Profesor
Margarito Filomeno Nicolas
2022-01-04T01:09:33Z
2022-12-31T02:05:36Z
16.00
836318a7-025e-496d-8d66-beb15bdd159a
6540
21765
32767
32767
False
False
| Universidad Autónoma Metropolitana. Unidad Lerma. |
| Ajuste de curvas: tablas equiespaciadas ejercicio 02 |
| Autores: Dra. Blanca Rafaela Silva López, M. en C. Hugo Pablo Leyva |
| Colaborador: Iván Córdova de la Fuente |
| Revisor: Margarito Filomeno Nicolás |
| Fecha: 10/11/2022 |
|
|
| Ejercicio 2 - Ajuste de curvas - Equiespaciadas |
|
|
|
|
| Hallar los valores solicitados con las curva solicitada |
| x |
y |
P1 |
y( |
14.6906 |
) |
| 14 |
7.7919999999999999E-7 |
P2 |
y( |
14.0604 |
) |
| 14.0343 |
7.6649999999999999E-7 |
P3 |
x( |
7.709E-7 |
) |
| 14.0687 |
7.5600000000000005E-7 |
P4 |
x( |
5.7479999999999999E-7 |
) |
| 14.103 |
7.4340000000000005E-7 |
| 14.1374 |
7.328E-7 |
Ajustar a la curva: |
| 14.1717 |
7.202E-7 |
| 14.206 |
7.0969999999999996E-7 |
Mejor curva |
| 14.240399999999999 |
6.9910000000000001E-7 |
| 14.274699999999999 |
6.8650000000000001E-7 |
| 14.308999999999999 |
6.7599999999999997E-7 |
| 14.343400000000001 |
6.6540000000000002E-7 |
| 14.377700000000001 |
6.5700000000000002E-7 |
| 14.412100000000001 |
6.4649999999999997E-7 |
| 14.446400000000001 |
6.3600000000000003E-7 |
| 14.480700000000001 |
6.2539999999999998E-7 |
| 14.5151 |
6.1699999999999998E-7 |
| 14.5494 |
6.0650000000000004E-7 |
| 14.5838 |
5.9800000000000003E-7 |
| 14.6181 |
5.8960000000000004E-7 |
| 14.6524 |
5.7909999999999999E-7 |
| Criterio de Convergencia |
| ND |
Tol |
NCSINV |
TolINV |
NumPtos |
MaxIter |
| 3 |
5.0000000000000001E-4 |
6 |
4.9999999999999996E-6 |
20 |
18 |
| Ajuste a curva polinomial |
|
Ajuste a curva exponencial |
|
|
Ajuste a curva potencial |
|
|
| n |
1 |
A*exp(B*x) |
A*x^B |
| x |
y |
∑x |
∑x2 |
∑y |
∑yx |
yp |
∑(y-yp)2 |
σxy |
Checa σxy |
Checa n |
∑ln(y) |
∑ln(y)x |
yp |
∑(y-yp)2 |
σxy |
Checa σxy |
∑ln(x) |
∑ln(x)2 |
∑ln(y)ln(x) |
yp |
∑(y-yp)2 |
σxy |
Checa σxy |
| 14 |
7.7919999999999999E-7 |
14 |
196 |
7.7919999999999999E-7 |
1.09088E-5 |
7.7423664148943382E-7 |
2.4634927704409662E-17 |
-14.064998084618086 |
-196.90997318465321 |
7.7899380668925554E-7 |
4.2515681395755905E-20 |
2.6390573296152584 |
6.9646235889960186 |
-37.11833628623593 |
7.798286378841342E-7 |
3.9518558936874047E-19 |
| 14.0343 |
7.6649999999999999E-7 |
14.0343 |
196.96157649 |
7.6649999999999999E-7 |
1.0757290949999999E-5 |
7.6374926873500054E-7 |
7.5665224922454476E-18 |
-14.081431138634542 |
-197.62302902893876 |
7.6695915837894602E-7 |
2.1082641695634775E-19 |
2.6415043332583106 |
6.9775451426224322 |
-37.196161371181653 |
7.675191609339037E-7 |
1.0386890091954797E-18 |
| 14.0687 |
7.5600000000000005E-7 |
14.0687 |
197.92831969 |
7.5600000000000005E-7 |
1.06359372E-5 |
7.5323132054979633E-7 |
7.6655858979803687E-18 |
-14.095224460766879 |
-198.30148437119098 |
7.5507615754435726E-7 |
8.5348488284810106E-19 |
2.6439524716905791 |
6.9904846725587229 |
-37.267103552078098 |
7.5539841344282106E-7 |
3.6190638577846876E-19 |
| 14.103 |
7.4340000000000005E-7 |
14.103 |
198.894609 |
7.4340000000000005E-7 |
1.04841702E-5 |
7.4274394779536305E-7 |
4.3040449520906635E-19 |
-14.11203157908326 |
-199.02198135981121 |
7.434110121664158E-7 |
1.2126780916807633E-22 |
2.6463875407101032 |
7.0033670156256678 |
-37.345904544993459 |
7.4353226017579267E-7 |
1.7492754100693854E-20 |
| 14.1374 |
7.328E-7 |
14.1374 |
199.86607875999999 |
7.328E-7 |
1.035988672E-5 |
7.3222599961015884E-7 |
3.2947644753780267E-19 |
-14.126393023586491 |
-199.71046873165164 |
7.3189285819236644E-7 |
8.2290625915668004E-19 |
2.6488237680308386 |
7.0162673540850902 |
-37.418325597420925 |
7.31846994142068E-7 |
9.0822016525270439E-19 |
| 14.1717 |
7.202E-7 |
14.1717 |
200.83708088999998 |
7.202E-7 |
1.0206458340000001E-5 |
7.2173862685572556E-7 |
2.3673726011599273E-18 |
-14.143736885731636 |
-200.44079602352303 |
7.2058587080230381E-7 |
1.4889627607058087E-19 |
2.6512470182778993 |
7.029110751927452 |
-37.498540245603145 |
7.2040615677260788E-7 |
4.2500614892094391E-20 |
| 14.206 |
7.0969999999999996E-7 |
14.206 |
201.81043599999998 |
7.0969999999999996E-7 |
1.0081998199999999E-5 |
7.1125125410129229E-7 |
2.4063892867762921E-18 |
-14.158423491415475 |
-201.13456411904824 |
7.0945356466839502E-7 |
6.0730372663233057E-20 |
2.653664410575618 |
7.041934803955642 |
-37.571704529027031 |
7.0917118327935104E-7 |
2.7964712403787791E-19 |
| 14.240399999999999 |
6.9910000000000001E-7 |
14.240399999999999 |
202.78899215999999 |
6.9910000000000001E-7 |
9.9554636399999992E-6 |
7.0073330591608808E-7 |
2.6676882155282876E-18 |
-14.173472043428472 |
-201.83591128723879 |
6.9846153568099075E-7 |
4.0763668664795208E-19 |
2.6560829954769565 |
7.0547768788618423 |
-37.645918081418394 |
6.9810600946684424E-7 |
9.8801718000327633E-19 |
| 14.274699999999999 |
6.8650000000000001E-7 |
14.274699999999999 |
203.76706008999997 |
6.8650000000000001E-7 |
9.7995815500000004E-6 |
6.902459331616548E-7 |
1.4032015251585049E-17 |
-14.191659611738386 |
-202.58168345968193 |
6.8767102763327723E-7 |
1.3713057178988422E-18 |
2.6584887395594183 |
7.067562378364225 |
-37.728367273466688 |
6.8727086494379084E-7 |
5.9423276156563666E-19 |
| 14.308999999999999 |
6.7599999999999997E-7 |
14.308999999999999 |
204.74748099999999 |
6.7599999999999997E-7 |
9.6728839999999997E-6 |
6.7975856040722153E-7 |
1.412677633473353E-17 |
-14.207072760903447 |
-203.28900413576741 |
6.7704722177026553E-7 |
1.0966734361181349E-18 |
2.6608887099245977 |
7.0803287266041899 |
-37.803439510565269 |
6.7662929144056149E-7 |
3.9600771716399904E-19 |
| 14.343400000000001 |
6.6540000000000002E-7 |
14.343400000000001 |
205.73312356000002 |
6.6540000000000002E-7 |
9.5440983600000006E-6 |
6.6924061222201731E-7 |
1.4750302239908646E-17 |
-14.222877473362034 |
-204.00442075142101 |
6.6655728548948981E-7 |
1.3393097041836349E-18 |
2.6632899060916531 |
7.0931131238896858 |
-37.87964601038346 |
6.6614718063451514E-7 |
5.5827890059442457E-19 |
| 14.377700000000001 |
6.5700000000000002E-7 |
14.377700000000001 |
206.71825729000003 |
6.5700000000000002E-7 |
9.4461489E-6 |
6.5875323946758404E-7 |
3.0738486306942993E-18 |
-14.235581818461801 |
-204.67492471129825 |
6.5625966509680229E-7 |
5.4809576889279117E-19 |
2.6656783951332597 |
7.1058413062802313 |
-37.947482895625463 |
6.5588164411271981E-7 |
1.2507198906143027E-18 |
| 14.412100000000001 |
6.4649999999999997E-7 |
14.412100000000001 |
207.70862641000002 |
6.4649999999999997E-7 |
9.3174226500000006E-6 |
6.4823529128237982E-7 |
3.0112358347035126E-18 |
-14.251692638734498 |
-205.39681947870548 |
6.4609180405380371E-7 |
1.6662393049106357E-19 |
2.6680681315240005 |
7.1185875544539714 |
-38.024486949682704 |
6.4576906523103781E-7 |
5.3426563647777484E-19 |
| 14.446400000000001 |
6.3600000000000003E-7 |
14.446400000000001 |
208.69847296 |
6.3600000000000003E-7 |
9.187910400000001E-6 |
6.3774791852794655E-7 |
3.0552191803387329E-18 |
-14.268067273606288 |
-206.12220706142588 |
6.3611035417423808E-7 |
1.2178043771760767E-20 |
2.6704452485710779 |
7.1312778256158458 |
-38.102092457094408 |
6.3586457738364913E-7 |
1.8339285019322766E-20 |
| 14.480700000000001 |
6.2539999999999998E-7 |
14.480700000000001 |
209.69067249000003 |
6.2539999999999998E-7 |
9.0562297800000007E-6 |
6.2726054577351328E-7 |
3.4616305753382147E-18 |
-14.284874391922671 |
-206.85498060711461 |
6.2628310736778537E-7 |
7.7987862303685418E-19 |
2.672816728330544 |
7.1439492632435933 |
-38.180851236831522 |
6.2613494988733865E-7 |
5.4015133689913712E-19 |
| 14.5151 |
6.1699999999999998E-7 |
14.5151 |
210.68812801000001 |
6.1699999999999998E-7 |
8.9558166999999999E-6 |
6.1674259758830906E-7 |
6.625600154430031E-20 |
-14.298396813041023 |
-207.54265958097176 |
6.1657969277753535E-7 |
1.7665816125593121E-19 |
2.6751894868775943 |
7.1566387907004065 |
-38.250920833451445 |
6.1654907291813307E-7 |
2.033352331610046E-19 |
| 14.5494 |
6.0650000000000004E-7 |
14.5494 |
211.68504036000002 |
6.0650000000000004E-7 |
8.824211100000001E-6 |
6.0625522483387579E-7 |
5.9914881951153394E-20 |
-14.315561108562306 |
-208.28282479291641 |
6.0705417448183424E-7 |
3.0710935631620895E-19 |
2.6775497556538261 |
7.1692726940018643 |
-38.330627148278417 |
6.0715925744422039E-7 |
4.3462037775995194E-19 |
| 14.5838 |
5.9800000000000003E-7 |
14.5838 |
212.68722244 |
5.9800000000000003E-7 |
8.7211124000000012E-6 |
5.9573727664867157E-7 |
5.1199169646471009E-18 |
-14.329675082995779 |
-208.98111547539384 |
5.9764868634964345E-7 |
1.2342128092686549E-19 |
2.6799113236235246 |
7.1819247024855919 |
-38.40225851876626 |
5.9790739453897528E-7 |
8.5757714116076414E-21 |
| 14.6181 |
5.8960000000000004E-7 |
14.6181 |
213.68884761000001 |
5.8960000000000004E-7 |
8.6188317600000012E-6 |
5.852499038942383E-7 |
1.8923336129363441E-17 |
-14.343821496071284 |
-209.67941701171964 |
5.8841563251587208E-7 |
1.4027263374595812E-18 |
2.6822604869159066 |
7.1945213196703559 |
-38.473865630287008 |
5.8884400349809501E-7 |
5.7153071089263837E-19 |
| 14.6524 |
5.7909999999999999E-7 |
14.6524 |
214.69282576000001 |
5.7909999999999999E-7 |
8.4852048399999994E-6 |
5.7476253113980503E-7 |
1.8813636113160997E-17 |
-14.361790662714666 |
-210.43470150636037 |
5.7932521981065056E-7 |
5.072396310947863E-20 |
2.684604144571229 |
7.2070994130490202 |
-38.555722736588173 |
5.7993876056504704E-7 |
7.0351928547804883E-19 |
| ∑ |
286.52430000000004 |
4105.5928509699997 |
1.3489899999999999E-5 |
1.9301945769E-4 |
1.4656245527881582E-16 |
2.8534818426968969E-9 |
AJUSTA |
|
-284.26678183937906 |
-4072.8229666788325 |
9.9218221670089695E-18 |
7.4243676000829147E-10 |
AJUSTA |
53.2399109244122 |
141.72822730699181 |
-756.74175540897954 |
9.8452357296671838E-18 |
7.3956577837070429E-10 |
AJUSTA |
| Ecuaciones Normales |
|
Ecuaciones Normales |
|
Ecuaciones Normales |
|
| NP |
∑x |
∑y |
NP |
∑x |
∑ln(y) |
NP |
∑ln(x) |
∑ln(y) |
| ∑x |
∑x2 |
∑yx |
∑x |
∑x2 |
∑ln(y)x |
∑ln(x) |
∑ln(x)2 |
∑ln(y)ln()x |
| 20 |
286.52430000000004 |
1.3489899999999999E-5 |
20 |
286.52430000000004 |
-284.26678183937906 |
20 |
53.2399109244122 |
-284.26678183937906 |
| 286.52430000000004 |
4105.5928509699997 |
1.9301945769E-4 |
286.52430000000004 |
4105.5928509699997 |
-4072.8229666788325 |
53.2399109244122 |
141.72822730699181 |
-756.74175540897954 |
| Matriz Inversa |
|
a |
A |
B |
Matriz Inversa |
|
| -7.7103467891865876 |
4.4816603104886108E-4 |
-0.4539225680182426 |
| 261.79405595485559 |
-18.27028674041647 |
-0.4539225680182426 |
1854.3315124766993 |
-696.5757381184693 |
| -18.27028674041647 |
1.2753045197504342 |
-696.5757381184693 |
261.67426880463358 |
| a |
a |
A |
B |
| 5.0547969494213821E-6 |
3.0953239763621241 |
22.094395440007393 |
-6.5021382522536442 |
| -3.0575430770942488E-7 |
-6.5021382522536442 |
| Resumen |
Mejor curva |
| Curva |
σxy |
y= |
22.094395440007393 |
*x^( |
-6.5021382522536442 |
) |
± |
7.3956577837070429E-10 |
| Pn(x) |
2.8534818426968969E-9 |
| A*exp(B*X) |
7.4243676000829147E-10 |
| A*x^B |
7.3956577837070429E-10 |
| Evaluación de puntos |
|
| Evaluando X |
| P1 |
|
|
|
|
|
|
|
| Y( |
14.6906 |
)= |
5.702033021018614E-7 |
| Redondeando a las cifras que representa la curva |
| Y( |
14.6906 |
)= |
5.702033021018614E-7 |
| P2 |
|
|
|
|
|
|
|
| Y( |
14.0604 |
)= |
7.5830255662093705E-7 |
| Redondeando a las cifras que representa la curva |
| Y( |
14.0604 |
)= |
7.5830255662093705E-7 |
| Evaluando Y |
| P3 |
|
|
|
|
|
|
|
| 7.709E-7 |
= |
22.094395440007393 |
*x^( |
-6.5021382522536442 |
) |
| Reacomodando para despejar x |
| x= |
(y/A)^ |
1/B |
| x= |
( |
7.709E-7 |
/ |
22.094395440007393 |
)^(1 |
/ |
-6.5021382522536442 |
) |
|
| Evaluando |
| X( |
7.709E-7 |
)= |
14.024816507759917 |
| Redodeando |
| X( |
7.709E-7 |
)= |
14.024816507759917 |
| P4 |
|
|
|
|
|
|
|
| 5.7479999999999999E-7 |
= |
22.094395440007393 |
*x^( |
-6.5021382522536442 |
) |
| Reacomodando para despejar x |
| x= |
(y/A)^ |
1/B |
| x= |
( |
5.7479999999999999E-7 |
/ |
22.094395440007393 |
)^(1 |
/ |
-6.5021382522536442 |
) |
|
| Evaluando |
| X( |
5.7479999999999999E-7 |
)= |
14.672470460671535 |
| Redodeando |
| X( |
5.7479999999999999E-7 |
)= |
14.672470460671535 |
1200
1200
85
3
6
12
False
False