Solutions Manual for MATLAB: An Introduction with Applications, 6th Edition by Amos Gilat – (Chapter 1 - 11))

All Chapters Covered




SOLUTION MANUAL

, Chapter 1
Solved Problems

Problem 1
Script file:

clear, clc
disp('Part (a)')
(22+5.1^2)/(50-6.3^2)
disp('Part (b)')
44/7+8^2/5-99/3.9^2


Command Window:

Part (a)
ans =
4.6566
Part (b)
ans =
12.5768



Problem 2
Script file:

clear, clc
disp('Part (a)')
sqrt(41^2-5.2^2)/(exp(5)-100.53)
disp('Part (b)')
%alternative: nthroot(132,3)+log(500)/8
132^(1/3)+log(500)/8


Command Window:

Part (a)
ans =
0.8493
Part (b)
ans =
5.8685

,Problem 3
Script file:

clear, clc
disp('Part (a)')
(14.8^3-6.3^2)/(sqrt(13)+5)^2
disp('Part (b)')
45*(288/9.3-4.6^2)-1065*exp(-1.5)


Command Window:

Part (a)
ans =
43.2392
Part (b)
ans =
203.7148



Problem 4
Script file:

clear, clc
disp('Part (a)')
(24.5+64/3.5^2+8.3*12.5^3)/(sqrt(76.4)-28/15)
disp('Part (b)')
(5.9^2-2.4^2)/3+(log10(12890)/exp(0.3))^2


Command Window:

Part (a)
ans =
2.3626e+03
Part (b)
ans =
18.9551

Problem 5
Script file:

clear, clc
disp('Part (a)')
%alternative: sin(15*pi/180) instead of sind(15)
cos(7*pi/9)+tan(7*pi/15)*sind(15)
disp('Part (b)')
%alternatives: could use nthroot(0.18,3), could convert to radians
%and use regular trig functions
sind(80)^2-(cosd(14)*sind(80))^2/(0.18)^(1/3)

,Command Window:

Part (a)
ans =
1.6965
Part (b)
ans =
-0.6473

Problem 6
Script file:

clear, clc
x=6.7;
disp('Part (a)')
0.01*x^5-1.4*x^3+80*x+16.7
disp('Part (b)')
sqrt(x^3+exp(x)-51/x)


Command Window:

ans =
266.6443
Part (b)
ans =
33.2499

Problem 7
Script file:

clear, clc
t=3.2;
disp('Part (a)')
56*t-9.81*t^2/2
disp('Part (b)')
14*exp(-0.1*t)*sin(2*pi*t)


Command Window:

Part (a)
ans =
128.9728
Part (b)
ans =
9.6685

,Problem 8
Script file:

clear, clc
x=5.1; y=4.2;
disp('Part (a)')
3/4*x*y-7*x/y^2+sqrt(x*y)
disp('Part (b)')
(x*y)^2-(x+y)/(x-y)^2 +sqrt((x+y)/(2*x-y))


Command Window:

Part (a)
ans =
18.6694
Part (b)
ans =
448.5799

Problem 9
Script file:

clear, clc
a=12; b=5.6; c=3*a/b^2; d=(a-b)^c/c;
disp('Part (a)')
a/b+(d-c)/(d+c)-(d-b)^2
disp('Part (b)')
exp((d-c)/(a-2*b))+log(abs(c-d+b/a))


Command Window:

Part (a)
ans =
-0.1459
Part (b)
ans =
2.2925e+03

,Problem 10
Script file:

clear, clc
r=24;
disp('Part (a)')
%need to solve (a)(a/2)(a/4)=4/3 pi r^3
%could also use ^(1/3)
a=nthroot(8*4/3*pi*r^3,3)
disp('Part (b)')
%need to solve 2(a^2/2+a^2/4+a^2/8)=4 pi r^2
a=sqrt(8/7*4*pi*r^2)
disp(' ')
disp('Problem 11')
a=11; b=9;
%could be one long expression
s=sqrt(b^2+16*a^2);
Labc = s/2 + b^2/(8*a)*log((4*a+s)/b)


Command Window:

Part (a)
a =
77.3756
Part (b)
a =
90.9520

Problem 11
Script file:

clear, clc
a=11; b=9;
%could be one long expression
s=sqrt(b^2+16*a^2);
Labc = s/2 + b^2/(8*a)*log((4*a+s)/b)


Command Window:

Labc =
24.5637

,Problem 12
Script file:

clear, clc
x=pi/12;
disp('Part (a)')
%compare LHS and RHS
LHS = sin(5*x)
RHS = 5*sin(x)-20*sin(x)^3+16*sin(x)^5
disp('Part (b)')
LHS = sin(x)^2*cos(x)^2
RHS = (1-cos(4*x))/8


Command Window:

Part (a)
LHS =
0.9659
RHS =
0.9659
Part (b)
LHS =
0.0625
RHS =
0.0625

Problem 13
Script file:

clear, clc
x=24;
disp('Part (a)')
%compare LHS and RHS
LHS = tand(3*x)
RHS = (3*tand(x)-tand(x)^3)/(1-3*tand(x)^2)
disp('Part (b)')
LHS = cosd(4*x)
RHS = 8*(cosd(x)^4-cosd(x)^2)+1



Command Window:

Part (a)
LHS =
3.0777
RHS =
3.0777

,Part (b)
LHS =
-0.1045
RHS =
-0.1045

Problem 14
Script file:

clear, clc
alpha=pi/6; beta=3*pi/8;
%compare LHS and RHS
LHS = sin(alpha)+sin(beta)
RHS = 2*sin((alpha+beta)/2)*cos((alpha-beta)/2)


Command Window:

LHS =
1.4239
RHS =
1.4239

Problem 15
Script file:

clear, clc
Integral=sin(a*3*pi/2)/a^2 - 3*pi/2*cos(a*3*pi/2)/a - ...
sin(a*pi/3)/a^2 + pi/3*cos(a*pi/3)/a

Command Window:

Integral =
8.1072

Problem 16
Script file:

clear, clc
a=5.3; gamma=42; b=6;
disp('Part (a)')
c=sqrt(a^2+b^2-2*a*b*cosd(gamma))
disp('Part (b)')
alpha = asind(a*sind(gamma)/c)
beta = asind(b*sind(gamma)/c)
disp('Part (c)')
Total = alpha+beta+gamma

,Command Window:

Part (a)
c =
4.1019
Part (b)
alpha =
59.8328
beta =
78.1672
Part (c)
Total = 180.0000

Problem 17
Script file:

clear, clc
a=5; b=7; gamma=25;
disp('Part (a)')
c=sqrt(a^2+b^2-2*a*b*cosd(gamma))
disp('Part (b)')
alpha = asind(a*sind(gamma)/c)
%note that beta is over 90 deg and asind will give 1st quadrant
beta = 180 - asind(b*sind(gamma)/c)
disp('Part (c)')
%compare LHS with RHS
LHS=(a-b)/(a+b)
RHS=tand((alpha-beta)/2)/tand((alpha+beta)/2)


Command Window:

Part (a)
c =
3.2494
Part (b)
alpha =
40.5647
beta =
114.4353
Part (c)
LHS =
-0.1667
RHS =
-0.1667

, Problem 18
Script file:

clear, clc
L=4; theta=35;
%radius of cone opening and height
r=L*sind(theta/2);
H=L*cosd(theta/2);
%volume of cone + volume of hemisphere
V=pi*r^2*H/3 + 2/3*pi*r^3


Command Window:

V =
9.4245

Problem 19
Script file:

clear, clc
x=48; b=34; gamma=83;
disp('Part (a)')
c=sqrt(a^2+b^2-2*a*b*cosd(gamma))
disp('Part (b)')
s=(a+b+c)/2;
r=a*b*c/(4*sqrt(s*(s-a)*(s-b)*(s-c)))


Command Window:

Part (a)
c =
33.7574
Part (b)
r =
17.0055

Problem 20
Script file:

clear, clc
x0=-4; y0=-2; z0=-3; a=0.6; b=0.5; c=0.7;
xA=2; yA=-3; zA=1;
dA0=sqrt((xA-x0)^2+(yA-y0)^2+(zA-z0)^2);
d=dA0*sin(acos(((xA-x0)*a+(yA-y0)*b+(zA-z0)*c)/(dA0*sqrt(a^2+b^2+c^2))))

Command Window:

d =
4.6211