Homework 1 - MATLAB Basics

Homework 1 - MATLAB Basics
Function Name: pythag
Inputs:
1. (double) length of side a
2. (double) length of side b
Outputs:
1. (double) length of the hypotenuse, c
Function Description:
The Pythagorean theorem states that when a triangle has a right angle, the square of
the hypotenuse is equal to the sum of the squares of the other two sides. You probably already
know this theorem from geometry class and have no doubt done used this formula countless
times.
a
2 + b
2 = c
2
Given the side lengths of a right triangle, a and b, use MATLAB to determine the length
of the hypotenuse. Now you'll never have to do this calculation yourself again!
Notes:
● Round your answer to the hundredths place (second decimal place).
Hints:
● The sqrt() and round() functions will prove useful.
Homework 1 - MATLAB Basics
Function Name: inscribe
Inputs:
3. (double) Side length of the square
Outputs:
2. (double) Area of the square not inscribed by the circle
Function Description:
When a circle is inscribed in a square, the diameter of the circle is equal to the side
length of the square.
Area of square = s
2
Area of a circle = πr
2
Use MATLAB to determine the area of the shaded region (the region not inscribed by the
circle), given the side length of the square. The area formulas for a square and circle are given
above.
Notes:
● Do not approximate the value of π .
● Round your answer to the hundredths place.
Hints:
● Use pi in MATLAB
Homework 1 - MATLAB Basics
Function Name: compound
Inputs:
4. (double) Future amount desired
5. (double) Initial investment
6. (double) Annual interest rate (given as a positive decimal)
7. (double) Number of times the interest is compounded per year
Outputs:
3. (double) Number of years
Function Description:
You have just come into a small fortune. Lucky you! Instead of spending it all at once,
you decide to invest your money so that it grows into an even larger desired amount. Use
MATLAB to determine how many years it will take for your investment to grow to that amount
based on a given annual interest rate and how many times the interest is compounded per year.
The compound interest formula, which may prove useful, is given below.
A = P(1 + )
r
n
nt
A = future value of investment
P = initial, principal investment
r = annual interest rate (decimal)
n = number of times the interest is compounded per year
t = number of years the money is invested
Notes:
● Round your answer up to the nearest year.
● The amount desired will always be greater than the initial investment
Hints:
● The log() and ceil() functions may prove useful.
Homework 1 - MATLAB Basics
Function Name: pizzaParty
Inputs:
1. (double) Number of party attendees
2. (double) Number of pizzas ordered
Outputs:
1. (double) Slices of pizza per person
2. (double) Slices of pizza left over
Function Description:
You decide to host a party and buy some pizzas for you and your friends. But, in order to
be fair, every person should get the same number of slices of pizza. Any extra slices will be left
over and saved for later.
You could try and calculate the pizza slice distribution yourself, but why bother when you
can have MATLAB do all the hard work! Given the number of people at the party and the
number of pizzas ordered, write a function that outputs how many slices of pizza each person
should should receive, and how many slices of pizza will be left over.
For example, if there are 5 people at the party, and 2 pizzas were ordered, each person
would get 3 slices, and 1 slice would be left over, so the first output would be 3 and the second
output would be 1.
Notes:
● Assume every pizza is cut into 8 slices.
● You cannot have fraction slices.
Hints:
● You may find the floor() and/or mod() functions useful.