MatLAB Answers

A security company/Ambulance Service/Fire Service/Police Service wishes to optimally place vehicles in an area such that the response time to any given call within the area is reached within a given time. It also wishes to find the optimal number of security patrol cars to be deployed within the given area. Use a computational geometric approach to develop a code that receives the alarm/homes points, the targeted time to reach the alarm/home and the average speed of cars within the area and identifies where the vehicles can be optimally placed and also determines the number of vehicles required. The alarm/call points (x1, y1), (x2, y2), ..., (xn, yn) are stored in vectors X = [x1, x2, ..., xn], Y = [y1, y2, ..., yn]. Clearly state your assumptions.

Consider the following signal

x(n) = ASin(2πf1n) + BSin(2πf2n) + CSin(2πf3n); 

where A = 9, B = 8, C = 9

Also f1 = 250 Hz, f2 = 750 Hz and f3 = 989

Sampling Frequency fs = 4000 Hz

Perform the following operation on signal x(n) in MATLAB by developing a code:

a) Plot the signal x(n) in time domain.

b) Perform the DFT of the signal and plot magnitude values of signal in frequency 

domain. 

c) Apply a Low-pass FIR filter (Use convolution to apply filter) with 500 Hz cut-off 

frequency to filter the signal x(n).

d) Plot the signal x(n) in time and frequency domain after filtration

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*h^2*

(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?

According to a dietician, a person should consume exactly 200 gm of carbohydrates, at least 175

gm of proteins and at most 150 gm of fats in a meal. The dietician also recommends to have as

much amount of vitamins as possible. The three food items that the person eats has 80, 65 and 30

gm of carbohydrates per kilogram of food item. The same food items contain 10, 12, 23 gm of

proteins in each kilogram. Per kilogram of the same food items comprise of 32, 56 and 42 gm of

fats. Vitamins contained in per kilogram of the same food items are 70, 37 and 58 gm.

Determine how much kilogram of each food item the person should consume so as to have

maximum intake of vitamins by using appropriate built-in function present in MATLAB.

In a coal-fired power plant, operating on Carnot Cycle, it is possible to set any value for the

temperature of boiler in which heat is added to water at high temperature (T) and any value for

the temperature of condenser in which heat is rejected from steam at low temperature (TO), from

the following temperature list

T - [500 320 1000 775 385 670 845 1245 410 300 627 514)ⓇK

Being an operator of power plant you have to select T and Te from the above temperature list so

that power plant operates at its highest efficiency

Write a generalized MATLAB program to select two temperature values Th, and Te for above

condition, without using min and max built-in function

Print the maximum efficiency of cycle and the temperatures at which it occurs.

The equation x3 − 1.2x2 − 8.19x + 13.23 = 0 has a double root close to x = 2.

Determine this root with the Newton–Raphson method within four decimal

places.

Determine a and b for which f(x) = a sin(πx/2) + b cos(πx/2) fits the following data in the least-squares sense:-

(solve using MATLAB with steps).

x = −0.5, −0.19, 0.02, 0.20, 0.35, 0.50.

y =−3.558 , −2.874 , −1.995 , −1.040, −0.068, 0.677.

Explain Divergence and apply it on Matlab.

The formula for normalizing data-in a vector x-into the range [0,1] is given by

Z1=(x1-min(x))/(max(x)-min(x))

implement the formula above in a function

Plot the following functions on the same graph for x values from -π to π. selecting spacing to create a smooth plot: y1 = sin (x) y2 = sin(2x) y3 = sin(3x)