Objectives:

1. (16 points) Create m-file scripts/functions to solve some basic vector problems in MATLAB
2. (4 points) Matrix Problem

Tasks:

1. Create m-file scripts/functions to solve some basic vector problems in MATLAB

A. (8 points) We have a vector of student letter grades in courses and a corresponding vector of the credit hours for each course. Here are two sample vectors you can use, but your code should work for any two vectors of the same length:

grades = ['A' 'B' 'A' 'C' 'A' 'D' 'B' 'B' 'A' 'A' 'D' 'C' 'A' 'B' 'A' 'A' 'A' 'B' 'C' 'A' 'C' 'C']; 
creditHours = [3 3 2 5 3 2 3 3 4 5 3 3 3 3 3 3 2 0 4 5 3 3];

Write a single MATLAB statement to create each result.

Aa. How many As did the student earn? s

Ab. Find the grades for courses worth 4 or more credit hours.

Ac. Remove any grades for zero credit hour courses.

Ad. Find the total number of credit hours for courses with a C grade.

B. (4 points) Individual ocean waves have crests (high points) and troughs (low points). The vertical distance between a crest and a trough is the wave height, and the horizontal distance from crest to crest is the wavelength. The interaction of individual waves creates a set of waves with varying peaks and troughs. If we consider two waves at a time, the combination can be constructive interference or destructive interference, depending if the crests meet crests or not.

To investigate the interference pattern of two waves, we will model a wave by a sinusoid s(t) = A * sin(2*pi*f*t + phi)

where A is amplitude, f is frequency in cycles per second, phi is the phase shift in radians, and t is time

Write a function called waveSum that takes 3 vector arguments (amplitude, frequency, phaseShift). Each argument is a vector of two elements, one for each wave. Calculate and plot the wave heights of the two waves combined for t ranging from 0 to 5 by .01. Also find and return the times t with the largest combined wave height. Here are some interesting waves to test (plots not shown).

Here are some interesting waves to test.

>> waveSum([3 5], [1 .2], [0,0]) ans = 1.25 
>> waveSum([3 5], [.25 .5], [0,pi/3]) ans = 0.2600 4.2600 
>> waveSum([5 5], [.2 .5], [0,0]) ans = 0.59 
>> waveSum([5 3], [1 .5], [0,pi/2]) ans = 0.2200 2.2200 4.2200

C. (4 points) A party store sells helium tanks to fill spherical balloons. Write a function that accepts two inputs: a vector of increasing balloon diameters in inches and a scalar of a helium tank size in cubic feet. The helium tank cannot fill balloons with diameters smaller than 6 inches, so your function should remove those diameters from the vector parameter and the table displayed. The function displays a table showing the size of balloon, volume of the balloon in cubic feet, and number of balloons of each diameter that size of tank can fill. Volume of a sphere: (4/3) pi r^3. The function should:

• calculate the total volume of each balloon in cubic feet
• calculate the # of balloons of each diameter the helium tank will fill
• display a of table of balloon diameter, balloon volume (cubic feet), # of each size of balloon helium tank will fill
• Do not worry about formatting the output to a specific number of decimal places.

SAMPLE RUN
>> balloons([8 5 12 9 2 15],25);
Diameter(in)Volume(ft^3)BalloonCount
    8.0000    0.1551  161.0000
   12.0000    0.5236   47.0000
    9.0000    0.2209  113.0000
   15.0000    1.0227   24.0000

2. (4 points) Matrix Problem

We want to estimate the amount of soil that must be removed to prepare the foundations of a building. The first step was to survey the land which results in a rectangular grid defining the depth (in feet) of the soil at every grid point. The depth matrix is given below (you can copy and paste this). The next step is to consider the drawing of the basement on the same grid, each square in the grid represents a 10 foot by 10 foot square. The shaded areas indicate places where the soil must be removed to make the building foundation. Create a matrix "area" containing a number between zero and one for each square in the grid determined by how much of the square needs to be removed (you estimate this by looking at the shaded grid). Then calculate and echo the total amount of soil to be removed.

depth = [8 8 9 8 8 8 8 8 7 8 7 7 7 7 8 8 8 7 8 8 8 8 8 8 8 7 7 7 7 7 8 7 8 8 8 7 8 8 8 8 7 7 8 7 8 8 8 8 8 7 8 8 8 8 7 7 7 8 7 8 8 8 8 8 8 8 7 6 7 7 7 7 8 8 8 8 8 8 8 8 7 7 7 7 7 6 6 7 7 8 8 7 7 8 7 7 8 7 7 7 7 7 7 7 7 7 7 8 9 8 8 9 8 7 8 7 7 7 7 7 6 7 6 7 7 8 8 8 8 9 9 8 8 8 7 6 6 6 6 7 7 8 7 8 9 8 8 7 7 7 7 7 7 6 6 7 7 7 8 8 7 8 9 8 8 7 7 7 6 7 7 6 6 8 8 8 9 9 7 8 9 9 8 8 8 8 7 7 7 7 7 8 8 9 9 9 8 8 9 8 8 7 7 8 7 7 7 7 8 8 9 9 9 8 7 8]; % 12 rows and 18 columns

Copyright CS, Illinois Institute of Technology