Practica General Computo 15-2425

8/17/2019 Practica General Computo 15-2425

1/83


2/83


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D Ea El Et P

100 0.00145444 0.0022 0.00263731 37917.44

150 0.00218166 0.0023 0.00317012 47316.85

200 0.00290888 0.0024 0.00377115 53034.18250 0.0036361 0.0025 0.00441262 56655.64

300 0.00436332 0.0026 0.00507923 59064.06

350 0.00509054 0.0027 0.00576226 60740.06

400 0.00581776 0.0028 0.0064565 61953.08

450 0.00654498 0.0029 0.00715869 62860.67

500 0.00727221 0.003 0.0078667 63559.05

550 0.00799943 0.0031 0.00857909 64109.35

600 0.00872665 0.0032 0.00929486 64551.83

650 0.00945387 0.0033 0.01001327 64913.85

700 0.01018109 0.0034 0.0107338 65214.53750 0.01090831 0.0035 0.01145605 65467.57

800 0.01163553 0.0036 0.01217972 65682.97

850 0.01236275 0.0037 0.01290456 65868.21

900 0.01308997 0.0038 0.01363038 66028.97

950 0.01381719 0.0039 0.01435704 66169.61

1000 0.01454441 0.004 0.01508442 66293.54

100 0.0022

EJERCICIO # 1 ) CALCULO DE DISTANCIA MINIMA DE LINEA BASE PARREQUERIDA CON TS


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ESTACION

3 1.45444E-005

2 mm

12

12

OBTENER LA PRESICION

PRESICION DE LAESTACION PRESICION DE

100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 95010000

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

LINEA BASE EN FUNCION DE PRESICION REQUERIDA

Ea El Et


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0.22% 22%

TOTAL

ra

2 !!m


6/83

400.787 400.796 400.792 400.787400.79 400.788 400.797 400.794

400.793 400.791 400.792 400.787

1) "EDIA ARIT"ETICA400.791

2) RESID#ALES

1 -0.004 1.28403E-0052 -0.001 3.40278E-007

3 0.002 5.84028E-006

4 0.005 2.93403E-005

5 -0.003 6.67361E-006

6 0.000 1.73611E-007

7 0.001 2.00694E-006

8 0.006 4.11736E-005

9 0.001 2.00694E-006

10 -0.004 1.28403E-005

11 0.003 1.16736E-00512 -0.004 1.28403E-005

13 -0.004 1.28403E-005

14 -0.002 2.50694E-006

15 -0.003 6.67361E-006

16 -0.005 2.10069E-005

17 -0.006 3.11736E-005

18 -0.001 3.40278E-007

19 0.001 2.00694E-006

20 0.000 1.73611E-007

21 0.007 5.50069E-005

22 0.003 1.16736E-005

23 0.000 1.73611E-007

24 -0.002 2.50694E-006

S#"ATORIA $2 0.0002838333

"EDIA RESID#AL 1.2340580E-005

DES$IACION ESTANDAR 0.004

D&t&rm'(& la )ar'a(*a+ m&'a la &,)'a'( &,ta(ar


7/83

400.787 400.786 400.792 400.794400.789 400.785 400.791 400.791

400.788 400.790 400.798 400.789

0.005 2.93403E-005


8/83

212.22 212.15 212.29212.25 212.23 212.34

212.23 212.11 212.22

1) "EDIA ARIT"ETICA212.229

2) RESID#ALES

1 -0.009 8.71111111105E-0052 0.021 0.0004271111

3 0.001 4.44444444474E-007

4 -0.079 0.0062937778

5 0.001 4.44444444474E-007

6 -0.119 0.0142404444

7 0.061 0.0036804444

8 0.111 0.0122471111

9 -0.009 8.71111111105E-005

10 0.011 0.0001137778

11 -0.039 0.001547111112 0.021 0.0004271111

13 0.041 0.0016537778

14 -0.029 0.0008604444

15 0.021 0.0004271111

S#"ATORIA $2 0.0420933333

$ARIAN/A 0.0030066667

DES$IACION ESTANDAR 0.055

COEICIENTES

E50 73% 0.6745

E95 93% 1.96

E99.7 100% 2.968

DATOS $ALORES EN EL RANO TOTAL PORCENTAE

Calla $"P+ DS+ E50+ E95 RE$SAR SI A AL


9/83

11 15 73%

14 15 93%

15 15 100%

212.22 212.15 212.29 212.24

212.25 212.23 212.34 212.19

212.23 212.11 212.22 212.25

212.22 212.15 212.29 212.24

212.25 212.23 212.34 212.19

212.23 212.11 212.22 212.25

212.22 212.15 212.29 212.24212.25 212.23 212.34 212.19

212.23 212.11 212.22 212.25


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212.24 212.27212.19 212.2

212.25 212.25

-0.079 0.0062937778

DESARROLLO

LI"ITE IN LI"ITE S#P

212.192 212.266

212.122 212.337

212.067 212.39

#NAS OSER$ACION #ERA DEL NI$EL DE PROAILIDAD DE 99.7


11/83

212.27

212.2

212.25

212.27

212.2

212.25

212.27212.2

212.25


12/83

IAG-201-01 - CÓMPUTOS Y AJUSTES DE MÍNIMOS CUADRADOSMATRICULA 15-2425

17.5 15 13.4 23.9 25.2

39.5 23.5 26.5 21.3 22.3

32.5 32.2 24.2 35.7 28

30.2 33.7 19.7 19.7 25.1

31.2 24.6 30.2 16.8 26.9

POBLACIO13.4 24

15 24.2 $"P 24.902

16.8 24.6

16.8 25.1 R&,'al 132.296004 0.813604

17.5 25.2 98.049604 0.492804

18.8 25.8 65.642404 0.091204

19 26.5 65.642404 0.039204

19.5 26.9 54.789604 0.088804

19.7 27.2 37.234404 0.806404

19.7 27.9 34.833604 2.553604

20.7 28

29.181604 3.99200421.1 28.4 27.060804 5.280804

21.1 28.5 27.060804 8.988004

21.3 30 17.656804 9.597604

21.4 30.2 14.455204 12.236004

21.5 30.2 14.455204 12.945604

21.6 30.7 12.974404 25.989604

22.3 31 12.264004 28.068804

1) Se realizaron 50 observaciones independientes de una misma poligonal de co

a) Determinar media de la población (µ)

b) Determinar la varianza de la población (σ2)

c) Determinar Deviación et!ndar población (σ)

d) Determinar media de la m"etra ( )# Calc"lar para la m"etra $% m"etra 2 & m

e) Determinar la varianza de la m"etra (S 2)# Calc"lar para la m"etra $% m"etra

) Determinar Deviación et!ndar m"etra (S )# Calc"lar para la m"etra $% m"e

) Crear intervalo de conianza del *+, para la media de la m"etra# Calc"lar par

-) Crear intervalo de conianza del *+, para la varianza de la m"etra# Calc"lar p

i) Crear intervalo de conianza del *+, para la comparación de la varianza de l

.) Realizar pr"eba de lo intervalo de conianza para la media% la varianza & la co


13/83

22.5 31.2 11.573604 28.068804

22.7 32.2 10.903204 33.616804

23.3 32.5 6.770404 37.185604

23.5 33.7 5.769604 39.664804

23.5 35.3 4.848804 53.260804

23.9 35.7 2.566404 57.729604

24 39.5 1.965604 77.4048041.965604 108.118404

( 50 1.004004 116.596804

Smatr'a 1245.1 0.813604 213.101604

( 7.07106781

S( 0.79208833

)S2 1568.5098


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15/83

19.5 25.8 30 22.5 35.3

21.6 27.2 21.1 24 23.5

24 16.8 21.1 19 30.7

27.9 28.5 22.7 31 28.4

23.3 21.5 18.8 21.4 20.7

MUE13.4 $"P

15 R&,'al

17.5

$ar'a(*a 31.370196 19.5

D&,)'a'( 5.60091028 22.5

23.9

25.2

25.8

30

35.3

( 10

(-1 9

Smatr'a 228.1

( 3.16227766

S( 2.14042831

)S2 412.329

nexión. Para este set de observaciones:

etra '#

2 & m"etra '#

ra 2 & m"etra '#

a la m"etra $% m"etra 2 & m"etra '#

ara la m"etra $% m"etra 2 & m"etra '#

m"etra $ & la m"etra '#

mparación de la varianza de do m"etra#


16/83

I(t&r)al & (:a(*a &l 95% & la m&'a !ara l

$alr ta;la 2.262

E95%!ara m&'a 17.9683511717

27.6516488283

I(t&r)al & (:a(*a &l 95% !ara la )ar'a(*a $alr ta;la !ara 0.025 19.02

$alr ta;la !ara 0.975 2.700

a

t

S&

a

t

S&


17/83

at

S&


18/83

TRA 122.81 16.8

88.5481 $ar'a(*a 45.8143333 19

60.9961 D&,)'a'( 6.76862862 21.1

28.1961 24

10.9561 24.2

0.0961 28

1.1881 30.7

5.7121 32.2

8.9401 32.5

51.6961 35.7

156.0001(

(-1

Smatr'a

(

S(

)S2


19/83

a m&,tra 1 I(t&r)al & (:a(*a

$alr ta;la

=-> E95%

=?>

& la m&,tra 1 I(t&r)al & (:a(*a 21.6787066246 $alr ta;la !ara 0.025

152.7144444444 $alr ta;la !ara 0.975

Inte!"#$ %e &$n'"n(" %e# *+ ,"" #" &$,""&./n %e #" !"."n("

"&,tra 1 "&,tra 3

$ar'a(*a 45.8143333 $ar'a(*a 22.2448888889$alr ta;la => 4.03 $alr ta;la = 4.03

0.51105317 8.2999633873

I(t&r)al, & (:a(*a !ara la m&'a

$"P m&,tra1 22.81

$"P m&,tra2 26.42

$"P m&,tra3 23.54$"P !;la'( 24.902

Para m&,tra 1

22.81 @ 24.902

0.9773744788 S&

2.262


20/83

0.754 B 2.262

Para m&,tra 3

23.54 @ 24.9020.9131917665 S&


21/83

MUESTRA 2$P" 26.42

R&,'al 92.5444 $ar'a(*a 40.444

55.0564D&,)'a'( 6.3595597332

28.3024

5.8564

4.9284

2.4964

18.3184

33.4084

36.9664

86.118410

9

264.2

3.16227766

2.01106937

363.996


22/83

&l 95% & la m&'a !ara la m&,tra 2

2.262

!ara m&'a 21.8709611 =->

30.9690389 =?>

&l 95% !ara la )ar'a(*a & la m&,tra 219.02 19.1375394

2.700 134.813333

%e #" et" 1 et" 3

I(t&r)al, & (:a(*a !ara la )ar'a(*a

$ar'a(*a m& 45.8143333

$ar'a(*a m& 40.444

$ar'a(*a m& 22.2448889$ar'a(*a !;l 31.370196

Para m&,tra 1

6.1625204

19.02 S&

6.16 B 19.02

S&

Para m&,tra 2

6.98080714

19.02

6.98 B 19.02


23/83

S&

Para m&,tra 3

12.691983619.02

12.69 B 19.02


24/83

MUESTRA 316.8 $"P 23.54

18.8 R&,'al 45.4276 $ar'a(*a

20.7 22.4676 D&,)'a'(

21.4 8.0656

21.5 4.5796

23.3 4.1616

24.6 0.0576

26.9 1.1236

30.2 11.2896

31.2 44.3556

58.6756( 10

(-1 9

Smatr'a 235.4

( 3.16227766

S( 1.49147205

)S2 200.204


25/83

I(t&r)al & (:a(*a &l 95% & la m&'a !ara la m&,tra 3

$alr ta;la 2.262

E95%!ara m&'a 20.1662902 =->

26.9137098 =?>

I(t&r)al & (:a(*a &l 95% !ara la )ar'a(*a & la m&,tr$alr ta;la !ara 0.025 19.02 10.5259727

$alr ta;la !ara 0.975 2.700 74.1496296

Cm!ara'( & )ar'a(*a &(tr& , m&,tra,

$ar'a(*a m& 45.8143333

$ar'a(*a m& 40.444

$ar'a(*a m& 22.2448889

Cm!ara'( m&,tra 1 m&,tra 2

1.28320056

3.72

1.28 B 3.72

Cm!ara'( m&,tra 2 m&,tra 33.30558038

3.72

3.30 B 3.72

Cm!ara'( m&,tra 1 m&,tra 3


26/83

0.09258506

3.72

0.09 B 3.72


27/83

22.2448889

4.71644876


28/83


29/83


30/83

DE AGRIMENSURAIAG-201-01 - CÓMPUTOS Y AJUSTES DE MÍNIMOS CUAMATRICULA 15-2425

468.09 468.13 468.11 468.13 468.1 468.13

468.1 468.1 468.12 468.14 468.16 468.12

468.13 468.12 468.18 468.15 468.08 468.15

4ALORES PARA LA POBLACION

468.08 ( 27 $"P 468.122963

468.09 (-1 26

468.09 ,matr'a12639.32 R&,'al 0.00184582

468.1 ( 5.19615242 0.00108656

468.1 S( 0.00479835 0.00108656468.1 )S2 0.01616296 0.0005273

468.1 0.0005273

468.1 0.0005273

468.11 0.0005273

468.11 0.0005273

468.12 0.00016804

468.12 0.00016804

1) Se realizaron 27 observaciones independientes de una misma poligonal de co

a) Determinar media de la población (µ)

b) Determinar la varianza de la población (σ2)

c) Determinar Deviación et!ndar población (σ)

d) Determinar media de la m"etra ( )# Calc"lar para la m"etra $% m"etra 2 & m

e) Determinar la varianza de la m"etra (S 2)# Calc"lar para la m"etra $% m"etra

) Determinar Deviación et!ndar m"etra (S )# Calc"lar para la m"etra $% m"e

2) Para los resultados obtenidos en el eercicio anterior:

a) Crear intervalo de conianza del *+, para la media de la m"etra# Calc"lar par

b) Crear intervalo de conianza del *+, para la varianza de la m"etra# Calc"lar p

c) Crear intervalo de conianza del *+, para la comparación de la varianza de l

!) "ealizar prueba de los intervalos de con#ianza para la media$ la varianza % la c

&) 'eterminar cu(l de las medias muestrales posee ma%or precisión con relació


31/83

468.12 8.7791E-006

468.12 8.7791E-006

468.12 8.7791E-006

468.13 8.7791E-006

468.13 8.7791E-006

468.13 4.9520E-005

468.13 4.9520E-005468.13 4.9520E-005

468.14 4.9520E-005

468.14 4.9520E-005

468.15 0.00029026

468.15 0.00029026468.16 0.000731468.17 0.000731

468.18 0.001371740.00221248

0.00325322


32/83

468.12 468.09 468.14

468.1 468.1 468.11

468.12 468.13 468.17

468.09 (

468.09 (-1

$ar'a(*a 0.00062165 468.1 ,matr'a

D&,)'a'( 0.02493296 468.11 (

468.12 S(468.13 )S2

468.13

468.13

468.14

nexión. Para este set de observaciones:

etra '#

2 & m"etra '#

ra 2 & m"etra '#

a la m"etra $% m"etra 2 & m"etra '#

ara la m"etra $% m"etra 2 & m"etra '#

a m"etra $ & la m"etra 2#

omparación de la varianza de dos muestras.

a la media poblacional.


33/83


34/83

4ALORES PARA LA MUESTRA 1

9 $"P 468.115556 $ar'a(*a 0.0003527778

8 D&,)'a'( 0.0187823794

4213.04 R&,'al 0.00065309

3 0.00065309

0.00626079 0.00024198 Inte!"#$ %e &$n'"n(" %e# *0.00282222 3.0864E-005 $alr ta;la 2.306

1.9753E-005 E95%!ara m&'a0.00020864

0.00020864

0.00020864

0.00059753 nte!"#$ %e &$n'"n(" %e# *$alr ta;la !ara 0.025


35/83

$alr ta;la !ara 0.975


36/83

468.1 (

468.1 (-1

468.1 ,matr'a

468.1 (

+ %e #" e%." ,"" #" et" 1 468.11 S(468.12 )S2

468.101118 =-> 468.12

468.129993 =?> 468.14

468.16

,"" #" !"."n(" %e #" et"17.53 0.00016099


37/83

2.180 0.0012946


38/83


9 $"P 468.116667 $ar'a(*a 0.00045

8 D&,)'a'( 0.0212132034

4213.05 R&,'al 0.00027778

3 0.00027778

0.00707107 0.00027778 Inte!"#$ %e &$n'"n(" %e# 0.0036 0.00027778 $alr ta;la 2.306

4.4444E-005 E95%!ara m&'a1.1111E-005

1.1111E-005

0.00054444

0.00187778 te!"#$ %e &$n'"n(" %e# *$alr ta;la !ara 0.025


39/83



40/83

468.08 (

468.12 (-1

468.12 ,matr'a

468.13 (

+ %e #" e%." ,"" #" et" 2 468.13 S(468.15 )S2

468.100361 =-> 468.15

468.132973 =?> 468.17

468.18

,"" #" !"."n(" %e #" et"17.53 0.00020536


41/83

2.180 0.00165138


42/83


9 $"P 468.136667 $ar'a(*a 0.0009

8 D&,)'a'( 0.03

4213.23 R&,'al 0.00321111

3 0.00027778

0.01 0.00027778 Inte!"#$ %e &$n'"n(" %e# *0.0072 4.4444E-005 $alr ta;la 2.306

4.4444E-005 E95%!ara m&'a0.00017778

0.00017778

0.00111111

0.00187778 nte!"#$ %e &$n'"n(" %e# *$alr ta;la !ara 0.025


43/83



44/83

Dete.n"

P;la'(

$"P

0.02627415

+ %e #" e%." ,"" #" et" 3

468.113607 =->

468.159727 =?>

,"" #" !"."n(" %e #" et"17.53 0.00041072


45/83

2.180 0.00330275


46/83

&5# %e #" e%." et"#e ,$ee "$ ,e&../n &$n e#"&.

"&,tra 1 "&,tra 2 "&,tra 3

468.122963 $"P 468.115556 $"P 468.116667 $"P

0.02469145 0.02492885 0.02920235


47/83


48/83

n " #" e% Inte!"#$ %e &$n'"n(" %e# *+"&,tra 1

$ar'a(*a 0.00035278

468.136667 $alr ta;la => 4.43

0.17696402


49/83


50/83

,"" #" &$,""&./n %e #" !"."n(" %e #" et" 1 et" 2"&,tra 2

$ar'a(*a 0.00045

$alr ta;la => 4.43

3.47290123


51/83


52/83

Pe6" %e .nte!"#$ %e$"P m&,tra 468.115556 Para m&,tra

$"P m&,tra 468.116667 a 468.1155 @

$"P m&,tra 468.136667 t 1.18314201

$"P !;la' 468.122963

S&


53/83


54/83

&$n'"n(" ,"" #" e%."1 Para m&,tra 2 Para m&,tra 3

a468.1166 @ a468.136 @ 468.122

t 0.89043076 t 1.37037037

S&


55/83


56/83

Pe6" %e .nte!"#$ %e &$n'"n(" ,"$ar'a(*a m&,tra1 0.00035278 Para m&,tra 1

$ar'a(*a m&,tra2 0.00045 14.0973

$ar'a(*a m&,tra3 0.0009

$ar'a(*a !;la'( 0.00062165 S&


57/83


58/83

#" !"."n("Para m&,tra 2 Para m&,tra 3

11.0515986 5.5257993036

17.53 S&


59/83


60/83

Pe6" %e .nte!"#$ %e &$n'"n(" ,"$ar'a(*a m&,tra1 0.00035278 Cm!ara'( m&,tra 1$ar'a(*a m&,tra2 0.00045 1.62713125

$ar'a(*a m&,tra3 0.0009 S&


61/83


62/83

#" &$,""&.$n %e #" !"."n(" %e %$ et" m&,tra 2Cm!ara'( m&,tra 2 m&,tra 3 Cm!ara'( m&,tra 1

4.00 6.50852502

S&


63/83


64/83

&,tra 3


65/83


66/83

*+,- -*/ -+3

-4 2!05&62!66 -1200761066

48 459!961066

8' 82&0065766

', ';5160&66

,< ,1020961;66

DETER"INAR LOS A/I"#TES

-4 120.1186111

1) Se observó una poligonal cerrada % se computaron sus (ngulos$ distancias % un

FS#"ATORIA AN#LOS INTERNOS - = N -2>180

$ALORASOL#TO

AN#LOCORREIDO


67/83

48 59.65194444

8' 248.015

', 86.85027778

,< 102.1536111

Pl'


68/83

5> Call, & r&(aa, '(al&,

J=> 399000DEP

=N> 2000000LAT

EST J

A 399000 2000000

C 398744.0934 1999792.08245878

CD 398941.0401 1999718.21856265

DE 398947.9914 1999438.97651913

E 399230.5105 1999461.59194336

A 399287.6027 1999890.82006274

399000 2000000

A/I"#T INAL DISTANCIAS INALES

230.9070321426 329.7239971106

110.5583078069 210.3423183519

178.5740011165 279.3285514667

85.423277 283.422782436

7.57651617 433.0084280428

290.7878 307.6289223696

ERROR DE CIERRE LINEAL0.0235162


69/83

'*S-+8*- ?m)

!29.722 CON$ERTIR DE RADOS A DECI"ALES

210.!&5

279.!! A 120.119444 A>2!.&2; B 59.6527778 >&!!.007 C 248.015833 C>!07.;25 D 86.8511111 D>

E 102.154444 E>F 103.211389 >

SUMATORIA 720.005

0.0 0.3 18

0.0050

351.025

azimut de partida para la l=nea AB. "ealizar auste de la poligonal por el m>todo de 8ompass ?4r@ula).

PR#EALOICA


70/83

ra "'(t S&


71/83

AN#LOS INALES AN#LOS INALES

325.483755 325.483755143 325.483755

59.6512757 59.6512756644 59.6512757

248.015693 248.01569331 248.015693

86.8492759 86.8492758835 86.8492759

398700 398800 398900 399000 399101999100

1999200

1999300

1999400

1999500

1999600

1999700

1999800

1999900

2000000

2000100


72/83

2.0964798 RADIANES SOLO PARA ENCONTRAR LOS SENOS COSENOS

1.04113738

4.32869289

1.51583785

1.78293141.80137856

531.025


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74/83

0 399200 399300 399400


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120.1194444444 0

59.6527777778 0

248.0158333333 0

86.8511111111 0

102.1544444444

103.2113888889720.005


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DE AGRIMENSURA

IAG-201-01 - CÓMPUTOS Y AJUSTES DE MÍNIMOS CUADRADOSMATRICULA 15-2425

8oordenadas:

=nea -4 48 8' '-

-zimut $2345*6'+66 7$4+863966 2*94$'6+266 2'94256+366

'istancia +3$#$8 M 7$2#3$ M 7$+#'+ M +23#$9 M

'eterminar:

*+,- GRADO MINUTO SEGUNDO DISTANCIADECIMALESAB 124 9 35 541.17 124.159722BC 61 57 48 612.41 61.9633333CD 298 13 52 615.35 298.231111DA 238 20 54 524.18 238.348333

S#" 2293.11

*+,- A*'mt C, S&( LAT DEPAB 124.1597222222 -0.56150182 0.8274755 -303.867939 447.804918BC 61.9633333333 0.47003651 0.88264697 287.855061 540.541832CD 298.2311111111 0.47302924 -0.88104673 291.07854 -542.152106DA 238.3483333333 -0.52475374 -0.85125408 -275.065416 -446.210365

0.00024599 -0.01572057

1) Para la siguiente poligonal cerrada realizar el auste el m>todo de la br@ula$ partiendo de l

: A

0$5%555#55

; A

0+%555#55

a) AB % AC corregidas.

b) ,rror de cierre lineal.

c) 8oordenadas B$C.

d) 'eterminar -zimutes % 'istancias


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J=> 10000 DEP

=N> 5000 LAT

*+,- J A:IMU

AB 5000 10000 124.159507BC 4696.1320030734 10447.8086 61.9635234CD 4983.9869980029 10988.3547 298.231292DA 5275.0654719387 10446.2068 238.348122

5000 10000

ERROR DE CIERRE LINEAL0.0157225

4600 4700 4800 4900 5000 5100 5200 5300 5400

9400

9600

9800

10000

10200

10400

10600

10800

11000

11200

10000

10447.8086280729

10988.3546585191

10446.2067710544

10000

Cl


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ACT. LAT ACT. DEP LAT Crr&


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FINAL DISTANCIAS FINALES ANGULOS FINALES

541.173103 65.8113847751 65.8113848612.413675 117.8040166311 117.804017

615.346252 416.2677681151 56.2677681

524.17697 120.1168304787 120.11683

( C


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83/83

ANGULOS FINALES

65.8113848117.804017

56.2677681

120.11683

Documents

Practica General Computo 15-2425