MatLAB Answers

y(n) −2.56y(n −1)+2.22y(n−2)−0.65y(n−3) = x(n)+x(n−3)

A 10.00cm. tall light bulb is placed at a distance of 90.0cm from a concave mirror having a focal length of 21 cm . Determine the images l distance and the image size

A typical chemical formula for aerobic growth of a microorganisms is

C2H5OH + a(O2) + (b)NH3 —> (c)CH1.7H0.15O0.4 + (d)H2O + (e)CO2

where term CH_1.7H_0.15O_0.4 represents metabolism of the microorganism. The ratio of moles of CO₂ produced per mole of O₂ consumed is called the respiratory quotient, RQ, which can be determined experimentally. Given this ratio we have 4 constants, a-d that are unknown. We can perform a mass balance on each of the four key elements

Carbon: 2 = c + (RQ)a

Hydrogen: 6 + 3b = 1.7c + 2d

Oxygen: 1 + 2a = 0.4c + d + 2(RQ)a

Nitrogen: b = 0.15c 

Let RQ = 0.8 and then find the vector [a b c d] using Gauss Elimination Method.

Integrate the functions below between the limits 0 and 1 by Simpson’s rule. 

a) f(x) = sin(x)/(1+x^4)

b) f(x) = e^-x(1+x)^-5

c) f(x) = cos(x)e^-x^2

Find the root of the polynomial given below within the interval (-1, 1) using (a) the bisection method and (b) the Newton’s method

P = x/8[(63x^4)-(70x^2)+15]

QI. Find the number n of distinct permutations that can be formed from all the letters of each word: (a) THOSE (b) UNUSUAL (c) SOCIOLOGICAL

The following table shows the acceleration (m/s2) of a vehicle over time. Calculate the velocity (m/s) and the displacement (m) of the vehicle at t=1, 2,….,10 s using trapezoidal rule.

Time (s) Acceleration (m/s2)

0 0

1 1

2 3

3 5

4 8

5 10

6 13

7 15

8 18

9 21

10 25

4 Solve the following questions: (15 points) Question Three: (04/15) Write a complete MATLAB program to input the first (X) number of series, and then: 1. Add the next 70th numbers; 2. Calculate the average value 3. Compare between the average vale and the input vale (X), if it is more than 50 or not. 4. If the output from step 3 was no, divide the input vale (X) by 2 and then repeat step 3. 5. Plot the relationship between the 71th numbers include the input number (X) and its square values.

1. The change in the heat capacity of a substance due to temperature is given in the table below. Calculate the heat required to raise the temperature of 1-mole of the substance from 300 K to 1000 K using (a) Trapezoidal rule and (b) Simpson’s rule.

(Hint: )

T (K) / C_p (Cal/mol.K)

300 19.65

400 26.74

500 32.80

600 37.74

700 41.75

800 45.6

900 47.83

1000 50.16

1. Integrate the function below between the limits 0 and 0.8 by (a) Trapezoidal rule and (b) Simpson’s rule.

Find the root of the following equation using the Newton-Raphson method. Choose the initial guess as x(0) = 10. Choose the error tolerance as tol=1e-6. In other words, the iterations should be stopped when the error

|x(1) − x(i-¹)| ≤ tol.

x^2.5 23x^1.5 - 50x + 1150 = 0

i. Please report the value of x after 2 iterations

ii. Please report the converged solution, where error is less than 1e-6.

iii. Please report the number of iterations required to reach this converged solution.