Asignación 2 - Ejercicio.docx

62
La ecuación obtenida, es una ecuación trascendental que debe ser resuelta para λ, lo que equivale a encontrar las raíces de la ecuación. e −λ 2 erf ( λ ) − ( 1−T M ) T M ¿ ( k ( A ) k ( B ) )( α ( B) α ( A) ) 1 2 ×e ⌈λ 2 α (A) α (B) ( ρ ( B) ρ ( A) ) 2 ⌉ erf⌈λ ρ (B) ρ ( A ) ( α ( B) α ( A) ) 1 2 ⌉ −λ √ π∆ ^ H ^ c B ( T M −T 1 ) =0 Para determinar las raices de la ecuación se supone un valor de λ y se realiza una iteración con la ecuación anterior tomando un tamaño de paso 0.00125. En la Figura 1, f(λ)=0 vs λ supuestto , se observa el punto donde la función f(λ) corta el eje x (cambia de signo), este valor representa la raíz de la ecuación (λ). Para realizar la iteración de la función, se expreso la ecuación de la siguiente forma: Prueba Error Y se calcularon los términos A, B, C, D y E, como se presenta en las tablas 1, 2, 3, 4 y 5. Tabla 1. Cálculo del término A y B A B λ exp(-λ^2)/ (erf(λ)) (1-T m *)/ (T m *) (k (A) )/ (k (B) ) (α (B) / α (A) )^0.5 (1-T m *)/ (T m *)*(k (A) )/ (k (B) )*(α (B) /α (A) )^0.5 0.001250 000 708.9830174 1.000 0.27165 39 2.8235123 91 0.767018148 0.002500 000 354.4937243 1.000 0.27165 39 2.8235123 91 0.767018148 0.003750 000 236.3316113 1.000 0.27165 39 2.8235123 91 0.767018148 0.005000 000 177.2512934 1.000 0.27165 39 2.8235123 91 0.767018148 0.006250 000 141.8036935 1.000 0.27165 39 2.8235123 91 0.767018148 1 [ −(( )/ ) ]− ∗ λ *E = 0

Transcript of Asignación 2 - Ejercicio.docx

La ecuacin obtenida, es una ecuacin trascendental que debe ser resuelta para , lo que equivale a encontrar las races de la ecuacin.

Para determinar las raices de la ecuacin se supone un valor de y se realiza una iteracin con la ecuacin anterior tomando un tamao de paso 0.00125. En la Figura 1, f()=0 vs supuestto , se observa el punto donde la funcin f() corta el eje x (cambia de signo), este valor representa la raz de la ecuacin (). Para realizar la iteracin de la funcin, se expreso la ecuacin de la siguiente forma:Prueba Error[ (()/) ] *E = 0

Y se calcularon los trminos A, B, C, D y E, como se presenta en las tablas 1, 2, 3, 4 y 5.Tabla 1. Clculo del trmino A y BAB

exp(-^2)/(erf())(1-Tm*)/(Tm*)(k(A))/(k(B))((B)/(A))^0.5(1-Tm*)/(Tm*)*(k(A))/(k(B))*((B)/(A))^0.5

0.001250000708.98301741.0000.27165392.8235123910.767018148

0.002500000354.49372431.0000.27165392.8235123910.767018148

0.003750000236.33161131.0000.27165392.8235123910.767018148

0.005000000177.25129341.0000.27165392.8235123910.767018148

0.006250000141.80369351.0000.27165392.8235123910.767018148

0.007500000118.17245261.0000.27165392.8235123910.767018148

0.008750000101.29341701.0000.27165392.8235123910.767018148

0.01000000088.634509651.0000.27165392.8235123910.767018148

0.01125000078.789021181.0000.27165392.8235123910.767018148

0.01250000070.912925951.0000.27165392.8235123910.767018148

0.01375000064.469116741.0000.27165392.8235123910.767018148

0.01500000059.099522091.0000.27165392.8235123910.767018148

0.01625000054.556246361.0000.27165392.8235123910.767018148

0.01750000050.662221241.0000.27165392.8235123910.767018148

0.01875000047.287596631.0000.27165392.8235123910.767018148

0.02000000044.334984981.0000.27165392.8235123910.767018148

0.02125000041.729913441.0000.27165392.8235123910.767018148

0.02250000039.414458691.0000.27165392.8235123910.767018148

0.02375000037.342891791.0000.27165392.8235123910.767018148

0.02500000035.478629611.0000.27165392.8235123910.767018148

0.02625000033.792057211.0000.27165392.8235123910.767018148

0.02750000032.258944211.0000.27165392.8235123910.767018148

0.02875000030.859274191.0000.27165392.8235123910.767018148

0.03000000029.576366811.0000.27165392.8235123910.767018148

0.03125000028.396210581.0000.27165392.8235123910.767018148

0.03250000027.306949651.0000.27165392.8235123910.767018148

0.03375000026.298484561.0000.27165392.8235123910.767018148

0.03500000025.362158661.0000.27165392.8235123910.767018148

0.03625000024.490509291.0000.27165392.8235123910.767018148

0.03750000023.677068851.0000.27165392.8235123910.767018148

0.03875000022.916204231.0000.27165392.8235123910.767018148

0.04000000022.20298651.0000.27165392.8235123910.767018148

0.04125000021.533084151.0000.27165392.8235123910.767018148

0.04250000020.902675261.0000.27165392.8235123910.767018148

0.04375000020.308374731.0000.27165392.8235123910.767018148

0.04500000019.747173541.0000.27165392.8235123910.767018148

0.04625000019.216388011.0000.27165392.8235123910.767018148

0.04750000018.713616941.0000.27165392.8235123910.767018148

0.04875000018.236705391.0000.27165392.8235123910.767018148

0.05000000017.783713941.0000.27165392.8235123910.767018148

0.05125000017.352892381.0000.27165392.8235123910.767018148

0.05250000016.942657161.0000.27165392.8235123910.767018148

0.05375000016.551572081.0000.27165392.8235123910.767018148

0.05500000016.178331461.0000.27165392.8235123910.767018148

0.05625000015.821745721.0000.27165392.8235123910.767018148

0.05750000015.480728711.0000.27165392.8235123910.767018148

0.05875000015.154286701.0000.27165392.8235123910.767018148

0.06000000014.841508791.0000.27165392.8235123910.767018148

0.06125000014.541558451.0000.27165392.8235123910.767018148

0.06250000014.253666041.0000.27165392.8235123910.767018148

0.06375000013.977122331.0000.27165392.8235123910.767018148

0.06500000013.711272591.0000.27165392.8235123910.767018148

0.06625000013.455511561.0000.27165392.8235123910.767018148

0.06750000013.209278791.0000.27165392.8235123910.767018148

0.06875000012.972054571.0000.27165392.8235123910.767018148

0.07000000012.743356361.0000.27165392.8235123910.767018148

0.07125000012.522735441.0000.27165392.8235123910.767018148

0.07250000012.309774051.0000.27165392.8235123910.767018148

0.07375000012.104082771.0000.27165392.8235123910.767018148

0.07500000011.905298131.0000.27165392.8235123910.767018148

0.07625000011.713080481.0000.27165392.8235123910.767018148

0.07750000011.527112111.0000.27165392.8235123910.767018148

0.07875000011.347095461.0000.27165392.8235123910.767018148

0.08000000011.172751591.0000.27165392.8235123910.767018148

0.08125000011.00381871.0000.27165392.8235123910.767018148

0.08250000010.840050881.0000.27165392.8235123910.767018148

0.08375000010.681216891.0000.27165392.8235123910.767018148

0.08500000010.52709911.0000.27165392.8235123910.767018148

0.08625000010.377492491.0000.27165392.8235123910.767018148

0.08750000010.232203751.0000.27165392.8235123910.767018148

0.08875000010.091050481.0000.27165392.8235123910.767018148

0.0900000009.9538604071.0000.27165392.8235123910.767018148

0.0912500009.8204706851.0000.27165392.8235123910.767018148

0.0925000009.6907272841.0000.27165392.8235123910.767018148

0.0937500009.5644843871.0000.27165392.8235123910.767018148

0.0950000009.441603851.0000.27165392.8235123910.767018148

0.0962500009.3219547091.0000.27165392.8235123910.767018148

0.0975000009.2054127131.0000.27165392.8235123910.767018148

0.0987500009.0918599041.0000.27165392.8235123910.767018148

0.1000000008.9811842241.0000.27165392.8235123910.767018148

0.1012500008.8732791461.0000.27165392.8235123910.767018148

0.1025000008.7680433431.0000.27165392.8235123910.767018148

0.1037500008.665380371.0000.27165392.8235123910.767018148

0.1050000008.5651983761.0000.27165392.8235123910.767018148

0.1062500008.4674098311.0000.27165392.8235123910.767018148

0.1075000008.3719312781.0000.27165392.8235123910.767018148

0.1087500008.2786830991.0000.27165392.8235123910.767018148

0.1100000008.1875892921.0000.27165392.8235123910.767018148

0.1112500008.0985772741.0000.27165392.8235123910.767018148

0.1125000008.0115776861.0000.27165392.8235123910.767018148

0.1137500007.9265242221.0000.27165392.8235123910.767018148

0.1150000007.8433534551.0000.27165392.8235123910.767018148

0.1162500007.7620046881.0000.27165392.8235123910.767018148

0.1175000007.6824198091.0000.27165392.8235123910.767018148

0.1187500007.6045431511.0000.27165392.8235123910.767018148

0.1200000007.5283213681.0000.27165392.8235123910.767018148

0.1212500007.4537033121.0000.27165392.8235123910.767018148

0.1225000007.3806399281.0000.27165392.8235123910.767018148

0.1237500007.3090841371.0000.27165392.8235123910.767018148

0.1250000007.238990751.0000.27165392.8235123910.767018148

0.1262500007.1703163621.0000.27165392.8235123910.767018148

0.1275000007.1030192761.0000.27165392.8235123910.767018148

0.1287500007.037059411.0000.27165392.8235123910.767018148

0.1300000006.9723982271.0000.27165392.8235123910.767018148

0.1312500006.9089986581.0000.27165392.8235123910.767018148

0.1325000006.8468250321.0000.27165392.8235123910.767018148

0.1337500006.7858430121.0000.27165392.8235123910.767018148

0.1350000006.7260195351.0000.27165392.8235123910.767018148

Tabla 2. Clculo del trmino CC

((B)/(A))^2(^2)((B)/(A))((B)/(A))^2*(^2)*((B)/(A))exp(-((B)/(A))^2*(^2)*((B)/(A)))

0.84640.00000156257.9722222-0.00001054330.9999894568

0.84640.00000625007.9722222-0.00004217310.9999578278

0.84640.00001406257.9722222-0.00009488940.9999051151

0.84640.00002500007.9722222-0.00016869220.9998313220

0.84640.00003906257.9722222-0.00026358160.9997364531

0.84640.00005625007.9722222-0.00037955750.9996205145

0.84640.00007656257.9722222-0.00051661990.9994835135

0.84640.00010000007.9722222-0.00067476890.9993254587

0.84640.00012656257.9722222-0.00085400440.9991463602

0.84640.00015625007.9722222-0.00105432640.9989462292

0.84640.00018906257.9722222-0.00127573490.9987250785

0.84640.00022500007.9722222-0.00151823000.9984829219

0.84640.00026406257.9722222-0.00178181160.9982197749

0.84640.00030625007.9722222-0.00206647970.9979356540

0.84640.00035156257.9722222-0.00237223440.9976305771

0.84640.00040000007.9722222-0.00269907560.9973045637

0.84640.00045156257.9722222-0.00304700330.9969576341

0.84640.00050625007.9722222-0.00341601750.9965898104

0.84640.00056406257.9722222-0.00380611830.9962011158

0.84640.00062500007.9722222-0.00421730560.9957915748

0.84640.00068906257.9722222-0.00464957940.9953612132

0.84640.00075625007.9722222-0.00510293970.9949100582

0.84640.00082656257.9722222-0.00557738660.9944381381

0.84640.00090000007.9722222-0.00607292000.9939454829

0.84640.00097656257.9722222-0.00658953990.9934321235

0.84640.00105625007.9722222-0.00712724640.9928980922

0.84640.00113906257.9722222-0.00768603940.9923434227

0.84640.00122500007.9722222-0.00826591890.9917681499

0.84640.00131406257.9722222-0.00886688490.9911723100

0.84640.00140625007.9722222-0.00948893750.9905559404

0.84640.00150156257.9722222-0.01013207660.9899190800

0.84640.00160000007.9722222-0.01079630220.9892617687

0.84640.00170156257.9722222-0.01148161440.9885840478

0.84640.00180625007.9722222-0.01218801310.9878859599

0.84640.00191406257.9722222-0.01291549830.9871675489

0.84640.00202500007.9722222-0.01366407000.9864288597

0.84640.00213906257.9722222-0.01443372830.9856699386

0.84640.00225625007.9722222-0.01522447310.9848908333

0.84640.00237656257.9722222-0.01603630440.9840915926

0.84640.00250000007.9722222-0.01686922220.9832722664

0.84640.00262656257.9722222-0.01772322660.9824329060

0.84640.00275625007.9722222-0.01859831750.9815735640

0.84640.00288906257.9722222-0.01949449490.9806942940

0.84640.00302500007.9722222-0.02041175890.9797951509

0.84640.00316406257.9722222-0.02135010940.9788761908

0.84640.00330625007.9722222-0.02230954640.9779374712

0.84640.00345156257.9722222-0.02329006990.9769790504

0.84640.00360000007.9722222-0.02429168000.9760009883

0.84640.00375156257.9722222-0.02531437660.9750033456

0.84640.00390625007.9722222-0.02635815970.9739861845

0.84640.00406406257.9722222-0.02742302940.9729495682

0.84640.00422500007.9722222-0.02850898560.9718935611

0.84640.00438906257.9722222-0.02961602830.9708182288

0.84640.00455625007.9722222-0.03074415750.9697236379

0.84640.00472656257.9722222-0.03189337330.9686098563

0.84640.00490000007.9722222-0.03306367560.9674769530

0.84640.00507656257.9722222-0.03425506440.9663249981

0.84640.00525625007.9722222-0.03546753970.9651540629

0.84640.00543906257.9722222-0.03670110160.9639642197

0.84640.00562500007.9722222-0.03795575000.9627555419

0.84640.00581406257.9722222-0.03923148490.9615281041

0.84640.00600625007.9722222-0.04052830640.9602819820

0.84640.00620156257.9722222-0.04184621440.9590172523

0.84640.00640000007.9722222-0.04318520890.9577339928

0.84640.00660156257.9722222-0.04454528990.9564322824

0.84640.00680625007.9722222-0.04592645750.9551122009

0.84640.00701406257.9722222-0.04732871160.9537738295

0.84640.00722500007.9722222-0.04875205220.9524172502

0.84640.00743906257.9722222-0.05019647940.9510425459

0.84640.00765625007.9722222-0.05166199310.9496498008

0.84640.00787656257.9722222-0.05314859330.9482391001

0.84640.00810000007.9722222-0.05465628000.9468105297

0.84640.00832656257.9722222-0.05618505330.9453641770

0.84640.00855625007.9722222-0.05773491310.9439001299

0.84640.00878906257.9722222-0.05930585940.9424184775

0.84640.00902500007.9722222-0.06089789220.9409193101

0.84640.00926406257.9722222-0.06251101160.9394027184

0.84640.00950625007.9722222-0.06414521750.9378687947

0.84640.00975156257.9722222-0.06580050990.9363176317

0.84640.01000000007.9722222-0.06747688890.9347493235

0.84640.01025156257.9722222-0.06917435440.9331639647

0.84640.01050625007.9722222-0.07089290640.9315616511

0.84640.01076406257.9722222-0.07263254490.9299424793

0.84640.01102500007.9722222-0.07439327000.9283065469

0.84640.01128906257.9722222-0.07617508160.9266539523

0.84640.01155625007.9722222-0.07797797970.9249847947

0.84640.01182656257.9722222-0.07980196440.9232991744

0.84640.01210000007.9722222-0.08164703560.9215971923

0.84640.01237656257.9722222-0.08351319330.9198789504

0.84640.01265625007.9722222-0.08540043750.9181445513

0.84640.01293906257.9722222-0.08730876830.9163940985

0.84640.01322500007.9722222-0.08923818560.9146276965

0.84640.01351406257.9722222-0.09118868940.9128454504

0.84640.01380625007.9722222-0.09316027970.9110474662

0.84640.01410156257.9722222-0.09515295660.9092338505

0.84640.01440000007.9722222-0.09716672000.9074047110

0.84640.01470156257.9722222-0.09920156990.9055601559

0.84640.01500625007.9722222-0.10125750640.9037002943

0.84640.01531406257.9722222-0.10333452940.9018252360

0.84640.01562500007.9722222-0.10543263890.8999350914

0.84640.01593906257.9722222-0.10755183490.8980299719

0.84640.01625625007.9722222-0.10969211750.8961099894

0.84640.01657656257.9722222-0.11185348660.8941752566

0.84640.01690000007.9722222-0.11403594220.8922258867

0.84640.01722656257.9722222-0.11623948440.8902619939

0.84640.01755625007.9722222-0.11846411310.8882836929

0.84640.01788906257.9722222-0.12070982830.8862910989

0.84640.01822500007.9722222-0.12297663000.8842843280

Tabla 3. Clculo del trmino D y EDE

((B)/(A))((B)/(A))^0.5*((B)/(A))*((B)/(A))^0.5erfc(*((B)/(A))*((B)/(A))^0.5)(()^(0.5) * H)/(C(B)*(Tm-T1))

0.00125000000.922.82351239100.00324703920.996336121456.3472178280

0.00250000000.922.82351239100.00649407850.992672320156.3472178280

0.00375000000.922.82351239100.00974111770.989008673356.3472178280

0.00500000000.922.82351239100.01298815700.985345258356.3472178280

0.00625000000.922.82351239100.01623519620.981682152256.3472178280

0.00750000000.922.82351239100.01948223550.978019432356.3472178280

0.00875000000.922.82351239100.02272927470.974357175856.3472178280

0.01000000000.922.82351239100.02597631400.970695459956.3472178280

0.01125000000.922.82351239100.02922335320.967034361556.3472178280

0.01250000000.922.82351239100.03247039250.963373957956.3472178280

0.01375000000.922.82351239100.03571743170.959714326156.3472178280

0.01500000000.922.82351239100.03896447100.956055543156.3472178280

0.01625000000.922.82351239100.04221151020.952397685756.3472178280

0.01750000000.922.82351239100.04545854950.948740830956.3472178280

0.01875000000.922.82351239100.04870558870.945085055556.3472178280

0.02000000000.922.82351239100.05195262800.941430436256.3472178280

0.02125000000.922.82351239100.05519966720.937777049756.3472178280

0.02250000000.922.82351239100.05844670650.934124972656.3472178280

0.02375000000.922.82351239100.06169374570.930474281456.3472178280

0.02500000000.922.82351239100.06494078500.926825052656.3472178280

0.02625000000.922.82351239100.06818782420.923177362456.3472178280

0.02750000000.922.82351239100.07143486350.919531287156.3472178280

0.02875000000.922.82351239100.07468190270.915886902956.3472178280

0.03000000000.922.82351239100.07792894200.912244285756.3472178280

0.03125000000.922.82351239100.08117598120.908603511456.3472178280

0.03250000000.922.82351239100.08442302050.904964656056.3472178280

0.03375000000.922.82351239100.08767005970.901327795056.3472178280

0.03500000000.922.82351239100.09091709900.897693004056.3472178280

0.03625000000.922.82351239100.09416413820.894060358456.3472178280

0.03750000000.922.82351239100.09741117750.890429933656.3472178280

0.03875000000.922.82351239100.10065821670.886801804656.3472178280

0.04000000000.922.82351239100.10390525600.883176046556.3472178280

0.04125000000.922.82351239100.10715229520.879552734156.3472178280

0.04250000000.922.82351239100.11039933450.875931942156.3472178280

0.04375000000.922.82351239100.11364637370.872313745156.3472178280

0.04500000000.922.82351239100.11689341300.868698217456.3472178280

0.04625000000.922.82351239100.12014045220.865085433256.3472178280

0.04750000000.922.82351239100.12338749150.861475466756.3472178280

0.04875000000.922.82351239100.12663453070.857868391656.3472178280

0.05000000000.922.82351239100.12988157000.854264281756.3472178280

0.05125000000.922.82351239100.13312860920.850663210456.3472178280

0.05250000000.922.82351239100.13637564850.847065251156.3472178280

0.05375000000.922.82351239100.13962268770.843470476856.3472178280

0.05500000000.922.82351239100.14286972700.839878960556.3472178280

0.05625000000.922.82351239100.14611676620.836290774956.3472178280

0.05750000000.922.82351239100.14936380550.832705992456.3472178280

0.05875000000.922.82351239100.15261084470.829124685456.3472178280

0.06000000000.922.82351239100.15585788400.825546926056.3472178280

0.06125000000.922.82351239100.15910492320.821972786056.3472178280

0.06250000000.922.82351239100.16235196250.818402337056.3472178280

0.06375000000.922.82351239100.16559900170.814835650556.3472178280

0.06500000000.922.82351239100.16884604100.811272797556.3472178280

0.06625000000.922.82351239100.17209308020.807713849156.3472178280

0.06750000000.922.82351239100.17534011950.804158875856.3472178280

0.06875000000.922.82351239100.17858715870.800607948256.3472178280

0.07000000000.922.82351239100.18183419800.797061136556.3472178280

0.07125000000.922.82351239100.18508123720.793518510456.3472178280

0.07250000000.922.82351239100.18832827650.789980139956.3472178280

0.07375000000.922.82351239100.19157531570.786446094156.3472178280

0.07500000000.922.82351239100.19482235500.782916442356.3472178280

0.07625000000.922.82351239100.19806939420.779391253456.3472178280

0.07750000000.922.82351239100.20131643350.775870596056.3472178280

0.07875000000.922.82351239100.20456347270.772354538356.3472178280

0.08000000000.922.82351239100.20781051200.768843148456.3472178280

0.08125000000.922.82351239100.21105755120.765336494156.3472178280

0.08250000000.922.82351239100.21430459050.761834642756.3472178280

0.08375000000.922.82351239100.21755162970.758337661656.3472178280

0.08500000000.922.82351239100.22079866900.754845617456.3472178280

0.08625000000.922.82351239100.22404570820.751358576956.3472178280

0.08750000000.922.82351239100.22729274750.747876606256.3472178280

0.08875000000.922.82351239100.23053978670.744399771256.3472178280

0.09000000000.922.82351239100.23378682600.740928137756.3472178280

0.09125000000.922.82351239100.23703386520.737461770956.3472178280

0.09250000000.922.82351239100.24028090450.734000735956.3472178280

0.09375000000.922.82351239100.24352794370.730545097256.3472178280

0.09500000000.922.82351239100.24677498300.727094919356.3472178280

0.09625000000.922.82351239100.25002202220.723650266156.3472178280

0.09750000000.922.82351239100.25326906150.720211201356.3472178280

0.09875000000.922.82351239100.25651610070.716777788256.3472178280

0.10000000000.922.82351239100.25976314000.713350089956.3472178280

0.10125000000.922.82351239100.26301017920.709928169056.3472178280

0.10250000000.922.82351239100.26625721850.706512087756.3472178280

0.10375000000.922.82351239100.26950425770.703101908056.3472178280

0.10500000000.922.82351239100.27275129700.699697691656.3472178280

0.10625000000.922.82351239100.27599833620.696299499556.3472178280

0.10750000000.922.82351239100.27924537550.692907392856.3472178280

0.10875000000.922.82351239100.28249241470.689521431956.3472178280

0.11000000000.922.82351239100.28573945400.686141676956.3472178280

0.11125000000.922.82351239100.28898649320.682768187656.3472178280

0.11250000000.922.82351239100.29223353250.679401023456.3472178280

0.11375000000.922.82351239100.29548057170.676040243356.3472178280

0.11500000000.922.82351239100.29872761100.672685905956.3472178280

0.11625000000.922.82351239100.30197465020.669338069556.3472178280

0.11750000000.922.82351239100.30522168950.665996791956.3472178280

0.11875000000.922.82351239100.30846872870.662662130556.3472178280

0.12000000000.922.82351239100.31171576800.659334142656.3472178280

0.12125000000.922.82351239100.31496280720.656012884656.3472178280

0.12250000000.922.82351239100.31820984650.652698413056.3472178280

0.12375000000.922.82351239100.32145688570.649390783656.3472178280

0.12500000000.922.82351239100.32470392500.646090051956.3472178280

0.12625000000.922.82351239100.32795096420.642796273056.3472178280

0.12750000000.922.82351239100.33119800350.639509501456.3472178280

0.12875000000.922.82351239100.33444504270.636229791556.3472178280

0.13000000000.922.82351239100.33769208200.632957197256.3472178280

0.13125000000.922.82351239100.34093912120.629691771756.3472178280

0.13250000000.922.82351239100.34418616050.626433568156.3472178280

0.13375000000.922.82351239100.34743319970.623182639156.3472178280

0.13500000000.922.82351239100.35068023900.619939036756.3472178280

=0.1175En la Tabla 4, se observa el cambio de signo en f()=0, lo que indica que el valor de se encuentra en el rando de 0.1175 y 0.11875. El valor de empleado para el clculo de los perfiles de temperatura es de 0.1175.Tabla 4. Supuesto y f()=0 SupuestoEvaluando la Funcin

0.001250000708.142752760

0.002500000353.580208724

0.003750000235.344840428

0.005000000176.191262802

0.006250000140.670398846

0.007500000116.965889574

0.008750000100.013581146

0.01000000087.281396651

0.01125000077.362626704

0.01250000069.413245680

0.01375000062.896146371

0.01500000057.453257313

0.01625000052.836682880

0.01750000048.869354776

0.01875000045.421422920

0.02000000042.395499759

0.02125000039.717112461

0.02250000037.328337717

0.02375000035.183446602

0.02500000033.245855982

0.02625000031.485950940

0.02750000029.879501097

0.02875000028.406490051

0.03000000027.050237474

0.03125000025.796731893

0.03250000024.634117448

0.03375000023.552294707

0.03500000022.542607016

0.03625000021.597591745

0.03750000020.710781284

0.03875000019.876542556

0.04000000019.089946621

0.04125000018.346661987

0.04250000017.642866755

0.04375000016.975175814

0.04500000016.340580179

0.04625000015.736396164

0.04750000015.160222576

0.04875000014.609904503

0.05000000014.083502525

0.05125000013.579266433

0.05250000013.095612712

0.05375000012.631105146

0.05500000012.184438092

0.05625000011.754421961

0.05750000011.339970612

0.05875000010.940090339

0.06000000010.553870251

0.06125000010.180473814

0.0625000009.819131419

0.0637500009.469133821

0.0650000009.129826332

0.0662500008.800603677

0.0675000008.480905417

0.0687500008.170211875

0.0700000007.868040493

0.0712500007.573942581

0.0725000007.287500391

0.0737500007.008324500

0.0750000006.736051449

0.0762500006.470341612

0.0775000006.210877275

0.0787500005.957360899

0.0800000005.709513542

0.0812500005.467073429

0.0825000005.229794651

0.0837500004.997445980

0.0850000004.769809794

0.0862500004.546681085

0.0875000004.327866563

0.0887500004.113183825

0.0900000003.902460608

0.0912500003.695534083

0.0925000003.492250230

0.0937500003.292463239

0.0950000003.096034978

0.0962500002.902834491

0.0975000002.712737540

0.0987500002.525626175

0.1000000002.341388348

0.1012500002.159917544

0.1025000001.981112444

0.1037500001.804876614

0.1050000001.631118213

0.1062500001.459749721

0.1075000001.290687691

0.1087500001.123852514

0.1100000000.959168200

0.1112500000.796562174

0.1125000000.635965089

0.1137500000.477310646

0.1150000000.320535431

0.1162500000.165578755

0.1175000000.012382516

0.118750000-0.139108942

0.120000000-0.288948957

0.121250000-0.437188665

0.122500000-0.583877114

0.123750000-0.729061369

0.125000000-0.872786614

0.126250000-1.015096241

0.127500000-1.156031939

0.128750000-1.295633779

0.130000000-1.433940288

0.131250000-1.570988528

0.132500000-1.706814157

0.133750000-1.841451504

0.135000000-1.974933623

En la Figura 1 se observa el corte en el eje x, correspondiente a la raz de la ecuacin ().

Figura 1:supuesttovs Funcin f()=0

En las ecuaciones 10 y xx , se obtuvieron los perfiles de temperatura para el slido y el lquido. Por regla de fases se puede asumir que la temperatura en la interfase es continua y por tanto Perfil de temperatura para el slido,

Perfil de temperatura para el lquido,

Como , es equivalente a decir que . Para ello se realiz una iteracin con un tamao de paso de de 0.0000025, hasta obtener un valor absoluto de la cercano a cero. Esta iteracin se realiz para valores de tiempo iguales a t=1, 5, 10 y 50 s. El valor de donde la diferencia es cercana a cero, representa la distancia a la cual se esta formando la interfase para cada tiempo. Este valor es importante de determinar porque nos indica el punto donde cambia la funcin de perfil de temperatura del slido al lquido, es decir que para valores de se debe usar la funcin de perfil de temperatura de la fase slida (), mientras que para valores de se usa la funcin de perfil de temperatura de la fase lquida.

En la tabla 5, se presenta el resumen para cada tiempo del valor de es decir donde se forma la interfase.Tabla 5. Datos para la iteracinFase Lquida (A)Fase Slida (B)

TM0.5

0.1175

K (J/(m s K)0.60282.219

(kg/m3)1000920

Cp (J/(Kg K))41872100

1.440E-071.148E-06

Tabla 6. Valor de para t=1 st=1 s

=*erf

0.000000000.000000000000.038985773200.038985773

0.000002500.004987305740.042408560330.037421255

5.00E-060.009974597910.045832118180.035857520

0.000007500.014961862920.049256372620.034294510

0.000010000.019949087210.052681249470.032732162

0.000012500.024936257190.056106674500.031170417

0.000015000.029923359300.059532573440.029609214

0.000017500.034910379950.062958872020.028048492

0.000020000.039897305580.066385495920.026488190

0.000022500.044884122610.069812370790.024928248

0.000025000.049870817470.073239422280.023368605

0.000027500.054857376580.076666576030.021809199

0.000030000.059843786380.080093757660.020249971

0.000032500.064830033310.083520892810.018690860

0.000035000.069816103780.086947907090.017131803

0.000037500.074801984240.090374726150.015572742

0.000040000.079787661120.093801275640.014013615

0.000042500.084773120860.097227481220.012454360

0.000045000.089758349890.100653268580.010894919

0.000047500.094743334670.104078563440.009335229

0.000050000.099728061630.107503291550.007775230

0.000052500.104712517210.110927378700.006214861

0.000055000.109696687870.114350750700.004654063

0.000057500.114680560040.117773333440.003092773

0.000060000.119664120200.121195052840.001530933

0.000062500.124647354780.12461583488-0.000031520

0.000065000.129630250260.12803560561-0.001594645

Tabla 7. Valor de para t=5 s=*erf

0.000000000.000000000000.038985773200.038985773

0.000002500.002230391740.040516390130.038285998

5.00E-060.004460782270.042047169400.037586387

0.000007500.006691170370.043578104380.036886934

0.000010000.008921554830.045109188440.036187634

0.000012500.011151934430.046640414950.035488481

0.000015000.013382307960.048171777270.034789469

0.000017500.015612674200.049703268780.034090595

0.000020000.017843031940.051234882830.033391851

0.000022500.020073379970.052766612790.032693233

0.000025000.022303717070.054298452020.031994735

0.000027500.024534042030.055830393870.031296352

0.000030000.026764353630.057362431700.030598078

0.000032500.028994650660.058894558870.029899908

0.000035000.031224931910.060426768740.029201837

0.000037500.033455196150.061959054650.028503858

0.000040000.035685442190.063491409970.027805968

0.000042500.037915668790.065023828030.027108159

0.000045000.040145874760.066556302210.026410427

0.000047500.042376058870.068088825830.025712767

0.000050000.044606219910.069621392260.025015172

0.000052500.046836356670.071153994840.024317638

0.000055000.049066467930.072686626930.023620159

0.000057500.051296552480.074219281870.022922729

0.000060000.053526609110.075751953000.022225344

0.000062500.055756636590.077284633680.021527997

0.000065000.057986633730.078817317260.020830684

0.000067500.060216599300.080349997070.020133398

0.000070000.062446532090.081882666480.019436134

0.000072500.064676430890.083415318830.018738888

0.000075000.066906294480.084947947460.018041653

0.000077500.069136121660.086480545730.017344424

0.000080000.071365911200.088013106980.016647196

0.000082500.073595661890.089545624560.015949963

0.000085000.075825372530.091078091820.015252719

0.000087500.078055041890.092610502120.014555460

0.000090000.080284668770.094142848800.013858180

0.000092500.082514251940.095675125220.013160873

0.000095000.084743790210.097207324730.012463535

0.000097500.086973282350.098739440680.011766158

0.000100000.089202727160.100271466430.011068739

0.000102500.091432123410.101803395340.010371272

0.000105000.093661469900.103335220760.009673751

0.000107500.095890765420.104866936050.008976171

0.000110000.098120008750.106398534570.008278526

0.000112500.100349198670.107930009680.007580811

0.000115000.102578333990.109461354750.006883021

0.000117500.104807413480.110992563150.006185150

0.000120000.107036435930.112523628230.005487192

0.000122500.109265400140.114054543370.004789143

0.000125000.111494304880.115585301950.004090997

0.000127500.113723148950.117115897320.003392748

0.000130000.115951931140.118646322870.002694392

0.000132500.118180650230.120176571970.001995922

0.000135000.120409305010.121706638000.001297333

0.000137500.122637894280.123236514350.000598620

0.000140000.124866416810.12476619440-0.000100222

0.000142500.127094871400.12629567154-0.000799200

Tabla 7. Valor de para t=10 s=*erf

0.000000000.000000000000.038985773200.038985773

0.000002500.001577125200.040068065710.038490941

5.00E-060.003154249970.041150440350.037996190

0.000007500.004731373870.042232894790.037501521

0.000010000.006308496500.043315426680.037006930

0.000012500.007885617400.044398033680.036512416

0.000015000.009462736160.045480713450.036017977

0.000017500.011039852340.046563463640.035523611

0.000020000.012616965520.047646281900.035029316

0.000022500.014194075260.048729165900.034535091

0.000025000.015771181140.049812113270.034040932

0.000027500.017348282720.050895121680.033546839

0.000030000.018925379590.051978188790.033052809

0.000032500.020502471300.053061312230.032558841

0.000035000.022079557430.054144489670.032064932

0.000037500.023656637550.055227718750.031571081

0.000040000.025233711230.056310997140.031077286

0.000042500.026810778040.057394322470.030583544

0.000045000.028387837550.058477692400.030089855

0.000047500.029964889340.059561104580.029596215

0.000050000.031541932970.060644556670.029102624

0.000052500.033118968020.061728046310.028609078

0.000055000.034695994040.062811571140.028115577

0.000057500.036273010630.063895128830.027622118

0.000060000.037850017340.064978717020.027128700

0.000062500.039427013750.066062333360.026635320

0.000065000.041003999430.067145975500.026141976

0.000067500.042580973940.068229641090.025648667

0.000070000.044157936870.069313327770.025155391

0.000072500.045734887770.070397033200.024662145

0.000075000.047311826230.071480755020.024168929

0.000077500.048888751810.072564490880.023675739

0.000080000.050465664080.073648238440.023182574

0.000082500.052042562620.074731995330.022689433

0.000085000.053619446990.075815759210.022196312

0.000087500.055196316770.076899527730.021703211

0.000090000.056773171520.077983298520.021210127

0.000092500.058350010820.079067069250.020717058

0.000095000.059926834240.080150837560.020224003

0.000097500.061503641350.081234601090.019730960

0.000100000.063080431720.082318357500.019237926

0.000102500.064657204920.083402104440.018744900

0.000105000.066233960520.084485839540.018251879

0.000107500.067810698090.085569560470.017758862

0.000110000.069387417210.086653264860.017265848

0.000112500.070964117450.087736950370.016772833

0.000115000.072540798370.088820614640.016279816

0.000117500.074117459550.089904255330.015786796

0.000120000.075694100550.090987870090.015293770

0.000122500.077270720960.092071456550.014800736

0.000125000.078847320330.093155012380.014307692

0.000127500.080423898250.094238535220.013814637

0.000130000.082000454280.095322022720.013321568

0.000132500.083576988000.096405472530.012828485

0.000135000.085153498970.097488882300.012335383

0.000137500.086729986760.098572249680.011842263

0.000140000.088306450960.099655572320.011349121

0.000142500.089882891120.100738847870.010855957

0.000145000.091459306820.101822073990.010362767

0.000147500.093035697640.102905248330.009869551

0.000150000.094612063130.103988368530.009376305

0.000152500.096188402880.105071432260.008883029

0.000155000.097764716460.106154437150.008389721

0.000157500.099341003430.107237380880.007896377

0.000160000.100917263370.108320261080.007402998

0.000162500.102493495850.109403075410.006909580

0.000165000.104069700430.110485821530.006416121

0.000167500.105645876710.111568497100.005922620

0.000170000.107222024230.112651099760.005429076

0.000172500.108798142580.113733627170.004935485

0.000175000.110374231330.114816076990.004441846

0.000177500.111950290040.115898446880.003948157

0.000180000.113526318300.116980734490.003454416

0.000182500.115102315660.118062937490.002960622

0.000185000.116678281710.119145053520.002466772

0.000187500.118254216010.120227080250.001972864

0.000190000.119830118140.121309015330.001478897

0.000192500.121405987670.122390856440.000984869

0.000195000.122981824170.123472601220.000490777

0.000197500.124557627200.12455424734-0.000003380

0.000200000.126133396360.12563579246-0.000497604

Tabla 8. Valor de para t=50 s=*erf

0.000000000.000000000000.038985773200.038985773

0.000002500.000705311860.039469778820.038764467

0.000005000.001410623670.039953801130.038543177

0.000007500.002115935410.040437839910.038321904

0.000010000.002821247040.040921894960.038100648

0.000012500.003526558510.041405966070.037879408

0.000015000.004231869790.041890053030.037658183

0.000017500.004937180840.042374155630.037436975

0.000020000.005642491620.042858273650.037215782

0.000022500.006347802090.043342406900.036994605

0.000025000.007053112220.043826555160.036773443

0.000027500.007758421960.044310718210.036552296

0.000030000.008463731290.044794895860.036331165

0.000032500.009169040150.045279087890.036110048

0.000035000.009874348510.045763294090.035888946

0.000037500.010579656330.046247514260.035667858

0.000040000.011284963580.046731748170.035446785

0.000042500.011990270210.047215995630.035225725

0.000045000.012695576190.047700256410.035004680

0.000047500.013400881480.048184530330.034783649

0.000050000.014106186040.048668817150.034562631

0.000052500.014811489840.049153116680.034341627

0.000055000.015516792820.049637428700.034120636

0.000057500.016222094960.050121753000.033899658

0.000060000.016927396220.050606089370.033678693

0.000062500.017632696560.051090437610.033457741

0.000065000.018337995930.051574797510.033236802

0.000067500.019043294310.052059168840.033015875

0.000070000.019748591650.052543551410.032794960

0.000072500.020453887920.053027945000.032574057

0.000075000.021159183070.053512349410.032353166

0.000077500.021864477070.053996764420.032132287

0.000080000.022569769880.054481189820.031911420

0.000082500.023275061460.054965625410.031690564

0.000085000.023980351770.055450070960.031469719

0.000087500.024685640780.055934526290.031248886

0.000090000.025390928450.056418991160.031028063

0.000092500.026096214730.056903465380.030807251

0.000095000.026801499590.057387948730.030586449

0.000097500.027506782990.057872441010.030365658

0.000100000.028212064900.058356941990.030144877

0.000102500.028917345270.058841451480.029924106

0.000105000.029622624060.059325969260.029703345

0.000107500.030327901250.059810495130.029482594

0.000110000.031033176780.060295028860.029261852

0.000112500.031738450620.060779570260.029041120

0.000115000.032443722730.061264119110.028820396

0.000117500.033148993080.061748675200.028599682

0.000120000.033854261620.062233238330.028378977

0.000122500.034559528320.062717808270.028158280

0.000125000.035264793140.063202384820.027937592

0.000127500.035970056040.063686967780.027716912

0.000130000.036675316980.064171556930.027496240

0.000132500.037380575930.064656152050.027275576

0.000135000.038085832830.065140752950.027054920

0.000137500.038791087670.065625359400.026834272

0.000140000.039496340390.066109971210.026613631

0.000142500.040201590970.066594588150.026392997

0.000145000.040906839350.067079210020.026172371

0.000147500.041612085510.067563836620.025951751

0.000150000.042317329400.068048467720.025731138

0.000152500.043022570990.068533103110.025510532

0.000155000.043727810240.069017742600.025289932

0.000157500.044433047110.069502385960.025069339

0.000160000.045138281550.069987032990.024848751

0.000162500.045843513540.070471683480.024628170

0.000165000.046548743040.070956337210.024407594

0.000167500.047253970000.071440993980.024187024

0.000170000.047959194390.071925653570.023966459

0.000172500.048664416170.072410315780.023745900

0.000175000.049369635290.072894980400.023525345

0.000177500.050074851730.073379647210.023304795

0.000180000.050780065450.073864316000.023084251

0.000182500.051485276400.074348986570.022863710

0.000185000.052190484550.074833658700.022643174

0.000187500.052895689850.075318332180.022422642

0.000190000.053600892280.075803006810.022202115

0.000192500.054306091790.076287682370.021981591

0.000195000.055011288340.076772358650.021761070

0.000197500.055716481900.077257035440.021540554

0.000200000.056421672430.077741712540.021320040

0.000202500.057126859880.078226389730.021099530

0.000205000.057832044230.078711066790.020879023

0.000207500.058537225420.079195743530.020658518

0.000210000.059242403430.079680419730.020438016

0.000212500.059947578220.080165095170.020217517

0.000215000.060652749740.080649769660.019997020

0.000217500.061357917960.081134442970.019776525

0.000220000.062063082840.081619114910.019556032

0.000222500.062768244340.082103785250.019335541

0.000225000.063473402420.082588453790.019115051

0.000227500.064178557050.083073120310.018894563

0.000230000.064883708190.083557784620.018674076

0.000232500.065588855790.084042446490.018453591

0.000235000.066293999830.084527105720.018233106

0.000237500.066999140250.085011762090.018012622

0.000240000.067704277030.085496415400.017792138

0.000242500.068409410120.085981065430.017571655

0.000245000.069114539490.086465711980.017351172

0.000247500.069819665100.086950354840.017130690

0.000250000.070524786910.087434993780.016910207

0.000252500.071229904870.087919628620.016689724

0.000255000.071935018960.088404259120.016469240

0.000257500.072640129140.088888885090.016248756

0.000260000.073345235360.089373506320.016028271

0.000262500.074050337590.089858122580.015807785

0.000265000.074755435790.090342733680.015587298

0.000267500.075460529920.090827339400.015366809

0.000270000.076165619940.091311939540.015146320

0.000272500.076870705810.091796533870.014925828

0.000275000.077575787500.092281122200.014705335

0.000277500.078280864970.092765704310.014484839

0.000280000.078985938180.093250279990.014264342

0.000282500.079691007090.093734849030.014043842

0.000285000.080396071660.094219411220.013823340

0.000287500.081101131860.094703966350.013602834

0.000290000.081806187640.095188514210.013382327

0.000292500.082511238970.095673054590.013161816

0.000295000.083216285810.096157587280.012941301

0.000297500.083921328110.096642112070.012720784

0.000300000.084626365850.097126628750.012500263

0.000302500.085331398990.097611137110.012279738

0.000305000.086036427480.098095636940.012059209

0.000307500.086741451290.098580128030.011838677

0.000310000.087446470370.099064610170.011618140

0.000312500.088151484700.099549083140.011397598

0.000315000.088856494230.100033546750.011177053

0.000317500.089561498920.100518000770.010956502

0.000320000.090266498740.101002445000.010735946

0.000322500.090971493640.101486879230.010515386

0.000325000.091676483600.101971303250.010294820

0.000327500.092381468560.102455716850.010074248

0.000330000.093086448500.102940119810.009853671

0.000332500.093791423370.103424511940.009633089

0.000335000.094496393130.103908893010.009412500

0.000337500.095201357760.104393262820.009191905

0.000340000.095906317200.104877621160.008971304

0.000342500.096611271420.105361967820.008750696

0.000345000.097316220380.105846302590.008530082

0.000347500.098021164050.106330625250.008309461

0.000350000.098726102380.106814935610.008088833

0.000352500.099431035340.107299233440.007868198

0.000355000.100135962890.107783518540.007647556

0.000357500.100840884990.108267790700.007426906

0.000360000.101545801600.108752049710.007206248

0.000362500.102250712690.109236295360.006985583

0.000365000.102955618210.109720527440.006764909

0.000367500.103660518120.110204745740.006544228

0.000370000.104365412400.110688950050.006323538

0.000372500.105070301000.111173140160.006102839

0.000375000.105775183870.111657315860.005882132

0.000377500.106480061000.112141476950.005661416

0.000380000.107184932320.112625623200.005440691

0.000382500.107889797820.113109754410.005219957

0.000385000.108594657440.113593870380.004999213

0.000387500.109299511150.114077970890.004778460

0.000390000.110004358920.114562055730.004557697

0.000392500.110709200700.115046124700.004336924

0.000395000.111414036450.115530177580.004116141

0.000397500.112118866140.116014214160.003895348

0.000400000.112823689730.116498234240.003674545

0.000402500.113528507180.116982237600.003453730

0.000405000.114233318460.117466224040.003232906

0.000407500.114938123510.117950193340.003012070

0.000410000.115642922310.118434145300.002791223

0.000412500.116347714820.118918079710.002570365

0.000415000.117052501000.119401996350.002349495

0.000417500.117757280810.119885895030.002128614

0.000420000.118462054210.120369775520.001907721

0.000422500.119166821170.120853637620.001686816

0.000425000.119871581640.121337481120.001465899

0.000427500.120576335580.121821305820.001244970

0.000430000.121281082970.122305111490.001024029

0.000432500.121985823760.122788897940.000803074

0.000435000.122690557910.123272664950.000582107

0.000437500.123395285380.123756412320.000361127

0.000440000.124100006140.124240139830.000140134

0.000442500.124804720150.12472384728-0.000080873

0.000445000.125509427370.12520753445-0.000301893

Tabla 9. Datos de Y(B)=h, para los tiempos t=1, 5, 10 y 50 s.tY(B)=hT(B)T(A)T(A) - T(B)

10.0000625000.1246473550.124615835-0.000031520

50.0001400000.1248664170.124766194-0.000100222

100.0001975000.1245576270.124554247-0.000003380

500.0004425000.1248047200.124723847-0.000080873

Con los h obtenidos se realiz la evaluacin de la funcin T(B)*(Y(B ) entre ([0,Y(B)=h] )yT(A)*(Y(B )=([Y(B)=[h,T(A)* ]).Tabla 10. Perfiles de temperatura, para los tiempos t=1, 5, 10 y 50 s.t=1t=5t=10t=50

Y(B)T*Y(B)T*Y(B)T*Y(B)T*

0.000000000.000000000000.000000000.000000000000.000000000.000000000000.000000000.00000000000

0.000002500.004987305740.000002500.002230391740.00000250000.001577125200.00000250000.00070531186

5.00E-060.009974597915.00E-060.004460782270.00000500000.003154249970.00000500000.00141062367

0.000007500.014961862920.000007500.006691170370.00000750000.004731373870.00000750000.00211593541

0.000010000.019949087210.000010000.008921554830.00001000000.006308496500.00001000000.00282124704

0.000012500.024936257190.000012500.011151934430.00001250000.007885617400.00001250000.00352655851

0.000015000.029923359300.000015000.013382307960.00001500000.009462736160.00001500000.00423186979

0.000017500.034910379950.000017500.015612674200.00001750000.011039852340.00001750000.00493718084

0.000020000.039897305580.000020000.017843031940.00002000000.012616965520.00002000000.00564249162

0.000022500.044884122610.000022500.020073379970.00002250000.014194075260.00002250000.00634780209

0.000025000.049870817470.000025000.022303717070.00002500000.015771181140.00002500000.00705311222

0.000027500.054857376580.000027500.024534042030.00002750000.017348282720.00002750000.00775842196

0.000030000.059843786380.000030000.026764353630.00003000000.018925379590.00003000000.00846373129

0.000032500.064830033310.000032500.028994650660.00003250000.020502471300.00003250000.00916904015

0.000035000.069816103780.000035000.031224931910.00003500000.022079557430.00003500000.00987434851

0.000037500.074801984240.000037500.033455196150.00003750000.023656637550.00003750000.01057965633

0.000040000.079787661120.000040000.035685442190.00004000000.025233711230.00004000000.01128496358

0.000042500.084773120860.000042500.037915668790.00004250000.026810778040.00004250000.01199027021

0.000045000.089758349890.000045000.040145874760.00004500000.028387837550.00004500000.01269557619

0.000047500.094743334670.000047500.042376058870.00004750000.029964889340.00004750000.01340088148

0.000050000.099728061630.000050000.044606219910.00005000000.031541932970.00005000000.01410618604

0.000052500.104712517210.000052500.046836356670.00005250000.033118968020.00005250000.01481148984

0.000055000.109696687870.000055000.049066467930.00005500000.034695994040.00005500000.01551679282

0.000057500.114680560040.000057500.051296552480.00005750000.036273010630.00005750000.01622209496

0.000060000.119664120200.000060000.053526609110.00006000000.037850017340.00006000000.01692739622

0.000062500.124647354780.000062500.055756636590.00006250000.039427013750.00006250000.01763269656

0.000087500.158755866230.000065000.057986633730.00006500000.041003999430.00006500000.01833799593

0.000112500.192721342100.000067500.060216599300.00006750000.042580973940.00006750000.01904329431

0.000137500.226439914800.000070000.062446532090.00007000000.044157936870.00007000000.01974859165

0.000162500.259840828920.000072500.064676430890.00007250000.045734887770.00007250000.02045388792

0.000187500.292855366150.000075000.066906294480.00007500000.047311826230.00007500000.02115918307

0.000212500.325417268260.000077500.069136121660.00007750000.048888751810.00007750000.02186447707

0.000237500.357463134070.000080000.071365911200.00008000000.050465664080.00008000000.02256976988

0.000262500.388932786360.000082500.073595661890.00008250000.052042562620.00008250000.02327506146

0.000287500.419769605230.000085000.075825372530.00008500000.053619446990.00008500000.02398035177

0.000312500.449920825020.000087500.078055041890.00008750000.055196316770.00008750000.02468564078

0.000337500.479337792090.000090000.080284668770.00009000000.056773171520.00009000000.02539092845

0.000362500.507976181690.000092500.082514251940.00009250000.058350010820.00009250000.02609621473

0.000387500.535796172560.000095000.084743790210.00009500000.059926834240.00009500000.02680149959

0.000412500.562762578250.000097500.086973282350.00009750000.061503641350.00009750000.02750678299

0.000437500.588844935320.000100000.089202727160.00010000000.063080431720.00010000000.02821206490

0.000462500.614017548320.000102500.091432123410.00010250000.064657204920.00010250000.02891734527

0.000487500.638259492860.000105000.093661469900.00010500000.066233960520.00010500000.02962262406

0.000512500.661554577820.000107500.095890765420.00010750000.067810698090.00010750000.03032790125

0.000537500.683891268750.000110000.098120008750.00011000000.069387417210.00011000000.03103317678

0.000562500.705262574740.000112500.100349198670.00011250000.070964117450.00011250000.03173845062

0.000587500.725665901310.000115000.102578333990.00011500000.072540798370.00011500000.03244372273

0.000612500.745102872480.000117500.104807413480.00011750000.074117459550.00011750000.03314899308

0.000637500.763579125080.000120000.107036435930.00012000000.075694100550.00012000000.03385426162

0.000662500.781104078920.000122500.109265400140.00012250000.077270720960.00012250000.03455952832

0.000687500.797690686330.000125000.111494304880.00012500000.078847320330.00012500000.03526479314

0.000712500.813355164770.000127500.113723148950.00012750000.080423898250.00012750000.03597005604

0.000737500.828116716210.000130000.115951931140.00013000000.082000454280.00013000000.03667531698

0.000762500.841997236970.000132500.118180650230.00013250000.083576988000.00013250000.03738057593

0.000787500.855021021640.000135000.120409305010.00013500000.085153498970.00013500000.03808583283

0.000812500.867214464430.000137500.122637894280.00013750000.086729986760.00013750000.03879108767

0.000837500.878605761410.000140000.124866416810.00014000000.088306450960.00014000000.03949634039

0.000862500.889224616500.000165000.140050744830.00014250000.089882891120.00014250000.04020159097

0.000887500.899101954270.000190000.155308409470.00014500000.091459306820.00014500000.04090683935

0.000912500.908269641900.000215000.170532626700.00014750000.093035697640.00014750000.04161208551

0.000937500.916760222730.000240000.185716878260.00015000000.094612063130.00015000000.04231732940

0.000962500.924606663220.000265000.200854697630.00015250000.096188402880.00015250000.04302257099

0.000987500.931842115120.000290000.215939678340.00015500000.097764716460.00015500000.04372781024

0.001012500.938499694090.000315000.230965482000.00015750000.099341003430.00015750000.04443304711

0.001037500.944612275890.000340000.245925846380.00016000000.100917263370.00016000000.04513828155

0.001062500.950212310770.000365000.260814593180.00016250000.102493495850.00016250000.04584351354

0.001087500.955331656640.000390000.275625635670.00016500000.104069700430.00016500000.04654874304

0.001112500.960001431060.000415000.290352986160.00016750000.105645876710.00016750000.04725397000

0.001137500.964251882160.000440000.304990763220.00017000000.107222024230.00017000000.04795919439

0.001162500.968112277970.000465000.319533198670.00017250000.108798142580.00017250000.04866441617

0.001187500.971610813910.000490000.333974644380.00017500000.110374231330.00017500000.04936963529

0.001212500.974774537510.000515000.348309578810.00017750000.111950290040.00017750000.05007485173

0.001237500.977629289730.000540000.362532613190.00018000000.113526318300.00018000000.05078006545

0.001262500.980199661810.000565000.376638497590.00018250000.115102315660.00018250000.05148527640

0.001287500.982508966640.000590000.390622126540.00018500000.116678281710.00018500000.05219048455

0.001312500.984579223450.000615000.404478544470.00018750000.118254216010.00018750000.05289568985

0.001337500.986431154740.000640000.418202950780.00019000000.119830118140.00019000000.05360089228

0.001362500.988084194170.000665000.431790704640.00019250000.121405987670.00019250000.05430609179

0.001387500.989556504100.000690000.445237329410.00019500000.122981824170.00019500000.05501128834

0.001412500.990865001810.000715000.458538516810.00019750000.124557627200.00019750000.05571648190

0.001437500.992025392880.000740000.471690130670.00022250000.135364768150.00020000000.05642167243

0.001462500.993052210900.000765000.484688210410.00024750000.146162855490.00020250000.05712685988

0.001487500.993958862180.000790000.497528974160.00027250000.156946183310.00020500000.05783204423

0.001512500.994757674510.000815000.510208821530.00029750000.167712435140.00020750000.05853722542

0.001537500.995459949080.000840000.522724335990.00032250000.178459305600.00021000000.05924240343

0.001562500.996076014470.000865000.535072287010.00034750000.189184501850.00021250000.05994757822

0.001587500.996615282120.000890000.547249631750.00037250000.199885745070.00021500000.06065274974

0.001612500.997086302410.000915000.559253516420.00039750000.210560771920.00021750000.06135791796

0.001637500.997496820740.000940000.571081277390.00042250000.221207335970.00022000000.06206308284

0.001662500.997853833050.000965000.582730441790.00044750000.231823209100.00022250000.06276824434

0.001687500.998163640260.000990000.594198727950.00047250000.242406182930.00022500000.06347340242

0.001712500.998431901250.001015000.605484045350.00049750000.252954070170.00022750000.06417855705

0.001737500.998663684060.001040000.616584494370.00052250000.263464705980.00023000000.06488370819

0.001762500.998863514960.001065000.627498365620.00054750000.273935949320.00023250000.06558885579

0.001787500.999035425180.001090000.638224138990.00057250000.284365684220.00023500000.06629399983

0.001812500.999182995320.001115000.648760482410.00059750000.294751821080.00023750000.06699914025

0.001837500.999309397030.001140000.659106250270.00062250000.305092297910.00024000000.06770427703

0.001862500.999417432190.001165000.669260481590.00064750000.315385081580.00024250000.06840941012

0.001887500.999509569380.001190000.679222397850.00067250000.325628168960.00024500000.06911453949

0.001912500.999587977770.001215000.688991400590.00069750000.335819588120.00024750000.06981966510

0.001937500.999654558370.001240000.698567068760.00072250000.345957399440.00025000000.07052478691

0.001962500.999710972860.001265000.707949155730.00074750000.356039696710.00025250000.07122990487

0.001987500.999758669890.001290000.717137586180.00077250000.366064608170.00025500000.07193501896

0.002012500.999798909110.001315000.726132452660.00079750000.376030297560.00025750000.07264012914

0.002037500.999832783040.001340000.734934011990.00082250000.385934965100.00026000000.07334523536

0.002062500.999861236770.001365000.743542681420.00084750000.395776848400.00026250000.07405033759

0.002087500.999885085800.001390000.751959034630.00087250000.405554223440.00026500000.07475543579

0.002112500.999905031980.001415000.760183797500.00089750000.415265405380.00026750000.07546052992

0.002137500.999921677840.001440000.768217843780.00092250000.424908749420.00027000000.07616561994

0.002162500.999935539370.001465000.776062190550.00094750000.434482651590.00027250000.07687070581

0.002187500.999947057260.001490000.783717993540.00097250000.443985549480.00027500000.07757578750

0.002212500.999956607030.001515000.791186542380.00099750000.453415923000.00027750000.07828086497

0.002237500.999964507820.001540000.798469255670.00102250000.462772294990.00028000000.07898593818

0.002262500.999971030190.001565000.805567675980.00104750000.472053231870.00028250000.07969100709

0.002287500.999976402960.001590000.812483464760.00107250000.481257344240.00028500000.08039607166

0.002312500.999980819170.001615000.819218397150.00109750000.490383287380.00028750000.08110113186

0.002337500.999984441240.001640000.825774356790.00112250000.499429761800.00029000000.08180618764

0.002362500.999987405550.001665000.832153330520.00114750000.508395513630.00029250000.08251123897

0.002387500.999989826280.001690000.838357403060.00117250000.517279335080.00029500000.08321628581

0.002412500.999991798840.001715000.844388751660.00119750000.526080064790.00029750000.08392132811

0.002437500.999993402700.001740000.850249640780.00122250000.534796588160.00030000000.08462636585

0.002462500.999994703960.001765000.855942416730.00124750000.543427837610.00030250000.08533139899

0.002487500.999995757420.001790000.861469502300.00127250000.551972792840.00030500000.08603642748

0.002512500.999996608420.001815000.866833391470.00129750000.560430480990.00030750000.08674145129

0.002537500.999997294390.001840000.872036644130.00132250000.568799976850.00031000000.08744647037

0.002562500.999997846120.001865000.877081880800.00134750000.577080402900.00031250000.08815148470

0.002587500.999998288920.001890000.881971777510.00137250000.585270929430.00031500000.08885649423

0.002612500.999998643540.001915000.886709060580.00139750000.593370774530.00031750000.08956149892

0.002637500.999998926910.001940000.891296501660.00142250000.601379204070.00032000000.09026649874

0.002662500.999999152860.001965000.895736912680.00144750000.609295531670.00032250000.09097149364

0.002687500.999999332640.001990000.900033141030.00147250000.617119118590.00032500000.09167648360

0.002712500.999999475360.002015000.904188064730.00149750000.624849373560.00032750000.09238146856

0.002737500.999999588430.002040000.908204587730.00152250000.632485752650.00033000000.09308644850

0.002762500.999999677810.002065000.912085635380.00154750000.640027759000.00033250000.09379142337

0.002787500.999999748300.002090000.915834149960.00157250000.647474942630.00033500000.09449639313

0.002812500.999999803790.002115000.919453086290.00159750000.654826900080.00033750000.09520135776

0.002837500.999999847360.002140000.922945407590.00162250000.662083274110.00034000000.09590631720

0.002862500.999999881510.002165000.926314081360.00164750000.669243753350.00034250000.09661127142

0.002887500.999999908210.002190000.929562075420.00167250000.676308071880.00034500000.09731622038

0.002912500.999999929050.002215000.932692354140.00169750000.683276008810.00034750000.09802116405

0.002937500.999999945270.002240000.935707874760.00172250000.690147387780.00035000000.09872610238

0.002962500.999999957870.002265000.938611583870.00174750000.696922076520.00035250000.09943103534

0.002987500.999999967640.002290000.941406414050.00177250000.703599986260.00035500000.10013596289

0.003012500.999999975190.002315000.944095280610.00179750000.710181071210.00035750000.10084088499

0.003037500.999999981020.002340000.946681078560.00182250000.716665327970.00036000000.10154580160

0.003062500.999999985520.002365000.949166679690.00184750000.723052794870.00036250000.10225071269

0.003087500.999999988970.002390000.951554929740.00187250000.729343551400.00036500000.10295561821

0.003112500.999999991610.002415000.953848645860.00189750000.735537717450.00036750000.10366051812

0.003137500.999999993640.002440000.956050614080.00192250000.741635452710.00037000000.10436541240

0.003162500.999999995190.002465000.958163587050.00194750000.747636955880.00037250000.10507030100

0.003187500.999999996360.002490000.960190281800.00197250000.753542463970.00037500000.10577518387

0.003212500.999999997260.002515000.962133377800.00199750000.759352251510.00037750000.10648006100

0.003237500.999999997940.002540000.963995515040.00202250000.765066629800.00038000000.10718493232

0.003262500.999999998450.002565000.965779292280.00204750000.770685946080.00038250000.10788979782

0.003287500.999999998840.002590000.967487265540.00207250000.776210582740.00038500000.10859465744

0.003312500.999999999130.002615000.969121946580.00209750000.781640956450.00038750000.10929951115

0.003337500.999999999350.002640000.970685801610.00212250000.786977517350.00039000000.11000435892

0.003362500.999999999520.002665000.972181250160.00214750000.792220748140.00039250000.11070920070

0.003387500.999999999640.002690000.973610663940.00217250000.797371163250.00039500000.11141403645

0.003412500.999999999740.002715000.974976366000.00219750000.802429307910.00039750000.11211886614

0.003437500.999999999800.002740000.976280629920.00222250000.807395757280.00040000000.11282368973

0.003462500.999999999860.002765000.977525679090.00224750000.812271115520.00040250000.11352850718

0.003487500.999999999890.002790000.978713686200.00227250000.817056014860.00040500000.11423331846

0.003512500.999999999920.002815000.979846772740.00229750000.821751114730.00040750000.11493812351

0.003537500.999999999940.002840000.980927008730.00232250000.826357100750.00041000000.11564292231

0.003562500.999999999960.002865000.981956412390.00234750000.830874683850.00041250000.11634771482

0.003587500.999999999970.002890000.982936950070.00237250000.835304599330.00041500000.11705250100

0.003612500.999999999980.002915000.983870536160.00239750000.839647605860.00041750000.11775728081

0.003637500.999999999980.002940000.984759033180.00242250000.843904484600.00042000000.11846205421

0.003662500.999999999990.002965000.985604251870.00244750000.848076038210.00042250000.11916682117

0.003687500.999999999990.002990000.986407951390.00247250000.852163089920.00042500000.11987158164

0.003712500.999999999990.003015000.987171839660.00249750000.856166482610.00042750000.12057633558

0.003737501.000000000000.003040000.987897573690.00252250000.860087077800.00043000000.12128108297

0.003762501.000000000000.003065000.988586760000.00254750000.863925754770.00043250000.12198582376

0.003787501.000000000000.003090000.989240955130.00257250000.867683409630.00043500000.12269055791

0.003812501.000000000000.003115000.989861666200.00259750000.871360954330.00043750000.12339528538

0.003837501.000000000000.003140000.990450351470.00262250000.874959315790.00044000000.12410000614

0.003862501.000000000000.003165000.991008421080.00264750000.878479434960.00044250000.12480472015

0.003887501.000000000000.003190000.991537237690.00267250000.881922265940.00046750000.12955977224

0.003912501.000000000000.003215000.992038117240.00269750000.885288775010.00049250000.13439346096

0.003937501.000000000000.003240000.992512329780.00272250000.888579939820.00051750000.13922470478

0.003962501.000000000000.003265000.992961100260.00274750000.891796748460.00054250000.14405329537

0.003987501.000000000000.003290000.993385609380.00277250000.894940198600.00056750000.14887902471

0.004012501.000000000000.003315000.993786994530.00279750000.898011296630.00059250000.15370168519

0.004037501.000000000000.003340000.994166350630.00282250000.901011056810.00061750000.15852106959

0.004062501.000000000000.003365000.994524731120.00284750000.903940500450.00064250000.16333697109

0.004087501.000000000000.003390000.994863148890.00287250000.906800655060.00066750000.16814918335

0.004112501.000000000000.003415000.995182577240.00289750000.909592553580.00069250000.17295750050

0.004137501.000000000000.003440000.995483950890.00292250000.912317233560.00071750000.17776171716

0.004162501.000000000000.003465000.995768166950.00294750000.914975736390.00074250000.18256162851

0.004187501.000000000000.003490000.996036085920.00297250000.917569106530.00076750000.18735703027

0.004212501.000000000000.003515000.996288532680.00299750000.920098390780.00079250000.19214771873

0.004237501.000000000000.003540000.996526297540.00302250000.922564637530.00081750000.19693349082

0.004262501.000000000000.003565000.996750137210.00304750000.924968896070.00084250000.20171414407

0.004287501.000000000000.003590000.996960775790.00307250000.927312215860.00086750000.20648947670

0.004312501.000000000000.003615000.997158905830.00309750000.929595645900.00089250000.21125928760

0.004337501.000000000000.003640000.997345189260.00312250000.931820234010.00091750000.21602337638

0.004362501.000000000000.003665000.997520258420.00314750000.933987026230.00094250000.22078154338

0.004387501.000000000000.003690000.997684717020.00317250000.936097066180.00096750000.22553358971

0.004412501.000000000000.003715000.997839141100.00319750000.938151394440.00099250000.23027931726

0.004437501.000000000000.003740000.997984080000.00322250000.940151047990.00101750000.23501852873

0.004462501.000000000000.003765000.998120057310.00324750000.942097059610.00104250000.23975102766

0.004487501.000000000000.003790000.998247571760.00327250000.943990457340.00106750000.24447661845

0.004512501.000000000000.003815000.998367098170.00329750000.945832263970.00109250000.24919510639

0.004537501.000000000000.003840000.998479088340.00332250000.947623496490.00111750000.25390629767

0.004562501.000000000000.003865000.998583971890.00334750000.949365165600.00114250000.25860999941

0.004587501.000000000000.003890000.998682157170.00337250000.951058275270.00116750000.26330601971

0.004612501.000000000000.003915000.998774032090.00339750000.952703822240.00119250000.26799416761

0.004637501.000000000000.003940000.998859964890.00342250000.954302795610.00121750000.27267425319

0.004662501.000000000000.003965000.998940305020.00344750000.955856176400.00124250000.27734608753

0.004687501.000000000000.003990000.999015383860.00347250000.957364937190.00126750000.28200948278

0.004712501.000000000000.004015000.999085515520.00349750000.958830041660.00129250000.28666425215

0.004737501.000000000000.004040000.999150997570.00352250000.960252444330.00131750000.29131020994

0.004762501.000000000000.004065000.999212111730.00354750000.961633090120.00134250000.29594717156

0.004787501.000000000000.004090000.999269124600.00357250000.962972914090.00136750000.30057495359

0.004812501.000000000000.004115000.999322288340.00359750000.964272841100.00139250000.30519337373

0.004837501.000000000000.004140000.999371841310.00362250000.965533785530.00141750000.30980225087

0.004862501.000000000000.004165000.999418008700.00364750000.966756650980.00144250000.31440140513

0.004887501.000000000000.004190000.999461003150.00367250000.967942330070.00146750000.31899065782

0.004912501.000000000000.004215000.999501025370.00369750000.969091704150.00149250000.32356983151

0.004937501.000000000000.004240000.999538264650.00372250000.970205643110.00151750000.32813875002

0.004962501.000000000000.004265000.999572899470.00374750000.971285005150.00154250000.33269723847

0.004987501.000000000000.004290000.999605098010.00377250000.972330636600.00156750000.33724512327

0.005012501.000000000000.004315000.999635018650.00379750000.973343371770.00159250000.34178223217

0.005037501.000000000000.004340000.999662810470.00382250000.974324032760.00161750000.34630839423

0.005062501.000000000000.004365000.999688613750.00384750000.975273429340.00164250000.35082343991

0.005087501.000000000000.004390000.999712560360.00387250000.976192358800.00166750000.35532720103

0.005112501.000000000000.004415000.999734774250.00389750000.977081605880.00169250000.35981951081

0.005137501.000000000000.004440000.999755371870.00392250000.977941942620.00171750000.36430020388

0.005162501.000000000000.004465000.999774462530.00394750000.978774128310.00174250000.36876911633

0.005187501.000000000000.004490000.999792148790.00397250000.979578909420.00176750000.37322608567

0.005212501.000000000000.004515000.999808526870.00399750000.980357019540.00179250000.37767095090

0.005237501.000000000000.004540000.999823686940.00402250000.981109179300.00181750000.38210355251

0.005262501.000000000000.004565000.999837713490.00404750000.981836096400.00184250000.38652373247

0.005287501.000000000000.004590000.999850685650.00407250000.982538465560.00186750000.39093133429

0.005312501.000000000000.004615000.999862677470.00409750000.983216968500.00189250000.39532620302

0.005337501.000000000000.004640000.999873758230.00412250000.983872273960.00191750000.39970818523

0.005362501.000000000000.004665000.999883992700.00414750000.984505037710.00194250000.40407712909

0.005387501.000000000000.004690000.999893441410.00417250000.985115902590.00196750000.40843288435

0.005412501.000000000000.004715000.999902160910.00419750000.985705498500.00199250000.41277530232

0.005437501.000000000000.004740000.999910203990.00422250000.986274442520.00201750000.41710423597

0.005462501.000000000000.004765000.999917619890.00424750000.986823338890.00204250000.42141953987

0.005487501.000000000000.004790000.999924454550.00427250000.987352779110.00206750000.42572107022

0.005512501.000000000000.004815000.999930750810.00429750000.987863342020.00209250000.43000868489

0.005537501.000000000000.004840000.999936548540.00432250000.988355593860.00211750000.43428224341

0.005562501.000000000000.004865000.999941884920.00434750000.988830088360.00214250000.43854160700

0.005587501.000000000000.004890000.999946794520.00437250000.989287366850.00216750000.44278663855

0.005612501.000000000000.004915000.999951309510.00439750000.989727958350.00219250000.44701720266

0.005637501.000000000000.004940000.999955459810.00442250000.990152379690.00221750000.45123316565

0.005662501.000000000000.004965000.999959273220.00444750000.990561135620.00224250000.45543439557

0.005687501.000000000000.004990000.999962775570.00447250000.990954718930.00226750000.45962076220

0.005712501.000000000000.005015000.999965990830.00449750000.991333610570.00229250000.46379213707

0.005737501.000000000000.005040000.999968941250.00452250000.991698279830.00231750000.46794839348

0.005762501.000000000000.005065000.999971647480.00454750000.992049184390.00234250000.47208940647

0.005787501.000000000000.005090000.999974128650.00457250000.992386770540.00236750000.47621505290

0.005812501.000000000000.005115000.999976402480.00459750000.992711473320.00239250000.48032521139

0.005837501.000000000000.005140000.999978485410.00462250000.993023716630.00241750000.48441976236

0.005862501.000000000000.005165000.999980392630.00464750000.993323913400.00244250000.48849858804

0.005887501.000000000000.005190000.999982138200.00467250000.993612465770.00246750000.49256157248

0.005912501.000000000000.005215000.999983735130.00469750000.993889765250.00249250000.49660860155

0.005937501.000000000000.005240000.999985195440.00472250000.994156192830.00251750000.50063956294

0.005962501.000000000000.005265000.999986530250.00474750000.994412119230.00254250000.50465434620

0.005987501.000000000000.005290000.999987749810.00477250000.994657905000.00256750000.50865284270

0.006012501.000000000000.005315000.999988863590.00479750000.994893900720.00259250000.51263494568

0.006037501.000000000000.005340000.999989880320.00482250000.995120447190.00261750000.51660055022

0.006062501.000000000000.005365000.999990808050.00484750000.995337875560.00264250000.52054955329

0.006087501.000000000000.005390000.999991654210.00487250000.995546507540.00266750000.52448185371

0.006112501.000000000000.005415000.999992425630.00489750000.995746655560.00269250000.52839735217

0.006137501.000000000000.005440000.999993128620.00492250000.995938622950.00271750000.53229595125

0.006162501.000000000000.005465000.999993768960.00494750000.996122704130.00274250000.53617755542

0.006187501.000000000000.005490000.999994351980.00497250000.996299184780.00276750000.54004207103

0.006212501.000000000000.005515000.999994882590.00499750000.996468341980.00279250000.54388940632

0.006237501.000000000000.005540000.999995365280.00502250000.996630444480.00281750000.54771947143

0.006262501.000000000000.005565000.999995804200.00504750000.996785752770.00284250000.55153217840

0.006287501.000000000000.005590000.999996203140.00507250000.996934519340.00286750000.55532744117

0.006312501.000000000000.005615000.999996565580.00509750000.997076988800.00289250000.55910517558

0.006337501.000000000000.005640000.999996894720.00512250000.997213398100.00291750000.56286529939

0.006362501.000000000000.005665000.999997193490.00514750000.997343976690.00294250000.56660773225

0.006387501.000000000000.005690000.999997464580.00517250000.997468946650.00296750000.57033239574

0.006412501.000000000000.005715000.999997710440.00519750000.997588522960.00299250000.57403921334

0.006437501.000000000000.005740000.999997933320.00522250000.997702913560.00301750000.57772811044

0.006462501.000000000000.005765000.999998135280.00524750000.997812319600.00304250000.58139901435

0.006487501.000000000000.005790000.999998318220.00527250000.997916935590.00306750000.58505185428

0.006512501.000000000000.005815000.999998483840.00529750000.998016949530.00309250000.58868656136

0.006537501.000000000000.005840000.999998633720.00532250000.998112543110.00311750000.59230306865

0.006562501.000000000000.005865000.999998769310.00534750000.998203891890.00314250000.59590131109

0.006587501.000000000000.005890000.999998891900.00537250000.998291165410.00316750000.59948122554

0.006612501.000000000000.005915000.999999002700.00539750000.998374527380.00319250000.60304275079

0.006637501.000000000000.005940000.999999102790.00542250000.998454135840.00321750000.60658582750

0.006662501.000000000000.005965000.999999193180.00544750000.998530143300.00324250000.61011039826

0.006687501.000000000000.005990000.999999274770.00547250000.998602696910.00326750000.61361640756

0.006712501.000000000000.006015000.999999348380.00549750000.998671938570.00329250000.61710380179

0.006737501.000000000000.006040000.999999414760.00552250000.998738005140.00331750000.62057252922

0.006762501.000000000000.006065000.999999474600.00554750000.998801028540.00334250000.62402254002

0.006787501.000000000000.006090000.999999528520.00557250000.998861135880.00336750000.62745378627

0.006812501.000000000000.006115000.999999577090.00559750000.998918449670.00339250000.63086622191

0.006837501.000000000000.006140000.999999620810.00562250000.998973087860.00341750000.63425980276

0.006862501.000000000000.006165000.999999660160.00564750000.999025164080.00344250000.63763448654

0.006887501.000000000000.006190000.999999695550.00567250000.999074787660.00346750000.64099023282

0.006912501.000000000000.006215000.999999727360.00569750000.999122063880.00349250000.64432700304

0.006937501.000000000000.006240000.999999755960.00572250000.999167093990.00351750000.64764476050

0.006962501.000000000000.006265000.999999781650.00574750000.999209975400.00354250000.65094347038

0.006987501.000000000000.006290000.999999804720.00577250000.999250801780.00356750000.65422309966

0.007012501.000000000000.006315000.999999825420.00579750000.999289663180.00359250000.65748361720

0.007037501.000000000000.006340000.999999843990.00582250000.999326646140.00361750000.66072499369

0.007062501.000000000000.006365000.999999860650.00584750000.999361833840.00364250000.66394720163

0.007087501.000000000000.006390000.999999875580.00587250000.999395306140.00366750000.66715021537

0.007112501.000000000000.006415000.999999888960.00589750000.999427139770.00369250000.67033401105

0.007137501.000000000000.006440000.999999900940.00592250000.999457408380.00371750000.67349856662

0.007162501.000000000000.006465000.999999911670.00594750000.999486182670.00374250000.67664386185

0.007187501.000000000000.006490000.999999921260.00597250000.999513530470.00376750000.67976987827

0.007212501.000000000000.006515000.999999929850.00599750000.999539516860.00379250000.68287659920

0.007237501.000000000000.006540000.999999937520.00602250000.999564204260.00381750000.68596400976

0.007262501.000000000000.006565000.999999944380.00604750000.999587652510.00384250000.68903209679

0.007287501.000000000000.006590000.999999950510.00607250000.999609918980.00386750000.69208084891

0.007312501.000000000000.006615000.999999955980.00609750000.999631058630.00389250000.69511025649

0.007337501.000000000000.006640000.999999960860.00612250000.999651124140.00391750000.69812031162

0.007362501.000000000000.006665000.999999965210.00614750000.999670165960.00394250000.70111100812

0.007387501.000000000000.006690000.999999969100.00617250000.999688232380.00396750000.70408234152

0.007412501.000000000000.006715000.999999972560.00619750000.999705369660.00399250000.70703430906

0.007437501.000000000000.006740000.999999975640.00622250000.999721622050.00401750000.70996690969

0.007462501.000000000000.006765000.999999978390.00624750000.999737031890.00404250000.71288014400

0.007487501.000000000000.006790000.999999980840.00627250000.999751639700.00406750000.71577401429

0.007512501.000000000000.006815000.999999983010.00629750000.999765484220.00409250000.71864852451

0.007537501.000000000000.006840000.999999984950.00632250000.999778602480.00411750000.72150368025

0.007562501.000000000000.006865000.999999986670.00634750000.999791029880.00414250000.72433948875

0.007587501.000000000000.006890000.999999988200.00637250000.999802800260.00416750000.72715595886

0.007612501.000000000000.006915000.999999989550.00639750000.999813945920.00419250000.72995310104

0.007637501.000000000000.006940000.999999990760.00642250000.999824497740.00421750000.73273092738

0.007662501.000000000000.006965000.999999991830.00644750000.999834485180.00424250000.73548945152

0.007687501.000000000000.006990000.999999992780.00647250000.999843936390.00426750000.73822868870

0.007712501.000000000000.007015000.999999993620.00649750000.999852878210.00429250000.74094865572

0.007737501.000000000000.007040000.999999994360.00652250000.999861336260.00431750000.74364937091

0.007762501.000000000000.007065000.999999995030.00654750000.999869334990.00434250000.74633085415

0.007787501.000000000000.007090000.999999995610.00657250000.999876897680.00436750000.74899312684

0.007812501.000000000000.007115000.999999996130.00659750000.999884046560.00439250000.75163621190

0.007837501.000000000000.007140000.999999996590.00662250000.999890802810.00441750000.75426013372

0.007862501.000000000000.007165000.999999996990.00664750000.999897186600.00444250000.75686491818

0.007887501.000000000000.007190000.999999997350.00667250000.999903217160.00446750000.75945059264

0.007912501.000000000000.007215000.999999997670.00669750000.999908912800.00449250000.76201718589

0.007937501.000000000000.007240000.999999997950.00672250000.999914290950.00451750000.76456472818

0.007962501.000000000000.007265000.999999998190.00674750000.999919368210.00454250000.76709325116

0.007987501.000000000000.007290000.999999998410.00677250000.999924160370.00456750000.76960278792

0.008012501.000000000000.007315000.999999998600.00679750000.999928682450.00459250000.77209337290

0.008037501.000000000000.007340000.999999998770.00682250000.999932948760.00461750000.77456504196

0.008062501.000000000000.007365000.999999998920.00684750000.999936972880.00464250000.77701783230

0.008087501.000000000000.007390000.999999999050.00687250000.999940767750.00466750000.77945178247

0.008112501.000000000000.007415000.999999999170.00689750000.999944345640.00469250000.78186693237

0.008137501.000000000000.007440000.999999999270.00692250000.999947718230.00471750000.78426332319

0.008162501.000000000000.007465000.999999999360.00694750000.999950896610.00474250000.78664099744

0.008187501.000000000000.007490000.999999999440.00697250000.999953891310.00476750000.78899999893

0.008212501.000000000000.007515000.999999999510.00699750000.999956712340.00479250000.79134037270

0.008237501.000000000000.007540000.999999999570.00702250000.999959369190.00481750000.79366216508

0.008262501.000000000000.007565000.999999999620.00704750000.999961870870.00484250000.79596542363

0.008287501.000000000000.007590000.999999999670.00707250000.999964225940.00486750000.79825019713

0.008312501.000000000000.007615000.999999999710.00709750000.999966442500.00489250000.80051653556

0.008337501.000000000000.007640000.999999999750.00712250000.999968528250.00491750000.80276449010

0.008362501.000000000000.007665000.999999999780.00714750000.999970490490.00494250000.80499411310

0.008387501.000000000000.007690000.999999999810.00717250000.999972336120.00496750000.80720545807

0.008412501.000000000000.007715000.999999999830.00719750000.999974071700.00499250000.80939857966

0.008437501.000000000000.007740000.999999999850.00722250000.999975703430.00501750000.81157353365

0.008462501.000000000000.007765000.999999999870.00724750000.999977237210.00504250000.81373037692

0.008487501.000000000000.007790000.999999999890.00727250000.999978678590.00506750000.81586916745

0.008512501.000000000000.007815000.999999999900.00729750000.999980032840.00509250000.81798996428

0.008537501.000000000000.007840000.999999999920.00732250000.999981304970.00511750000.82009282753

0.008562501.000000000000.007865000.999999999930.00734750000.999982499680.00514250000.82217781835

0.008587501.000000000000.007890000.999999999940.00737250000.999983621450.00516750000.82424499892

0.008612501.000000000000.007915000.999999999940.00739750000.999984674510.00519250000.82629443241

0.008637501.000000000000.007940000.999999999950.00742250000.999985662830.00521750000.82832618301

0.008662501.000000000000.007965000.999999999960.00744750000.999986590220.00524250000.83034031587

0.008687501.000000000000.007990000.999999999960.00747250000.999987460220.00526750000.83233689709

0.008712501.000000000000.008015000.999999999970.00749750000.999988276220.00529250000.83431599373

0.008737501.000000000000.008040000.999999999970.00752250000.999989041400.00531750000.83627767375

0.008762501.000000000000.008065000.999999999980.00754750000.999989758780.00534250000.83822200604

0.008787501.000000000000.008090000.999999999980.00757250000.999990431180.00536750000.84014906037

0.008812501.000000000000.008115000.999999999980.00759750000.999991061300.00539250000.84205890738

0.008837501.000000000000.008140000.999999999980.00762250000.999991651670.00541750000.84395161857

0.008862501.000000000000.008165000.999999999990.00764750000.999992204670.00544250000.84582726629

0.008887501.000000000000.008190000.999999999990.00767250000.999992722550.00546750000.84768592368

0.008912501.000000000000.008215000.999999999990.00769750000.999993207450.00549250000.84952766472

0.008937501.000000000000.008240000.999999999990.00772250000.999993661360.00551750000.85135256416

0.008962501.000000000000.008265000.999999999990.00774750000.999994086170.00554250000.85316069753

0.008987501.000000000000.008290000.999999999990.00777250000.999994483660.00556750000.85495214112

0.009012501.000000000000.008315000.999999999990.00779750000.999994855510.00559250000.85672697193

0.009037501.000000000000.008340001.000000000000.00782250000.999995203290.00561750000.85848526771

0.009062501.000000000000.008365001.000000000000.00784750000.999995528500.00564250000.86022710691

0.009087501.000000000000.008390001.000000000000.00787250000.999995832520.00566750000.86195256866

0.009112501.000000000000.008415001.000000000000.00789750000.999996116690.00569250000.86366173276

0.009137501.000000000000.008440001.000000000000.00792250000.999996382240.00571750000.86535467966

0.009162501.000000000000.008465001.000000000000.00794750000.999996630330.00574250000.86703149047

0.009187501.000000000000.008490001.000000000000.00797250000.999996862060.00576750000.86869224691

0.009212501.000000000000.008515001.000000000000.00799750000.999997078470.00579250000.87033703128

0.009237501.000000000000.008540001.000000000000.00802250000.999997280530.00581750000.87196592650

0.009262501.000000000000.008565001.000000000000.00804750000.999997469130.00584250000.87357901606

0.009287501.000000000000.008590001.000000000000.00807250000.999997645150.00586750000.87517638398

0.009312501.000000000000.008615001.000000000000.00809750000.999997809390.00589250000.87675811484

0.009337501.000000000000.008640001.000000000000.00812250000.999997962600.00591750000.87832429374

0.009362501.000000000000.008665001.000000000000.00814750000.999998105490.00594250000.87987500628

0.009387501.000000000000.008690001.000000000000.00817250000.999998238720.00596750000.88141033856

0.009412501.000000000000.008715001.000000000000.00819750000.999998362930.00599250000.88293037715

0.009437501.000000000000.008740001.000000000000.00822250000.999998478700.00601750000.88443520907

0.009462501.000000000000.008765001.000000000000.00824750000.999998586580.00604250000.88592492180

0.009487501.000000000000.008790001.000000000000.00827250000.999998687080.00606750000.88739960323

0.009512501.000000000000.008815001.000000000000.00829750000.999998780690.00609250000.88885934168

0.009537501.000000000000.008840001.000000000000.00832250000.999998867870.00611750000.89030422584

0.009562501.000000000000.008865001.000000000000.00834750000.999998949030.00614250000.89173434480

0.009587501.000000000000.008890001.000000000000.00837250000.999999024580.00616750000.89314978801

0.009612501.000000000000.008915001.000000000000.00839750000.999999094880.00619250000.89455064528

0.009637501.000000000000.008940001.000000000000.00842250000.999999160300.00621750000.89593700672

0.009662501.000000000000.008965001.000000000000.00844750000.999999221150.00624250000.89730896280

0.009687501.000000000000.008990001.000000000000.00847250000.999999277740.00626750000.89866660428

0.009712501.000000000000.009015001.000000000000.00849750000.999999330370.00629250000.90001002219

0.009737501.000000000000.009040001.000000000000.00852250000.999999379280.00631750000.90133930786

0.009762501.000000000000.009065001.000000000000.00854750000.999999424750.00634250000.90265455286

0.009787501.000000000000.009090001.000000000000.00857250000.999999466990.00636750000.90395584903

0.009812501.000000000000.009115001.000000000000.00859750000.999999506240.00639250000.90524328841

0.009837501.000000000000.009140001.000000000000.00862250000.999999542700.00641750000.90651696328

0.009862501.000000000000.009165001.000000000000.00864750000.999999576550.00644250000.90777696611

0.009887501.000000000000.009190001.000000000000.00867250000.999999607970.00646750000.90902338956

0.009912501.000000000000.009215001.000000000000.00869750000.999999637150.00649250000.91025632647

0.009937501.000000000000.009240001.000000000000.00872250000.999999664220.00651750000.91147586982

0.009962501.000000000000.009265001.000000000000.00874750000.999999689330.00654250000.91268211277

0.0099875


2 2 - blogs.sch.gr · $qguhdv $wkdqdvvrsrxorv 0 " 0 / ù . 0 2 # . 0 # # ) . 1 2 0 . ) 1 1 . 2 0 & ! * 0 2 ! 0 # $qguhdv $wkdqdvvrsrxorv . ! # 1 . 1 2 # ! . 2 "

2 2 - blogs.sch.gr · $qguhdv $wkdqdvvrsrxorv 0 " 0 / ù . 0 2 # . 0 # # ) . 1 2 0 . ) 1 1 . 2 0 & ! * 0 2 ! 0 # $qguhdv $wkdqdvvrsrxorv . ! # 1 . 1 2 # ! . 2 "

0 + ! . ! . $ · 1 2 ! . ü . ! . $ " þ ! 1 . & " ) / ! 1 " & . 2 0 $ + . 2 1 2 + / & ù # 1 2 # 2 1 2 * 0 ! 2 " 1 2 " 0 1 . # 0 # "

0 + ! . ! . $ · 1 2 ! . ü . ! . $ " þ ! 1 . & " ) / ! 1 " & . 2 0 $ + . 2 1 2 + / & ù # 1 2 # 2 1 2 * 0 ! 2 " 1 2 " 0 1 . # 0 # "

ΟΔΗΓΟΣΣΠΟΥΔ2Ν ΤΜΗΜΑΤΟΣ ΜΑθΗΜΑΤΙΚ2Ν · 3-1 3-1 3-1 3-1 2-2 2-2 2-2 2-2 2-2 2-2 2-2 2-2 2-2 2-2 •. Δεν είναι βέβαιο ότι κατά την

ΟΔΗΓΟΣΣΠΟΥΔ2Ν ΤΜΗΜΑΤΟΣ ΜΑθΗΜΑΤΙΚ2Ν · 3-1 3-1 3-1 3-1 2-2 2-2 2-2 2-2 2-2 2-2 2-2 2-2 2-2 2-2 •. Δεν είναι βέβαιο ότι κατά την

!0 .2 #- + ù # ) ! $ . 2 3&.12!. + 12 · .2.1 .!.$ 0 . )2.1.! 3 ..#2 +. #3. 02. )2 $ # .2. . 0 .2.12. 0 12 ! . ! 3. +" * . 20 * !) . . 12 ) . 2 2! 3 .

!0 .2 #- + ù # ) ! $ . 2 3&.12!. + 12 · .2.1 .!.$ 0 . )2.1.! 3 ..#2 +. #3. 02. )2 $ # .2. . 0 .2.12. 0 12 ! . ! 3. +" * . 20 * !) . . 12 ) . 2 2! 3 .

2 & / . ! 1 & + 1 $ 1 0 & , - kordoutis.gr€¦ · . . + 2 " ! / * 2 " 7 . # $ . " 2 0 . 0 1 2 & + . 2 + ü 1 2 +

2 & / . ! 1 & + 1 $ 1 0 & , - kordoutis.gr€¦ · . . + 2 " ! / * 2 " 7 . # $ . " 2 0 . 0 1 2 & + . 2 + ü 1 2 +

0 +10 .2.1 0# · 2019. 1. 14. · 4 *! $.!. 2 ! 12 ) 2 #" 2 0 % .12 )2 2." 12 / . )!3&1 2 # 1+ .2 " .2 2. # . 2 $!) . 2. .2+20!0". 1 2 . 20$ 2! . ))2 2. 12 ü 12 0 $ õ &" .!2#! 0"2

0 +10 .2.1 0# · 2019. 1. 14. · 4 *! $.!. 2 ! 12 ) 2 #" 2 0 % .12 )2 2." 12 / . )!3&1 2 # 1+ .2 " .2 2. # . 2 $!) . 2. .2+20!0". 1 2 . 20$ 2! . ))2 2. 12 ü 12 0 $ õ &" .!2#! 0"2

แคดเมียมในปัสสาวะของผู้ป่วยโรคเบาหวานชนิดที2 ค่ลินิกโรค ... · /:+2:+&

แคดเมียมในปัสสาวะของผู้ป่วยโรคเบาหวานชนิดที2 ค่ลินิกโรค ... · /:+2:+&

h = ca. 44) Preview - OCP | OCP · 12$0 (2 ,7 & & & b b b 2 3 2 3 2 3 2 2 2 2 2 2 16 L ight from light, 1. S on of God. C hrist our light.

h = ca. 44) Preview - OCP | OCP · 12$0 (2 ,7 & & & b b b 2 3 2 3 2 3 2 2 2 2 2 2 16 L ight from light, 1. S on of God. C hrist our light.

4(%2/,%/&,%!$%23). $%-/#2!4)#$%,)%2!4)/.3 2ESULTSFROMA ...

4(%2/,%/&,%!$%23). $%-/#2!4)#$%,)%2!4)/.3 2ESULTSFROMA ...

Artful thinking 2 (Ξενοφώντος, Ελληνικά 2 2, 3-4)

Artful thinking 2 (Ξενοφώντος, Ελληνικά 2 2, 3-4)

Find the surface area of each. S = (Pℓ)/2 + B = (20×3)(15)/2 + 20√(10 2 +20 2 )/2 = 623.2 in 2 S = (Pℓ)/2 + B = (10×6)(14)/2 + (8.7)(10×6)/2 = 679.8 ft.

Find the surface area of each. S = (Pℓ)/2 + B = (20×3)(15)/2 + 20√(10 2 +20 2 )/2 = 623.2 in 2 S = (Pℓ)/2 + B = (10×6)(14)/2 + (8.7)(10×6)/2 = 679.8 ft.

! .2 /)2 1 & + ü $0 ! 10& 12 ! !. .2 0! / -2020 · ü $0 ! 1 . )!) !. . 2 "# /! " ú !0 #ù . # 252.751.145,55 ! 2 " 353.150.139,23 ù22 " 1.104.251.868,11 2 #ù .

! .2 /)2 1 & + ü $0 ! 10& 12 ! !. .2 0! / -2020 · ü $0 ! 1 . )!) !. . 2 "# /! " ú !0 #ù . # 252.751.145,55 ! 2 " 353.150.139,23 ù22 " 1.104.251.868,11 2 #ù .

Materiales docentes para Electrónica con... · Ejercicios Tecnología ... Parametrizamos β: impedancias de carga y transferencia inversa. ... y la asignación en serie o paralelo

Materiales docentes para Electrónica con... · Ejercicios Tecnología ... Parametrizamos β: impedancias de carga y transferencia inversa. ... y la asignación en serie o paralelo

ü ü .! ÿ ÿ 7 ÿ ù! 70 1 · 2018-08-03 · (i) 1 2 # 1 ) . 2 . ! + # 0 . (ii) 1 2 ) 2 2 . . / . 2 0 ! . 2 . ! 1 2 . 2 0 # ) 0 . 2 # .

ü ü .! ÿ ÿ 7 ÿ ù! 70 1 · 2018-08-03 · (i) 1 2 # 1 ) . 2 . ! + # 0 . (ii) 1 2 ) 2 2 . . / . 2 0 ! . 2 . ! 1 2 . 2 0 # ) 0 . 2 # .

1 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 3 ü / )2 2. #1 !. */ 2 2 2 2 2 ...iek-patras.ach.sch.gr/.../odigos118-MOYSIKI-TRAGOYDI.pdf• τη βασική μουσική θεωρία και

1 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 3 ü / )2 2. #1 !. */ 2 2 2 2 2 ...iek-patras.ach.sch.gr/.../odigos118-MOYSIKI-TRAGOYDI.pdf• τη βασική μουσική θεωρία και

ü , ü þ + ü · 2020. 12. 4. · ü ! 0 0 " ù ü . 0 . 2 # # 0 # 2 . ú . 2 ! 2 1 ü . . . 2 ! 2 1 . ü . 0 . 2 . 2 ! 2 1 # . * 0 0 " & " ! 0 1 0 " + 0 * *

ü , ü þ + ü · 2020. 12. 4. · ü ! 0 0 " ù ü . 0 . 2 # # 0 # 2 . ú . 2 ! 2 1 ü . . . 2 ! 2 1 . ü . 0 . 2 . 2 ! 2 1 # . * 0 0 " & " ! 0 1 0 " + 0 * *

Statistics Assignment 2-2

Statistics Assignment 2-2

2.omada3διαφημιση (2)

2.omada3διαφημιση (2)

สหกรณ์เคหสถานราชนาวี จำกัด · 2017. 6. 20. · 2 2- 2 2 ea2- C) O O 2 O 2- 2- 2) 00 2) 2- O O 2 2 2 2 2 2 2 O 2

สหกรณ์เคหสถานราชนาวี จำกัด · 2017. 6. 20. · 2 2- 2 2 ea2- C) O O 2 O 2- 2- 2) 00 2) 2- O O 2 2 2 2 2 2 2 O 2

03 . 12 . /!) 1 · 2016-06-08 · ù #1 # 02. 2& 0$ + ü3.! "0! 2+10& 89 03 . 12 . /!) 1 * % þ 12 . /!) 1 0!0# 2 !. ). 2 01 . ."0 .!2 " .2 ! " 02. 2 ". .3 ! 0 2 /! 1 + . 0 !2 2&

03 . 12 . /!) 1 · 2016-06-08 · ù #1 # 02. 2& 0$ + ü3.! "0! 2+10& 89 03 . 12 . /!) 1 * % þ 12 . /!) 1 0!0# 2 !. ). 2 01 . ."0 .!2 " .2 ! " 02. 2 ". .3 ! 0 2 /! 1 + . 0 !2 2&