51 1530 331321.5000000000 -166049.6250000000002 76 2280 1165781.5384615400 -44841.1285844333003 62 1860 616822.5000000000 -77131.9960937500004 94 2820 2253667.0909090900 -102445.2484973700005 90 2700 1969481.2500000000 -123103.1469726560006 110 3300 3661185.0000000000 -183067.5137500000007 155 4650 10494972.5000000000 -349837.5890740740008 74 2220 1070854.0000000000 -178537.6759259260009 104 3120 3078608.0000000000 -256572.39351851800010 190 5700 19547132.1428571000 -698119.14130830900011 72 2160 981936.0000000000 -245620.12500000000012 194 5820 20828567.5000000000 -867867.09736689800013 115 3450 4196407.5000000000 -419675.36500000000014 148 4440 9107962.2857142800 -650591.44169096200015 185 5550 18017920.8333333000 -1001012.76320302000016 194 5820 20826999.3333333000 -1157073.51474623000017 271 8130 57577129.0384615000 -2214517.00506372000018 122 3660 5032042.5000000000 -629062.738281250000

0DXCXBXA 4

1

2

1

4

3

19 259 7770 50178059.5909091000 -2280836.96853869000020 210 6300 26514731.2500000000 -1657195.36376953000021 260 7800 50767860.0000000000 -2538412.53250000000022 380 11400 160383560.0000000000 -5346131.34740741000023 119 3570 4659266.5000000000 -776644.13425925900024 194 5820 20823863.0000000000 -1735362.44560185000025 400 12000 187302857.1428570000 -6689403.07944606000026 102 3060 2894301.0000000000 -723768.09375000000027 374 11220 152839307.5000000000 -6368323.98538773000028 190 5700 19540170.0000000000 -1954074.19000000000029 253 7590 46724744.7857143000 -3337520.58709913000030 260 7800 50763514.2857143000 -3626005.19679300000031 329 9870 103667296.8333330000 -5759324.78789438000032 466 13980 297184151.5384620000 -11430180.38154300000033 182 5460 17134162.5000000000 -2141855.98046875000034 424 12720 223384477.0909090000 -10153866.18858000000035 330 9900 104622581.2500000000 -6538950.08056641000036 410 12300 201817785.0000000000 -10090920.05125000000037 605 18150 653499522.5000000000 -21783337.60574070000038 164 4920 12461704.0000000000 -2077088.09259259000039 284 8520 66364268.0000000000 -5530414.99768519000040 610 18300 669923132.1428570000 -23925849.51758380000041 132 3960 6403716.0000000000 -1601178.56250000000042 554 16620 501014747.5000000000 -20875643.37340860000043 265 7950 53780557.5000000000 -5378135.51500000000044 270 8100 56921130.0000000000 -5692194.27000000000045 365 10950 141965576.7857140000 -10140454.34220120000046 464 13920 293336469.3333330000 -16296513.56104250000047 661 19830 853454599.0384620000 -32825206.25802230000048 242 7260 40811182.5000000000 -5101511.72265625000049 589 17670 602731169.5909090000 -27396907.90862130000050 450 13500 267397031.2500000000 -16712367.29736330000051 560 16800 517560960.0000000000 -25878090.070000000000

52 830 24900 1694874110.0000000000 -56495831.36407410000053 209 6270 26118416.5000000000 -4353244.55092593000054 374 11220 152821823.0000000000 -12735230.04976850000055 820 24600 1634105957.1428600000 -58360958.45572160000056 162 4860 11996181.0000000000 -2999351.53125000000057 734 22020 1170330887.5000000000 -48763825.26142940000058 746 22380 1228941563.5000000000 -51205937.38729740000059 345 10350 119687917.5000000000 -11968895.59500000000060 470 14100 304935664.2857140000 -21781190.98760930000061 599 17970 634121266.8333330000 -35229014.83419070000062 856 25680 1859856221.5384600000 -71532969.63450160000063 302 9060 79951102.5000000000 -9994029.96484375000064 754 22620 1269076387.0909100000 -57685337.12866270000065 570 17100 545942081.2500000000 -34121447.01416020000066 710 21300 1058747385.0000000000 -52937422.58875000000067 1055 31650 3489538572.5000000000 -116317987.62240700000068 254 7620 47269654.0000000000 -7878488.50925926000069 464 13920 293318528.0000000000 -24443307.60185190000070 1030 30900 3246549332.1428600000 -115948229.89385900000071 192 5760 20157696.0000000000 -5039787.00000000000072 194 5820 20805045.0000000000 -5201628.03125000000073 926 27780 2356514663.5000000000 -98188159.27531830000074 420 12600 217045080.0000000000 -21704634.42000000000075 575 17250 560511026.7857140000 -40036590.13301750000076 734 22020 1170308439.3333300000 -65017203.60733880000077 1051 31530 3449856769.0384600000 -132686845.51098100000078 362 10860 138441922.5000000000 -17305410.70703130000079 919 27570 2303278379.5909100000 -104694528.84870400000080 690 20700 971361731.2500000000 -60710189.23095700000081 860 25800 1886127060.0000000000 -94306417.60750000000082 1280 38400 6242524160.0000000000 -208084181.38074100000083 299 8970 77555666.5000000000 -12926194.96759260000084 554 16620 500976383.0000000000 -41748147.653935200000

85 1240 37200 5673951257.1428600000 -202641163.83199700000086 1254 37620 5868837428.1428600000 -209601384.76120600000087 224 6720 32242560.0000000000 -8061063.50000000000088 1106 33180 4022178863.5000000000 -167590843.66333900000089 495 14850 356586367.5000000000 -35658785.74500000000090 680 20400 929528914.2857140000 -66395026.77842570000091 869 26070 1946184736.8333300000 -108121454.88048700000092 1246 37380 5756923991.5384600000 -221420208.88746000000093 422 12660 220171642.5000000000 -27521653.94921880000094 1084 32520 3786195397.0909100000 -172099858.06874500000095 810 24300 1574759981.2500000000 -98422593.94775390000096 1010 30300 3060449985.0000000000 -153022575.12625000000097 1505 45150 10158862122.5000000000 -338628787.63907400000098 344 10320 118616704.0000000000 -19769738.92592590000099 644 19320 788917388.0000000000 -65743250.206018500000

100 650 19500 811289375.0000000000 -67607583.709490700000101 1464 43920 9349266713.1428600000 -333902438.699344000000102 254 7620 47253525.0000000000 -11813861.468750000000103 1286 38580 6330910163.5000000000 -263787990.551360000000104 570 17100 545905530.0000000000 -54590724.570000000000105 785 23550 1432826576.7857100000 -102344875.923834000000106 1004 30120 3006036909.3333300000 -167002143.653635000000107 1441 43230 8914525639.0384600000 -342866434.763940000000108 482 14460 329028262.5000000000 -41128759.691406300000109 1249 37470 5798685689.5909100000 -263576699.788787000000110 930 27900 2387240831.2500000000 -149202661.164551000000111 1160 34800 4642466160.0000000000 -232123395.145000000000112 1730 51900 15443583710.0000000000 -514786181.397408000000113 389 11670 172093016.5000000000 -28682495.384259300000114 392 11760 176139712.0000000000 -29356947.148148100000115 740 22200 1199329100.0000000000 -99944246.261574100000116 1674 50220 13989163748.1429000000 -499613055.137482000000117 284 8520 66323940.0000000000 -16581521.937500000000

118 1466 43980 9387684563.5000000000 -391153599.939381000000119 645 19350 792596317.5000000000 -79259825.895000000000120 890 26700 2091241264.2857100000 -149374512.569242000000121 1139 34170 4394151706.8333300000 -244119644.926783000000122 1636 49080 13056129461.5385000000 -502158898.140419000000123 542 16260 468899782.5000000000 -58612727.933593800000124 1414 42420 8421607507.0909100000 -382800429.008828000000125 1050 31500 3439908281.2500000000 -214994390.881348000000126 1310 39300 6692925585.0000000000 -334646377.663750000000127 1955 58650 22301720172.5000000000 -743390737.655741000000128 1970 59100 22819894910.0000000000 -760663229.406296000000129 437 13110 244666904.5000000000 -40778183.606481500000130 830 24900 1694770775.0000000000 -141231071.313657000000131 1884 56520 19955226533.1429000000 -712686734.075619000000132 314 9420 89939805.0000000000 -22485544.906250000000133 1646 49380 13297478063.5000000000 -554061671.827402000000134 720 21600 1104252480.0000000000 -110425464.720000000000135 995 29850 2925610226.7857100000 -208972311.714650000000136 1274 38220 6154815879.3333300000 -341934333.699931000000137 1831 54930 18315203209.0385000000 -704430974.016898000000138 602 18060 643674202.5000000000 -80459558.675781300000139 1579 47370 11735819099.5909000000 -533446420.728869000000140 1170 35100 4763866331.2500000000 -297741783.098145000000141 1460 43800 9272578260.0000000000 -463629022.682500000000142 1470 44100 9464858865.0000000000 -473243053.683750000000143 2195 65850 31582330572.5000000000 -1052744425.664630000000144 482 14460 328999222.0000000000 -54833607.564814800000145 920 27600 2310736400.0000000000 -192561558.865741000000146 2094 62820 27414153068.1429000000 -979076975.513757000000147 344 10320 118587120.0000000000 -29647430.375000000000148 1826 54780 18165266663.5000000000 -756886206.215422000000149 795 23850 1488467767.5000000000 -148847016.045000000000150 1100 33000 3956770714.2857100000 -282626648.360058000000

CASO QUINCE

ENCONTRAR EL O LOS VALORES DE "X"

ECUACIÓN :

DATOS A LOS ESTUDIANTESN° A B C D1 81 2430 6549822 31267429652 79 2370 6079998 28369401653 82 2460 6793536 32796982404 78 2340 5853744 26998358405 83 2490 7043214 34381965656 77 2310 5633166 25677609657 84 2520 7298928 36023702408 76 2280 5418192 24405910409 85 2550 7560750 377235312510 75 2250 5208750 231820312511 86 2580 7828752 394828064012 74 2220 5004768 220047584013 87 2610 8103006 413028976514 73 2190 4806174 208728936515 88 2640 8383584 431851904016 72 2160 4612896 197852544017 89 2670 8670558 451310856518 71 2130 4424862 187406736519 90 2700 8964000 471420000020 70 2100 4242000 177380000021 91 2730 9263982 4921936565

C

X

D

X

CD

B

CD

AX 12

1

2

1

22 69 2070 4064238 167760976523 92 2760 9570576 513646304024 68 2040 3891504 158538464025 93 2790 9883854 535792576526 67 2010 3723726 149701416527 94 2820 10203888 558647264028 66 1980 3560832 141238944029 95 2850 10530750 582225312530 65 1950 3402750 133140312531 96 2880 10864512 606541824032 64 1920 3249408 125394944033 97 2910 11205246 631612056534 63 1890 3100734 117992416535 98 2940 11553024 657451424036 62 1860 2956656 110922464037 99 2970 11907918 684075496538 61 1830 2817102 104174976539 100 3000 12270000 711500000040 60 1800 2682000 97740000041 101 3030 12639342 739740816542 59 1770 2551278 91607736543 102 3060 13016016 768813984044 58 1740 2424864 85768544045 103 3090 13400094 798735696546 57 1710 2302686 80212936547 104 3120 13791648 829522304048 56 1680 2184672 74931584049 105 3150 14190750 861190312550 55 1650 2070750 69915312551 106 3180 14597472 893756384052 54 1620 1960848 65155104053 107 3210 15011886 927237336554 53 1590 1854894 606420965

55 108 3240 15434064 961650144056 52 1560 1752816 56367584057 109 3270 15864078 997011936558 51 1530 1654542 52323016559 110 3300 16302000 1033340000060 50 1500 1560000 48500000061 111 3330 16747902 1070651776562 49 1470 1469118 44890296563 112 3360 17201856 1108964864064 48 1440 1381824 41485824065 113 3390 17663934 1148297016566 47 1410 1298046 38278656567 114 3420 18134208 1188666144068 46 1380 1217712 35261024069 115 3450 18612750 1230090312570 45 1350 1140750 32425312571 116 3480 19099632 1272587744072 44 1320 1067088 29764064073 117 3510 19594926 1316176816574 43 1290 996654 27269976575 118 3540 20098704 1360876064076 42 1260 929376 24935904077 119 3570 20611038 1406704176578 41 1230 865182 22754856579 120 3600 21132000 1453680000080 40 1200 804000 20720000081 121 3630 21661662 1501822536582 39 1170 745758 18824656583 122 3660 22200096 1551150944084 38 1140 690384 17062304085 123 3690 22747374 1601684536586 37 1110 637806 15426576587 124 3720 23303568 16534427840

88 36 1080 587952 13911264089 125 3750 23868750 1706445312590 35 1050 540750 12510312591 126 3780 24442992 1760711904092 34 1020 496128 11217824093 127 3810 25026366 1816262496594 33 990 454014 10028056595 128 3840 25618944 1873117184096 32 960 414336 8935424097 129 3870 26220798 1931296216598 31 930 377022 7934496599 130 3900 26832000 19908200000

100 30 900 342000 70200000101 131 3930 27452622 20517090965102 29 870 309198 61868165103 132 3960 28082736 21139842240104 28 840 278544 54299840105 133 3990 28722414 21776662565106 27 810 249966 47446965107 134 4020 29371728 22427762240108 26 780 223392 41263040109 135 4050 30030750 23093353125110 25 750 198750 35703125111 136 4080 30699552 23773648640112 24 720 175968 30723840113 137 4110 31378206 24468863765114 23 690 154974 26283365115 138 4140 32066784 25179215040116 22 660 135696 22341440117 139 4170 32765358 25904920565118 21 630 118062 18859365119 140 4200 33474000 26646200000120 20 600 102000 15800000

121 141 4230 34192782 27403274565122 19 570 87438 13127765123 142 4260 34921776 28176367040124 18 540 74304 10808640125 143 4290 35661054 28965701765126 17 510 62526 8810165127 144 4320 36410688 29771504640128 16 480 52032 7101440129 145 4350 37170750 30594003125130 15 450 42750 5653125131 146 4380 37941312 31433426240132 14 420 34608 4437440133 147 4410 38722446 32290004565134 13 390 27534 3428165135 148 4440 39514224 33163970240136 12 360 21456 2600640137 149 4470 40316718 34055556965138 11 330 16302 1931765139 150 4500 41130000 34965000000140 10 300 12000 1400000141 151 4530 41954142 35892536165142 9 270 8478 985365143 152 4560 42789216 36838403840144 8 240 5664 669440145 153 4590 43635294 37802842965146 7 210 3486 435365147 154 4620 44492448 38786095040148 6 180 1872 267840149 155 4650 45360750 39788403125150 5 150 750 153125

CASO DIECISÉIS

CALCULAR EL O LOS VALORES DE "X" :

ECUACIÓN :

DATOS A ESTUDIANTES :N° A B C D1 52 1560 -892944 894013122 76 2280 -1640688 1171609923 71 2130 -1491000 1114636814 94 2820 -1933392 1356878725 90 2700 -2014200 1392753606 110 3300 -1963500 1845662507 155 4650 -1971600 6006291858 74 2220 -1324896 841847689 104 3120 -2305056 17906220810 190 5700 2764500 127297625011 149 4470 -2086596 51893079312 98 2940 -1555260 12429016613 206 6180 2607960 177349849614 120 3600 -1346400 22499616015 80 2400 -1857600 13499136016 258 7740 20046600 397281609617 169 5070 -1320228 82996322518 248 7440 17418528 340306790419 202 6060 1774368 164707244820 250 7500 18637500 347780025021 365 10950 67254900 15346385945

2345 X

D

X

C

X

B

X

A

22 116 3480 -1014768 19348243223 188 5640 -155664 125113248024 386 11580 105157980 1613954046625 275 8250 18232500 539656562526 154 4620 1113420 55110270627 374 11220 73127472 1686452768028 190 5700 5688600 121998848029 108 3240 -2906928 22934620830 440 13200 172048800 2435024416031 267 8010 14623056 485247161732 402 12060 127141344 1761538272033 314 9420 33222456 894842726434 390 11700 115560900 1566381297035 575 17250 361215000 7797047782536 158 4740 2294160 59630969637 272 8160 15174336 523690739238 582 17460 452371140 5892490602639 401 12030 92741676 2209211375340 210 6300 11308500 170317875041 542 16260 289226376 6428025475242 260 7800 27658800 363967344043 136 4080 -3843360 42745561644 622 18660 571227384 6989080608045 365 10950 60860100 1585921970546 556 16680 398952240 4737076409647 426 12780 114457680 2784462777648 530 15900 343137900 3974234521049 785 23550 1035493500 23152132562550 200 6000 10380000 136938880051 356 10680 52575504 1460137702452 778 23340 1189616460 13584726230653 527 15810 253446948 5979419943354 266 7980 32981340 3686579386

55 710 21300 729141600 16732089472056 330 9900 71973000 762630000057 164 4920 -4469328 79721712058 804 24120 1334443824 14267963452859 463 13890 151912152 3835008211360 710 21300 904568400 9324103968061 538 16140 267607656 6538348432062 670 20100 755699700 7566137073063 995 29850 2245675200 52777392870564 242 7260 25020864 248710176065 440 13200 120,938,400 32,312,934,72066 974 29220 2462106420 24497999202667 653 19590 532354332 12949208167368 322 9660 70083300 638240160669 878 26340 1471110072 35367899436870 400 12000 146040000 1290261440071 192 5760 -4587264 141943603272 986 29580 2578559592 23824563395273 561 16830 302300460 7764457724174 864 25920 1715707008 15177173299275 650 19500 514800000 12985932960076 810 24300 1407577500 12031709625077 1205 36150 4147344900 102722986498578 284 8520 47994864 382149036879 524 15720 229153584 6184337708880 1170 35100 4415053500 37625167125081 779 23370 961469844 24397565423382 378 11340 126565740 944677830683 1046 31380 2593368720 65543943225684 470 14100 257268600 1877186016085 220 6600 -3999600 238782544086 1168 35040 4420436160 34556148057687 659 19770 526546272 139881867265

88 1018 30540 2904085248 21548206342489 762 22860 878162328 23081301868890 950 28500 2353102500 16755396145091 1415 42450 6896087400 179911729094592 326 9780 81080112 514225619293 608 18240 386111616 10716790400094 1366 40980 7193670180 51144606938695 905 27150 1572799500 41783544562596 434 13020 206380020 1231087828697 1214 36420 4174154472 110907941872098 540 16200 413067600 2411777808099 248 7440 -2508768 3809006208

100 1350 40500 6976935000 447043622400101 757 22710 839170836 232020758137102 1172 35160 4541420304 272864946240103 874 26220 1379822256 379031929024104 1090 32700 3646605900 208164638970105 1625 48750 10647487500 2921390941625106 368 11040 126054720 6116760576107 692 20760 600703056 172765118592108 1562 46860 10943168940 624202149186109 1031 30930 2398349316 667462619113110 490 14700 313477500 14180906250111 1382 41460 6291704256 1755468495872112 610 18300 620845800 27404606240113 276 8280 82800 5802506976114 1532 45960 10364917584 518552279200115 855 25650 1254695400 361839699585116 1326 39780 6699429360 308386992576117 986 29580 2041907400 586549960416118 1230 36900 5342418900 229890034410119 1835 55050 15557130000 4480732130625120 410 12300 184696800 6310024640

121 776 23280 881818464 263617027264122 1758 52740 15808762260 680014066746123 1157 34710 3470125308 1011048972713124 546 16380 451809540 14038102806125 1550 46500 9024255000 2639868537600126 680 20400 888012000 26677080000127 304 9120 3972672 8500764160128 1714 51420 14701245384 529391442528129 953 28590 1787641212 537936785113130 1480 44400 9449829600 302488509440131 1098 32940 2886545376 866647535040132 1370 41100 7494872700 217419286330133 2045 61350 21780599700 6572548750105134 452 13560 258784464 5184729280135 860 25800 1238348400 385209039680136 1954 58620 21935662620 636231171506137 1283 38490 4820133492 1468586939193138 602 18060 625327500 10638744466139 1718 51540 12450043632 3811933749568140 750 22500 1221975000 19560432000141 332 9960 9358416 12049121952142 1896 56880 20102779872 442308875712143 1051 31530 2452529520 769729752001144 1634 49020 12864338208 231583499712145 1210 36300 3935863800 1233851597440146 1510 45300 10158298500 152389766250147 2255 67650 29473481400 9300975270785148 494 14820 350095824 2101215168149 944 28320 1679183424 543529968768150 2150 64500 29469082500 442058006250

CASO DIECISIETE

CALCULAR EL O LOS VALORES DE "X"

ECUACIÓN :

DATOS :N° A B C D1 294 8820 -6647790996 -4953993397736838.002 272 8160 -6816952128 -7881014056239104.003 290 8700 -6307665300 -4531863921793290.004 272 8160 -6507994944 -6857315645361152.005 276 8280 -5219039664 -3287690667045888.006 268 8040 -6171468624 -6297228137166400.007 280 8400 -5514415200 -3608873749022080.008 280 8400 -5957532000 -4550612684800000.009 272 8160 -4935686976 -2991328043040000.0010 254 7620 -5480622516 -5767397429524718.0011 262 7860 -4277746836 -2348592861029350.0012 270 8100 -5333793300 -3916988066367630.0013 252 7560 -3687855696 -1828065349958400.0014 264 7920 -5035178016 -3687126909193728.0015 266 7980 -4532478804 -2589803283889458.0016 244 7320 -4645520880 -4293544223676096.0017 250 7500 -3577612500 -1736814059985250.0018 244 7320 -4416902640 -3690351981397696.0019 248 7440 -3469858272 -1649495397573504.0020 254 7620 -4249657236 -2688810891835838.00

0X

D

X

C

X

B

X

A2468

21 238 7140 -2967111252 -1267055283408334.0022 238 7140 -3939122292 -2964692798662014.0023 244 7320 -3261666096 -1486091019301888.0024 226 6780 -3648137652 -3050264286679450.0025 234 7020 -2782136916 -1136938813591698.0026 242 7260 -3551892564 -1999741954263482.0027 224 6720 -2357502336 -860602978948608.0028 236 7080 -3331329744 -1870532390608448.0029 222 6660 -2278776276 -812882890218750.0030 216 6480 -3036960864 -2206577937627648.0031 218 6540 -2127251412 -724209798208194.0032 234 7020 -2956918068 -1364948028504450.0033 220 6600 -2202037200 -767449174117120.0034 222 6660 -2743622964 -1418683182128142.0035 210 6300 -1846977300 -571458097766010.0036 224 6720 -2590519680 -1141829976139776.0037 216 6480 -2054385504 -683075718119808.0038 198 5940 -2316073716 -1512195447187062.0039 206 6180 -1717705044 -506068223512878.0040 214 6420 -2258182356 -950369996132118.0041 196 5880 -1424175984 -369929612136448.0042 208 6240 -2100750912 -882050008612864.0043 194 5820 -1370306196 -346860397456938.0044 188 5640 -1884980496 -1056366981630272.0045 190 5700 -1267161300 -304398479172190.0046 188 5640 -1773010704 -879087051502400.0047 192 5760 -1317977856 -325035501542400.0048 198 5940 -1699786836 -597795531278022.0049 186 5580 -1169946324 -266472554154018.0050 196 5880 -1583218224 -508207884764608.0051 188 5640 -1217827152 -284894952585984.0052 170 5100 -1384461300 -692295156858530.0053 178 5340 -992384532 -202614122986714.00

54 186 5580 -1354273812 -413294976730050.0055 168 5040 -799761312 -141605485897344.0056 180 5400 -1246633200 -379805865727680.0057 182 5460 -1078429716 -232671385387350.0058 160 4800 -1094352000 -462994099200000.0059 166 4980 -764877204 -131517499025158.0060 160 4800 -1021852800 -376942467266560.0061 164 4920 -731145456 -122051919495168.0062 96 2880 -570902400 -845345758150656.0063 154 4620 -578885076 -82974933819778.0064 168 5040 -902383776 -203403020900352.0065 160 4800 -667036800 -104859987304960.0066 142 4260 -764394804 -286571173376062.0067 150 4500 -525172500 -70669642356150.0068 158 4740 -752841876 -160533690118622.0069 140 4200 -407206800 -46517579216640.0070 152 4560 -683232096 -145623679040000.0071 158 4740 -636609492 -97072990141374.0072 132 3960 -580911408 -181217343113664.0073 138 4140 -386228052 -42653523923634.0074 132 3960 -537421104 -143490753312192.0075 136 4080 -366069024 -39067924874368.0076 36 1080 -82764720 -347400566202816.0077 126 3780 -276823764 -24752810289438.0078 140 4200 -468594000 -70881690600000.0079 132 3960 -328124016 -32665215897600.0080 114 3420 -378032436 -103952164961898.0081 122 3660 -246129876 -20444703041250.0082 130 3900 -377625300 -53736590303370.0083 112 3360 -180524736 -12372790393600.0084 124 3720 -335866896 -47885752629568.0085 130 3900 -310295700 -29816719069930.0086 126 3780 -306924660 -33735105507726.00

87 110 3300 -169161300 -11140422488910.0088 104 3120 -248196000 -46563100153856.0089 108 3240 -158341392 -10014793185024.0090 88 2640 -194797152 -51899604765184.0091 98 2940 -111789972 -5729922522954.0092 112 3360 -213490368 -20461368546304.0093 104 3120 -138262176 -8052941939328.0094 86 2580 -158596212 -31423678324550.0095 94 2820 -96381396 -4523325287038.0096 102 3060 -163426644 -14652089113062.0097 84 2520 -64791216 -2412239950848.0098 96 2880 -140920704 -12721014448128.0099 102 3060 -128968596 -7202457438150.00

100 76 2280 -104257104 -16565263760448.00101 78 2340 -50005332 -1606818916014.00102 34 1020 -31205268 -24794576375050.00103 80 2400 -54619200 -1844730650880.00104 82 2460 -89075124 -7067300863882.00105 70 2100 -34391700 -898421714470.00106 84 2520 -79778160 -4501788908736.00107 76 2280 -45688464 -1395695212288.00108 58 1740 -50371956 -7220107762162.00109 66 1980 -28115604 -658982610858.00110 74 2220 -56112276 -2952933198098.00111 56 1680 -16146144 -284131628928.00112 68 2040 -45840432 -2457549531584.00113 74 2220 -41655636 -1208797734258.00114 48 1440 -28034496 -3207864778752.00115 54 1620 -14304276 -237037873878.00116 48 1440 -24606144 -2169568281600.00117 52 1560 -12622896 -196788966400.00118 12 360 -2361168 -1968343293504.00119 42 1260 -6300756 -71379517650.00

120 56 1680 -21226464 -644925431808.00121 48 1440 -9703872 -133515151104.00122 30 900 -8709300 -1010097302670.00123 38 1140 -4584852 -45434828934.00124 46 1380 -12612372 -362092027950.00125 28 840 -1793232 -12603345664.00126 40 1200 -9136800 -277061424640.00127 46 1380 -8448084 -109044329998.00128 20 600 -2982000 -308795000000.00129 26 780 -1438164 -9439035138.00130 20 600 -2521200 -186837552320.00131 24 720 -1136736 -6974567808.00132 26 780 -3044340 -88661380626.00133 6 180 -29844 -151234278.00134 28 840 -2668176 -41292634432.00135 20 600 -673200 -3633361920.00136 2 60 -21684 -12807760442.00137 10 300 -105300 -471541810.00138 18 540 -920916 -15588767322.00139 -2 -60 -2772 11835746.00140 12 360 -384336 -8693697600.00141 16 480 -362304 -1751166208.00142 -8 -240 -254688 18147442176.00143 2 60 -2196 -25324650.00144 -8 -240 -202464 9048915968.00145 -4 -120 -8784 15697152.00146 -2 -60 -8244 516871250.00147 -6 -180 -16596 15272862.00148 -2 -60 -6036 185862978.00149 -8 -240 -25056 12905600.00150 -26 -780 -1786356 17519410922.00

CASO DIECIOCHO

CALCULAR EL O LOS VALORES DE X

ECUACIÓN :

DATOS A ESTUDIANTES :N° A B C D1 22 13689 1602 132 26 4563 534 233 19 6534 780 134 27 46464 1110 215 27 69696 1665 186 30 17424 1233 217 26 1728 300 148 25 3888 540 139 31 105840 3480 1610 39 238140 4155 2411 37 23328 1746 1912 32 41472 2880 1413 43 75600 3549 2214 36 25725 1554 1515 41 169344 4632 1716 46 279936 5400 2217 46 19683 2430 1918 40 15552 1971 1319 48 30720 2400 1820 44 58080 4110 14

)1X(Log

)1X(LogDC

)1X(Log

B)1X(LogA 2

3

4

21 54 399300 7293 2122 53 13200 3432 2023 48 24336 6228 1224 59 492804 9000 2325 58 202176 5655 1926 57 359424 8112 1827 64 217728 7560 2228 58 182952 6594 1629 66 920205 13050 2130 68 920205 13050 2331 69 23232 6000 2132 60 15552 4080 1233 70 148716 5967 1934 67 45900 3111 1635 69 135000 6750 1536 74 264600 8046 2037 74 547428 13965 1738 81 44688 11400 2439 72 3840 1200 1240 74 47040 3900 1441 80 77175 4662 1742 78 190575 9198 1543 87 1349634 19140 2144 89 713856 15378 2345 87 441600 11316 1846 89 441600 11316 2047 90 225792 8136 1848 89 285768 9360 1749 94 54675 6750 1950 88 33075 4350 1351 95 550368 15054 1752 100 718848 16224 2253 99 186624 8100 18

54 97 419904 14580 1655 106 48384 12432 2256 96 3024 1092 1257 100 112752 13311 1358 109 1252800 21228 2259 110 1089000 19890 2060 111 533610 15300 2161 110 18228 4929 1762 105 45012 11625 1263 117 104544 12480 2164 109 69984 8640 1365 118 1571724 27423 1966 123 1241856 25740 2467 120 163200 9078 1868 117 367200 17238 1569 127 740880 20265 2270 122 185220 8925 1771 124 657072 22140 1672 131 894348 23544 2373 128 658119 18870 1774 132 483516 17427 2175 130 65664 5928 1676 128 182400 13224 1477 137 105300 12753 2078 130 26325 3978 1379 135 588000 26520 1580 144 1152480 29400 2481 140 96432 7995 1782 137 125952 9840 1483 144 72576 9198 1884 139 18144 3150 1385 143 8256 2580 1486 141 33024 8772 12

87 150 684288 19140 1888 151 42768 11220 1989 147 26460 7155 1290 152 59535 7830 1791 151 124200 15042 1392 158 345000 17250 2093 156 56400 5781 1594 155 182736 13677 1495 163 291600 15264 1996 159 230400 12816 1597 165 37632 9996 1898 159 14700 4263 1299 165 633750 29100 15

100 173 101400 25950 23101 165 22032 6120 12102 169 352512 15300 16103 174 1687296 36348 18104 179 949104 31980 23105 175 51516 7155 16106 172 5724 2067 13107 174 64800 16848 12108 182 1312200 29322 20109 184 654885 21450 19110 182 808500 24585 17111 188 268800 19488 20112 182 67200 6888 14113 186 346275 18126 15114 190 1121931 27702 19115 193 1409400 31494 19116 194 69600 18096 20117 189 101952 26196 12118 199 3084048 46905 22119 201 544500 26280 21

120 195 162000 10980 15121 199 322812 15555 16122 200 573888 20679 17123 204 2333184 48360 18124 210 5249664 63240 24125 211 435456 30240 22126 203 108864 9828 14127 208 559872 22464 16128 211 2239488 43200 19129 217 252720 29835 22130 208 343980 39975 13131 222 1397088 45936 24132 214 712800 26928 16133 221 2894400 49044 20134 223 4167936 57888 22135 226 5757696 69360 22136 228 999600 45084 24137 222 129375 10350 15138 222 253575 15318 15139 227 504210 20580 17140 227 41160 11130 17141 225 3408 1704 12142 225 41748 11289 12143 233 1280664 36720 17144 237 2117016 43632 21145 238 2997891 54750 19146 242 592176 40515 23147 236 696192 47064 14148 246 391608 45510 24149 238 18225 4050 13150 238 164025 20250 13

CASO DIECINUEVE

SÓLO CINCO DE ELLOS ES "B", LA DIFERENCIA ENTRE LOS DOS RESTANTES ES "C".

CALCULAR EL VALOR DE CADA UNO DE ESOS DOS NÚMEROS.

DATOS A LOS ESTUDIANTES :N° A B C1 34214.40 960 1.202 73305.60 960 0.903 28569.60 960 1.404 108595.20 960 1.105 5385.60 960 1.606 160588.80 960 1.307 13084.80 960 1.808 74649.60 960 1.509 10137.60 960 2.0010 404716.80 960 1.7011 25804.80 960 2.2012 124992.00 960 1.9013 116899.20 960 2.4014 180441.60 960 2.1015 34099.20 960 2.6016 650188.80 960 2.3017 114278.40 960 2.8018 144921.60 960 2.5019 114000.00 960 3.0020 215692.80 960 2.70

EL PRODUCTO DE SIETE NÚMEROS POSITIVOS ES "A", PERO EL PRODUCTO DE

21 344102.40 960 3.2022 813715.20 960 2.9023 4752.00 960 3.4024 1416960.00 960 3.1025 329011.20 960 3.6026 758112.00 960 3.3027 781776.00 960 3.8028 561600.00 960 3.5029 759590.40 960 4.0030 2076940.80 960 3.7031 888806.40 960 4.2032 185856.00 960 3.9033 654336.00 960 4.4034 756691.20 960 4.1035 185779.20 960 4.6036 1841472.00 960 4.3037 484800.00 960 4.8038 3584889.60 960 4.5039 14313.60 960 5.0040 549964.80 960 4.7041 622656.00 960 5.2042 809971.20 960 4.9043 1876992.00 960 5.4044 4106112.00 960 5.1045 1044259.20 960 5.6046 2829024.00 960 5.3047 1154524.80 960 5.8048 1690214.40 960 5.5049 1636761.60 960 6.0050 524620.80 960 5.7051 1042560.00 960 6.2052 4837824.00 960 5.9053 1518499.20 960 6.40

54 1616659.20 960 6.1055 3872707.20 960 6.6056 376396.80 960 6.3057 199180.80 960 6.8058 5913158.40 960 6.5059 3085430.40 960 7.0060 5396428.80 960 6.7061 1569984.00 960 7.2062 434400.00 960 6.9063 4334976.00 960 7.4064 764928.00 960 7.1065 3,061,555.2 960 7.60 192066 9926150.40 960 7.3067 2561308.80 960 7.8068 1798886.40 960 7.5069 6298761.60 960 8.0070 3276748.80 960 7.7071 1597622.40 960 8.2072 10219161.60 960 7.9073 2344819.20 960 8.4074 7960243.20 960 8.1075 1807171.20 960 8.6076 1538726.40 960 8.3077 5482684.80 960 8.8078 1050393.60 960 8.5079 1388774.40 960 9.0080 14282188.80 960 8.7081 2947392.00 960 9.2082 1751904.00 960 8.9083 4084867.20 960 9.4084 1186560.00 960 9.1085 1029667.20 960 9.6086 707884.80 960 9.30

87 4521052.80 960 9.8088 7693977.60 960 9.5089 256713.60 960 10.0090 5170636.80 960 9.7091 659404.80 960 10.2092 10092019.20 960 9.9093 2005401.60 960 10.4094 2219731.20 960 10.1095 6925363.20 960 10.6096 3299328.00 960 10.3097 5708284.80 960 10.8098 869510.40 960 10.5099 2304230.40 960 11.00

100 19071820.80 960 10.70101 357744.00 960 11.20102 4996627.20 960 10.90103 6486979.20 960 11.40104 20560128.00 960 11.10105 3790051.20 960 11.60106 1756800.00 960 11.30107 414480.00 960 11.80108 13665830.40 960 11.50109 9260697.60 960 12.00110 7494604.80 960 11.70111 11877840.00 960 12.20112 3025152.00 960 11.90113 3082137.60 960 12.40114 12517747.20 960 12.10115 10365235.20 960 12.60116 15655488.00 960 12.30117 518256.00 960 12.80118 22596998.40 960 12.50119 16610534.40 960 13.00

120 4944844.80 960 12.70121 5144342.40 960 13.20122 9095424.00 960 12.90123 9442051.20 960 13.40124 33117427.20 960 13.10125 21873571.20 960 13.60126 3737606.40 960 13.30127 5705424.00 960 13.80128 15599001.60 960 13.50129 23345481.60 960 14.00130 2506060.80 960 13.70131 32736604.80 960 14.20132 8052595.20 960 13.90133 17316873.60 960 14.40134 28867104.00 960 14.10135 25643203.20 960 14.60136 39609062.40 960 14.30137 4678348.80 960 14.80138 6396710.40 960 14.50139 9373977.60 960 15.00140 11786956.80 960 14.70141 814320.00 960 15.20142 1604064.00 960 14.90143 9950515.20 960 15.40144 28230451.20 960 15.10145 16821043.20 960 15.60146 39562944.00 960 15.30147 3512246.40 960 15.80148 46681305.60 960 15.50149 2059200.00 960 16.00150 3231820.80 960 15.70

CASO VEINTE

CALCULAR EL VALOR DE "N"

ECUACIÓN :

DATOS :N° A X B1 225 0.015000 14974.186541571100002 125 0.065000 9166.571783242080003 150 0.015000 6439.963727318750004 200 0.055000 36623.833053821900005 75 0.040000 2322.690128915170006 325 0.055000 272826.021678066000007 75 0.020000 2088.372240717740008 275 0.015000 28932.647628193100009 200 0.030000 22359.3734580472000010 275 0.070000 337432.7060177140000011 100 0.045000 6766.6245241502500012 75 0.020000 2703.8407731522200013 150 0.060000 29813.7047817005000014 350 0.025000 99847.4993414352000015 225 0.035000 45763.8691004025000016 100 0.060000 12626.8118664036000017 300 0.045000 199561.5503871000000018 125 0.015000 7586.1084926998300019 175 0.040000 33277.8552736318000020 300 0.020000 59294.2190882747000021 225 0.055000 143504.5763201990000022 75 0.050000 8003.2159348634700023 200 0.010000 17609.2373895911000024 100 0.065000 24532.45866235930000

B)1X(A.....)1X(A)1X(A)1X(A N32

25 275 0.045000 209656.6436174270000026 250 0.040000 121569.9215075850000027 50 0.060000 6745.2102891939100028 325 0.030000 163207.4352887780000029 225 0.055000 222542.1965097050000030 200 0.065000 265838.6258029250000031 300 0.055000 745842.1319269900000032 150 0.010000 12926.1663784092000033 275 0.045000 300848.4227872520000034 325 0.030000 197043.5131259420000035 275 0.025000 92780.3551420690000036 50 0.050000 8855.9710923258200037 225 0.035000 105074.8098047640000038 150 0.070000 225990.3048016680000039 125 0.010000 11242.0811021794000040 250 0.020000 63024.9473603944000041 175 0.035000 65518.0856494961000042 350 0.025000 213644.7385897050000043 50 0.055000 15418.1272805387000044 100 0.065000 90578.5722348809000045 175 0.040000 100326.5857679240000046 125 0.050000 81237.8353822601000047 275 0.040000 383426.9864861580000048 325 0.035000 459219.0687523860000049 200 0.045000 228853.8013183120000050 250 0.015000 58058.7722378006000051 200 0.035000 129440.6610115950000052 175 0.060000 488724.6598049230000053 225 0.040000 267313.7822466510000054 75 0.030000 17219.5547803043000055 175 0.060000 582669.4472222200000056 300 0.010000 65799.6901266815000057 200 0.015000 43826.89573669390000

58 150 0.060000 444200.2623370440000059 300 0.050000 2087171.9140032100000060 50 0.055000 39735.0560230500000061 75 0.035000 28079.1795640697000062 300 0.010000 71711.7575359844000063 250 0.055000 2029236.2472526900000064 275 0.015000 90829.2526592246000065 175 0.045000 327502.7830023170000066 50 0.070000 129980.0389328530000067 275 0.040000 848652.2742260730000068 75 0.025000 20799.0416741676000069 225 0.060000 3045364.4556841500000070 350 0.035000 1267822.0625878600000071 200 0.030000 175807.8251799730000072 125 0.065000 918948.9288807800000073 300 0.035000 852241.4463365570000074 175 0.055000 1145976.2940874400000075 150 0.030000 109590.2582644350000076 325 0.020000 253869.2520562880000077 175 0.050000 864203.3192530820000078 275 0.015000 116192.0403663130000079 150 0.025000 84585.3342630865000080 100 0.070000 1324837.8119372300000081 250 0.035000 662488.8786487100000082 75 0.020000 22287.4787999291000083 125 0.040000 221388.4041762690000084 350 0.015000 210854.7295805820000085 175 0.020000 87154.0800802506000086 100 0.010000 18899.2652739076000087 200 0.040000 752046.7787764890000088 75 0.045000 160418.0422510050000089 100 0.010000 19777.9720109723000090 50 0.035000 44640.15323216890000

91 200 0.015000 81627.0786329113000092 225 0.050000 3773917.3300741700000093 50 0.025000 24030.2647889794000094 175 0.020000 105898.3946039750000095 75 0.045000 218935.2916388130000096 250 0.025000 366808.0460048110000097 125 0.040000 385751.0337391240000098 100 0.010000 22577.0979660759000099 225 0.025000 313775.34874891600000

100 125 0.065000 5368854.02050111000000101 200 0.010000 61960.87821979880000102 50 0.030000 45322.01498384290000103 125 0.040000 488960.40620471800000104 325 0.065000 223045239.16413600000000105 50 0.030000 49683.77081724970000106 150 0.015000 66736.09221071190000107 200 0.010000 67015.42782139120000108 325 0.050000 31605132.89467430000000109 150 0.045000 1578345.20985508000000110 75 0.035000 161266.90996007400000111 50 0.050000 383625.46419809100000112 250 0.020000 302560.19287874000000113 225 0.025000 447166.03694761500000114 175 0.045000 2861889.36210633000000115 250 0.045000 8274220.60843410000000116 100 0.050000 1597325.32489912000000117 125 0.010000 39239.05437624800000118 225 0.060000 52985933.68917040000000119 225 0.055000 28080764.27735890000000120 250 0.025000 671744.67230780700000121 50 0.030000 80765.94633626870000122 300 0.035000 4637749.26788370000000123 275 0.040000 7688413.69260791000000

124 125 0.070000 45641556.33901070000000125 150 0.060000 22161699.51190620000000126 175 0.020000 207464.34805403700000127 200 0.030000 949363.61214708700000128 350 0.045000 49536586.65350360000000129 300 0.060000 321423217.06350300000000130 100 0.015000 56369.92312747230000131 150 0.070000 123355106.24899100000000132 225 0.030000 1438005.22588793000000133 300 0.050000 77417640.31113350000000134 75 0.060000 7811170.90520363000000135 350 0.060000 952625537.29967000000000136 150 0.070000 173012840.75381500000000137 250 0.025000 1027485.54740904000000138 300 0.025000 1621618.75929779000000139 300 0.035000 8330305.13116098000000140 350 0.035000 14193752.78460930000000141 125 0.010000 53228.58685486530000142 125 0.010000 53887.12272341400000143 175 0.035000 2356894.20307701000000144 175 0.055000 48762750.85871470000000145 50 0.045000 1065186.49987408000000146 50 0.065000 15132878.94906720000000147 175 0.020000 319049.05202351800000148 275 0.070000 3877259160.76525000000000149 225 0.015000 258282.66235246900000150 325 0.015000 518087.25487243500000