Write a script to create the following arrays (10 points).r = [100, 99, 98, . . . , 2, 1]

s = [0,199,299,…,9899,1]

Create a 3-by-2 array of random numbers

Concatenate the matrix in part (c) horizontally to a 3-by-1 array of random numbers

Suppose that $1000 is left to sit in a bank account that pays 8% interest per year, compounded annually. (20 points)

Write a function that takes N as input and finds the account balance after N years. Use for loop.

Repeat (a) without using any loop.

For −π/2 ≤ x ≤ π/2, with point spacing Δx = 1/50:

Plot sin(x), cos(x), tan(x), and exp(x) in a single plot. Make sin a red line, cos a black dotted line, tan a blue line, and exp a green dashed line. Make a legend. Label your axes and give the figure a title. Set the y axis to be -1<y<1. (20 points)

Extra credit. Write a script that finds the x values at which cos(x)=exp(x). (hint: use find function for |cos(x)-exp(x)|<0.001) (5 points)

While. Write a script that takes an integer, N, from the user input. Then computes the largest integer k such that 2k<=N. For example, if N =100, then k would be 6, because 2^6=64 100.

Display/print the message showing the k value: ‘the largest integer k is ….’

Hint: initially, set k=0. In a while loop, check if 2^k is less than N, if not, break the loop. (25 points)

Choose only one question (25 points). You can get extra credit for solving two or three questions:

5. Function, switch statement. Write a function that takes two square matrices of the same size and an operator name as inputs and apply the operator on the two matrices. The operator name can be ‘ ’, ‘-‘, ‘*’, and ‘/’. For example, when the function opName input is ‘ ‘, the function calculates A B; when the function opName input is ‘-‘, the function calculates A-B.

Function C = ApplyOp(A, B, opName)

Switch opName

Case ‘ ’

C=…;

…

In your main script, create the following matrices and call your function with all operators.

A=421020109,B=340715095

Function. You work for an engineering design firm that has been contracted to evaluate the concentration of pollutants. A tall chimney releases (20 kg/s) of smoke into a steady uniform wind of speed (u( m/s)). An expression for the decay of the peak pollutant concentration C(ppm) with distance downwind is given as:

C(x,y,z)=M4πρDx.e−(y2 z2)u4Dx

Assuming that the diffusion coefficient D to be 0.01 m2/s, and the density of air to be ρ=1.225kgm3

Write a function which gets the location(x,y,z) and the wind speed, u, as inputs and calculates the pollutant concentration.

Call your function to find how pollution concentration at location (x=3000, y=0, z=10) changes with wind speed 0<u<12 m/s. Plot the pollution concentration vs wind speed.

Loops and flow control. Make function called loopTest(N) that loops through the values 1 through N and for each number n it should display ‘n is divisible by 2’, ‘n is divisible by 3’, ‘n is divisible by 2 AND 3’ or ‘n is NOT divisible by 2 or 3’. Use a for loop, the function mod or rem to figure out if a number is divisible by 2 or 3, and num2str to convert each number to a string for displaying. You can use any combination of if, else, and elseif