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)
Case ‘ ’
In your main script, create the following matrices and call your function with all operators.
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:
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