ap assignment 1
TRANSCRIPT
-
7/31/2019 AP Assignment 1
1/17
Q#01: Solve the following system of linear equations by using crammers rule.
10x+4y-z+2w+u=112
x-10y+z-3w+2u=120
2x-3y+10z+w-2u=135
-x+3y+z-10w+u=145
3x-y+3z-w+10u=99
A B C D E F G H I
1 Matrix
A B X
2 10 4 -1 2 1 112 x
3 1 -10 1 -3 2 120 y
4 2 -3 10 1 -2 135 z
5 -1 3 1 -10 1 145 w
6 3 -1 3 -1 10 99 u
78 det A= 111993
9
10 D1
11 112 4 -1 2 1
12 120 -10 1 -3 2 det D1= 1941372
13 135 -3 10 1 -2 x= 17.33476
14 145 3 1 -10 1
15 99 -1 3 -1 10
16
17 D218 10 112 -1 2 1
19 1 120 1 -3 2
20 2 135 10 1 -2 det D2= -488857
21 -1 145 1 -10 1 y= -4.36507
22 3 99 3 -1 10
23
-
7/31/2019 AP Assignment 1
2/17
24 D3
25 10 4 112 2 1
26 1 -10 120 -3 2 det D3= 1151746
27 2 -3 135 1 -2 z= 10.28409
28 -1 3 145 -10 1
29 3 -1 99 -1 10
30
31 D4
32 10 4 -1 112 1
33
1 -10 1 120 2 det D4=
-
1854876
34 2 -3 10 135 -2 w= -16.5624
35 -1 3 1 145 1
36 3 -1 3 99 10
37
38 D539 10 4 -1 2 112
40 1 -10 1 -3 120 det D5= -53578
41 2 -3 10 1 135 u= -0.4784
42 -1 3 1 -10 145
43 3 -1 3 -1 99
X=|D1|/|A|
Y=|D2|/|A|
Z=|D3|/|A|
w=|D4|/|A|
u=|D5|/|A|
-
7/31/2019 AP Assignment 1
3/17
Q#1(b): Solve the following system of equation by using inversion of matrices.
10x+4y-z+2w+u=112
X-10y+z-3w+2u=120
2x-3y+10z+w-2u=135
-x+3y+z-10w+u=145
3x-y+3z-w+10u=99
A B C D E F G H I
1 Matrix A B X2 10 4 -1 2 1 112 x
3 1 -10 1 -3 2 120 y
4 2 -3 10 1 -2 135 z
5 -1 3 1 -10 1 145 w
6 3 -1 3 -1 10 99 u
7
8 Inverse
A
9 0.100051 0.041815 0.010018 0.010206 -0.01739 x= 17.33476
10 0.006786 -0.09132 0.002464 0.027466 0.015331 y= -4.3650711 -0.02155 -0.03506 0.092175 0.012795 0.026323 z= 10.28409
12 -0.01254 -0.03656 0.005974 -0.09285 0.019046 w= -16.5624
13 -0.02413 -0.01481 -0.02981 -0.01344 0.100756 u= -0.4784
14
BAX1
-
7/31/2019 AP Assignment 1
4/17
Q#1(c): Solve the following system of equation by using Jacobi Method.
10x+4y-z+2w+u=112
X-10y+z-3w+2u=120
2x-3y+10z+w-2u=135
-x+3y+z-10w+u=145
3x-y+3z-w+10u=99
A B C D E F G H
1 Matrix
A B
2 10 4 -1 2 1 1123 1 -10 1 -3 2 120
4 2 -3 10 1 -2 135
5 -1 3 1 -10 1 145
6 3 -1 3 -1 10 99
7 k x y z w u
8 0 0 0 0 0 0
9 1 11.2 -12 13.5 -14.5 9.9
10 2 16.56 -6.1 18.29 -3.03 5.14
11 3 11.903 -7.184 13.349 -4.047 0.358
124 13.5123 -8.9985 13.7509
-11.1022 3.4475
13
5 15.3
-
7.47396 15.29681
-
8.27555 3.73111
14
6 13.9419
-
7.36654 14.25597
-
6.89204 2.295908
15
7 13.86984
-
8.03183 14.06997
-
8.74307 2.866498
16
8 14.4677
-
7.75841 14.58319
-
8.43508 3.195549
17
9 14.21251
-
7.61229 14.4166
-
7.81025 2.80408318
10 14.0849
-
7.79525 14.28303
-
8.23337 2.853522
19
11 14.25112
-
7.76917 14.41564
-
8.29165 2.992484
20
12 14.22519
-
7.70566 14.40819
-
8.08846 2.906055
21 13 14.16853 - 14.35672 - 2.889401
-
7/31/2019 AP Assignment 1
5/17
7.74661 8.16067
22
14 14.20616
-
7.75353 14.38422
-
8.21071 2.933152
23
15 14.21182
-
7.73326 14.39253
-
8.15702 2.919308
24 16 14.19353 -7.74 14.37718-
8.16173 2.907725
25
17 14.19986
-
7.74521 14.38101
-
8.18177 2.918962
26
18 14.20444
-
7.73994 14.38556
-
8.17031 2.918437
27
19 14.19964
-
7.74028 14.38181
-
8.16743 2.914025
28
20 14.20002
-
7.74231 14.3817
-
8.17355 2.916335
29
The following formulas are used in Jacobi Method.
=($G$2-$B$2*C8+$C$2*D8-$D$2*E8-$E$2*F8)/$A$2
=($G$3-$A$3*B8-$C$3*D8+$D$4*E8-$E$3*F8)/$B$3
=($G$4-$A$4*B8+$B$4*C8-$D$4*E8-$E$4*F8)/$C$4
=($G$5+$A$5*B8-$B$5*C8-$C$6*D8-$E$6*F8)/$D$5
=($G$6-$A$6*B8+$B$6*C8-$C$6*D8+$D$6*E8)/$E$6
-
7/31/2019 AP Assignment 1
6/17
Q#1(d): Solve the following system of equation by using Gauss seidal Method.
10x+4y-z+2w+u=112
X-10y+z-3w+2u=120
2x-3y+10z+w-2u=135
-x+3y+z-10w+u=145
3x-y+3z-w+10u=99
A B C D E F G
1 Gauss
seidal
method
2 Matrix A B
3 10 4 -1 2 1 112
41 -10 1 -3 2 120
5 2 -3 10 1 -2 135
6 -1 3 1 -10 1 145
7 3 -1 3 -1 10 99
8 K x y z w u
9 0 0 0 0 0 0
10
1 11.2 -10.88 14.524-
15.1916 4.78996
11
2 16.65892-
12.4812 16.38973-
14.4605 2.679574
12
3 17.17765-
12.4455 15.78008-
14.6699 2.724222
13
4 17.26175
-
12.5519 15.82507
-
14.6845 2.69759614
5 17.30541-
12.5528 15.81272-
14.6843 2.688266
15
6 17.30786-
12.5556 15.81118-
14.6859 2.688438
16
7 17.30945 -12.556 15.8112-
14.6859 2.687997
17
8 17.30967-
12.5561 15.81108 -14.686 2.687978
18
9 17.30972-
12.5561 15.81108 -14.686 2.687967
19
10 17.30973-
12.5561 15.81108 -14.686 2.687965
=($G$3-$B$3*C9+$C$3*D9-$D$3*E9-$E$3*F9)/$A$3
=($G$4-$A$4*B10-$C$4*D9+$D$4*E9-$E$4*F9)/$B$4
=($G$5-$A$5*B10+$B$5*C10-$D$5*E9-$E$5*F9)/$C$5
=($G$6+$A$6*B10-$B$6*C10-$C$6*D10-$E$6*F9)/$D$6
=($G$7-$A$7*B10+$B$7*C10-$C$7*D10+$D$7*E10)/$E$7
-
7/31/2019 AP Assignment 1
7/17
Q#02(a): If y=f(x), then ()
=
[+2(++) +]
Where, h= ( ) , n= 10 given, = f ()
Then evaluate the following integral.
1:
A B C D E F G
1 Trapezoidal
Rule
2 n Xo Xn h X f(x) Integral
3
10 0 1 0.1 0 **0 *0.691478424 0.1 0.198025 0.2 0.384615
6 0.3 0.550459
7 0.4 0.689655
8 0.5 0.8
9 0.6 0.882353
10 0.7 0.939597
11 0.8 0.97561
12 0.9 0.994475
13 1 1
The following formulas have been used:
*=$D$3*(F3+2*SUM (F4:F12) +F13)/2
**=2*E3/ (1+E3^2)
-
7/31/2019 AP Assignment 1
8/17
(b): If y=f(x), then ()
=
[+2(++) +]
Where, h= ( ) , n= given, = f ()
Then evaluate the following integral.
With n=16
A B C D E F G
1 Trapezoidal
Rule
2 n Xo Xn h X f(x) Integral
3
16 0 1 0.0625 0 **1 *0.7852354034 0.0625 0.9961095 0.125 0.984615
6 0.1875 0.966038
7 0.25 0.941176
8 0.3125 0.911032
9 0.375 0.876712
10 0.4375 0.839344
11 0.5 0.8
12 0.5625 0.759644
13 0.625 0.71910114 0.6875 0.679045
15 0.75 0.64
16 0.8125 0.602353
17 0.875 0.566372
18 0.9375 0.532225
19 1 0.5
The Following formulas have been used:
*=$D$3*(F3+2*SUM(F4:F18) +F19)/2
**=1/(1+E3^2)
-
7/31/2019 AP Assignment 1
9/17
(c): If y=f(x), then ()
=
[+2(++) +]
Where, h= ( ) , n= given, = f ()
Then evaluate the following integral.
dx and n=16
A B C D E F G
1 Trapezoidal
Rule
2 n Xo Xn h X f(x) Integral
316 0 90 5.625 0 0 68.2819728
4 5.625 0.313077
5 11.25 0.441696 16.875 0.538781
7 22.5 0.618614
8 28.125 0.686583
9 33.75 0.745366
10 39.375 0.796488
11 45 0.840896
12 50.625 0.87921
13 56.25 0.91185
14 61.875 0.939107
15 67.5 0.96118716 73.125 0.978233
17 78.75 0.990346
18 84.375 0.997589
19 90 1
The following formulas have been used:
*=$D$3*(F3+2*SUM(F4:F18)+F19)/2
**=SQRT(SIN(RADIANS(E3)))
-
7/31/2019 AP Assignment 1
10/17
Q#03: Find the value of sinx.
Sinx= x-
+
-
x=10
A B C D E F G
1
n
x in
degrees x in radians Terms
2 0 10 0.17453293 *0.174533
3 1 -0.00089
4 2 1.35E-06
5
3 -9.8E-10 sinx= 0.1736486 4 4.14E-137 5 -1.1E-16
8 6 2.24E-20
9 7 -3.2E-24
10 8 3.64E-28
11 9 -3.2E-32
12 10 2.35E-36
13 11 -1.4E-40
14 12 7.18E-45
15 13 -3.1E-4916 14 1.17E-53
17 15 -3.8E-58
18 16 1.1E-62
19 17 -2.8E-67
20 18 6.47E-72
21 19 -1.3E-76
22 20 2.47E-81
The following formulas have been used:
*=((-1)^A2)*($C$2^(2*A2+1))/FACT(2*A2+1)
-
7/31/2019 AP Assignment 1
11/17
(b): X=15
A B C D E F G
1
n
x in
degrees x in radians Terms
2 0 15 0.26179939 0.261799
3 1 -0.00299
4 2 1.02E-05
53 -1.7E-08 sinx= 0.258819
6 4 1.59E-11
7 5 -9.9E-15
8 6 4.36E-189 7 -1.4E-21
10 8 3.58E-25
11 9 -7.2E-29
12 10 1.17E-32
13 11 -1.6E-36
14 12 1.81E-40
15 13 -1.8E-44
16 14 1.49E-48
17 15 -1.1E-52
18 16 7.15E-5719 17 -4.1E-61
20 18 2.12E-65
21 19 -9.8E-70
22 20 4.1E-74
The following formulas have been used:
*=((-1)^A2)*($C$2^(2*A2+1))/FACT(2*A2+1)
-
7/31/2019 AP Assignment 1
12/17
(c): x=30
A B C D E F G
1n
x indegrees x in radians Terms
2 0 30 0.52359878 0.523599
3 1 -0.02392
4 2 0.000328
53 -2.1E-06 sinx= 0.5
6 4 8.15E-09
7 5 -2E-11
8 6 3.57E-14
97 -4.7E-1710 8 4.7E-20
11 9 -3.8E-23
12 10 2.46E-26
13 11 -1.3E-29
14 12 6.09E-33
15 13 -2.4E-36
16 14 8.02E-40
17 15 -2.4E-43
18 16 6.14E-47
19 17 -1.4E-5020 18 2.91E-54
21 19 -5.4E-58
22 20 9.01E-62
The following formulas have been used:
*=((-1)^A2)*($C$2^(2*A2+1))/FACT(2*A2+1)
-
7/31/2019 AP Assignment 1
13/17
Q#03(b): Find the value of cosx.
Cosx= 1 -
+
-.
(1) X=10
A B C D E F G
1
n
x in
degrees x in radians Terms
2 0 10 0.17453293 *1
3
1
-
0.01523
4
2
3.87E-
05
5 3 -3.9E-08
6
4
2.14E-
11
75 -7.2E-15 cosx= 0.984807753
8
6
1.67E-
18
9 7 -2.8E-22
10
8
3.54E-
26
11 9 -3.5E-30
12
10
2.83E-
3413 11 -1.9E-38
14
12
1.03E-
42
15 13 -4.8E-47
16
14
1.94E-
51
17 15 -6.8E-56
18
19
20
21
22
The following formulas have been used:
*=(-1)^(A2)*($C$2^(2*A2))/FACT(2*A2)
-
7/31/2019 AP Assignment 1
14/17
(2) X=15
A B C D E F G
1
n
x in
degrees x in radians Terms
2 0 15 0.26179939 1
3 1 -0.03427
4 2 0.000196
5 3 -4.5E-07
6 4 5.47E-10
75 -4.2E-13 cosx= 0.965925826
8 6 2.16E-16
9 7 -8.1E-20
10 8 2.33E-23
11 9 -5.2E-27
12 10 9.4E-31
13 11 -1.4E-34
14 12 1.73E-38
15 13 -1.8E-42
16 14 1.66E-46
17 15 -1.3E-50
The following formulas have been used:
*= (-1)^(A2)*($C$2^(2*A2))/FACT(2*A2)
-
7/31/2019 AP Assignment 1
15/17
-
7/31/2019 AP Assignment 1
16/17
Q#04: If ( )
,then find the value offrom the following data.
12,29,34,37,25,60,15,20,30,35,42,47,48,50,57,59,24,53,51,58.
A B C D E F
1 x x- ( )2 12 39.3 -27.3 745.29
3 15 -24.3 590.49
4 20 -19.3 372.49
5 24 -15.3 234.09
6 25 -14.3 204.49
7 29 -10.3 106.09
8 30 -9.3 86.49 ( )= 4452.29 34 -5.3 28.09
1035 -4.3 18.49 = 222.61
11 37 -2.3 5.29
1242 2.7 7.29 = 14.92012
13 47 7.7 59.29
14 48 8.7 75.69
15 50 10.7 114.49
16 51 11.7 136.89
17 53 13.7 187.69
16 57 17.7 313.29
19 58 18.7 349.69
20 59 19.7 388.09
60 20.7 428.49
-
7/31/2019 AP Assignment 1
17/17
Q#05: Find the area of circle, perimeter of circle, volume of cylinder, with given
height (h), volume of the sphere for radius r. (radius for circle and sphere is the
same).radius is taken as 4cm, and height is taken as 6cm.
a) Area of circle= = PI()*A2^2b) Perimeter of circle= p= =2*PI()*A2c) Volume of cylinder= v= =PI()*A2^2*B2
d) Volume of sphere= v=
=(4*PI()*A2^3)/3
A B C D E F
1 Radius
(r)
Height
(h)
Area of
circle
perimeter of
circle
volume of
cylinder
volume of
sphere2 4 6 50.26548246 25.13274123 301.5928947 268.0825731
3
4
5
6
7
8
9