MatLAB Answers

Make an octave code to find the root of cos(x) – x * e x = 0 by using bisection method. The answer should be corrected up to four decimal places.

You are designing a spherical tank, as shown in figure below, to hold water for a sonll village in

a developing country. The volume of liquid it can hold can be compuned as

V=pi*h2*

(3R-h)/3

where V is the volume of water in the tank in m3, b is the height of water in the tank in m, R is

the radius of tank in m. If R is 3m and V is 30 m.

Formulate the equation in terms of height (h), from above generalized equation, representing the

present situation

Use the correct built-in function in MATLAB to determine all possible values of height (h) that

will satisfy the formulated equation i.e. determine all possible roots of the formulated equation.

From those values height (h) which one is the correct and why?

11. The battery life of a certain battery is normally distributed with a mean of 90 days and a standard deviation of 3 days.

For each of the following questions, construct a normal distribution curve and provide the answer.

a)    About what percent of the products last between 87 and 93 days?

b)    About what percent of the products last 84 or less days?

For each of the following questions, use the standard normal table and provide the answer.

c) About what percent of the products last between 89 and 94 days?

d) About what percent of the products last 95 or more days? 

Write a MatLab program to find the value of ×, y and z using Gauss-Elimination method in

the following equations

2x+4y + 2 - 3;

3x+2y - 2z= -2;

x-y+z=6.

Write a MatLab program to solve the following system of equation using Gauss-Seidel

methad:

54x+y+2=110；2x+ 15y+6z=72;=x+6y+272=85

11. The battery life of a certain battery is normally distributed with a mean of 90 days and a standard deviation of 3 days.

For each of the following questions, construct a normal distribution curve and provide the answer.

a)    About what percent of the products last between 87 and 93 days?

b)    About what percent of the products last 84 or less days?

For each of the following questions, use the standard normal table and provide the answer.

c) About what percent of the products last between 89 and 94 days?

d) About what percent of the products last 95 or more days? 

• Do the calculations on Matlab, print it out and then write your answers on the attached answer

sheet.

• Attach your Matlab printout to your answer sheet before you hand in.

1. Find all solutions for each of the following systems of equations (if the system is consistent):

(a) 6.5x − 2y = 7 (b) 3.5x1 + 4.5x2 + 5.5x3 = 11

2x − 0.75y = 1.75 x1 + 4x2 − 7x3 = −16

12x − y = 21 0.5x1 − 0.75x2 + 0.75x3 = 3.5

(c) − 0.75x1 + 0.75x2 = −6

2.5x1 + 2x2 − 4.5x3 = 2

1.25x1 + 1.25x2 − 2.5x3 = 0

(d) 3.4x1 + 3.4x2 − 15.3x3 = −20.4

0.5x1 + 0.25x2 − 0.75x3 = 1

0.75x1 + 0.5x2 − 1.5x3 = 1

Please note: You should use Matlab to write your systems in reduced row echelon form, but have to

interpret the results and give the solution(s) if the system is consistent.

The “Titans” cricket team has a winning rate of 75%. The team is planning to play 10 matches in the next season.

a)    Let X be the number of matches that will be won by the team. What are the possible values of X?

b)    What is the probability that the team will win exactly 6 matches?

c)    What is the probability that the team will lose 2 or less matches?

d)    What is the mean number of matches that the team will win?

e)    What are the variance and the standard deviation of the number of matches that the team will win?

write the Mathlab statement requried to calculate y(t) from the equation of y(t)={-3t² + 5, t>=0

3t² +5,t<0

write the mathlab statement required to calculate y(t) from the equation y(t)= -3t²+5