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Generate 1 Hz , 5 Hz and 10 Hz signals with amplitudes 3, 2, 1

NB:Sine Waves

• A game where the user has to try to form the longest dictionary word from a set of random letters (vowels and consonants).

This is the criteria:

The code that you use to produce that application must use a combination of at least two of:

Loops

Vectors or Arrays

Conditional execution

Functions.

Visualisation of data

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.

. Make an octave code to integrate e* with respect to dx from 0 to 1, by Simpson’s ⅓ rule. Divide the limits into 6 equal parts.

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?

FWHM = 2𝜎sqrt2ln2

(v) Compare the theoretical and the experimental results of FWHM. (5)

(vi) What are the theoretical and experimental values of 𝒚 at FWHM? (5)

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

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

The Gaussian distribution also known as the Normal distribution, is given by the following

equation:

𝑦(𝑥) = 𝑒𝑥𝑝 −(𝑥−𝜇)^2/2𝜎2

where parameter 𝝁 is the mean and 𝝈 the standard deviation.

(i) Write a MATLAB code to create a 1000 point Gaussian distribution of random numbers

having 𝜇 = 0 and 𝜎 = 1. (20)

(ii) Plot this distribution. (10)

(iii) Prove that the full width–half maximum (FWHM), of the above distribution is given by :

FWHM = 2𝜎√2ln 2 (10)

(iv) Write a program that estimates the FWHM from your data/graph. (10)

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