CS 3540 Homework 2

Homework Assignment 2

Basic Functions in Racket

CS 3540
Programming Languages and Paradigms
Spring Semester 2023

Due: Tuesday, January 31, at 10:00 AM

Introduction

Template Source File
This assignment gives you your first chance to write Racket procedures. Download the file homework02.rkt and use it as a template for your submission. Please use the name homework02.rkt for your file!

This file includes a require expression at the top. It imports the rackunit module and enables you to write test cases for your solutions [ example code ]. The template file contains several test cases for each problem.
Do Not Use...
You do not need any advanced Racket features to solve these problems, only simple expressions.

Do not use a let expression in any function.

Do not use an internal define in any function.
Helpful Functions
You will find these Racket primitives useful on this assignment:

sqrt

expt

abs

You may want to use each for at least one problem.

To cause a number to evaluate as a floating-point number, you can make one of the arguments floating-point. In Problem 1, dividing by 180.0 instead of 180 will cause Racket to return a floating-point number.

Problems

Write a Racket function named quiz-percentage that takes exactly three integer arguments. Each argument will be in the range 0 .. 60. quiz-percentage returns the percentage of the points earned. For example:
```
     > (quiz-percentage 40 20 30)     ; average is 50% -- 90/180
     0.5
     > (quiz-percentage 60 50 40)     ; average is 150/180, or 0.83...
     0.8333333333333334
     > (quiz-percentage 60 60 60)     ; perfect score: 100%!
     1.0
```
I have provided check-= expressions for these three examples in your template file.

On Homework 1, you used the quadratic formula to find the roots of a quadratic equation. The expression under the radical, b² - 4ac, is called the discriminant. It can be used to determine how many solutions (0, 1, or 2) the equation has.

Write a Racket function named disc that takes three arguments, all integers: a, b, and c. disc returns b² - 4ac. For example:
```
     > (disc 1 4 4)     ; x² + 4x + 4
     0                  ; ... has one real solution

     > (disc -3 8 -4)   ; -3x² + 8x - 4
     16                 ; ... has two real solutions

     > (disc 2 1 3)     ; 2x² + x + 3
     -23                ; ... has zero real solutions
```
I have provided check-= expressions for these three examples in your template file.

A 10-foot ladder leans against a wall. If its base is 6 feet away from the bottom of the wall, then it reaches 8 feet high on the wall. This is a simple example of the Pythagorean theorem.

Write a Racket function named ladder-height that takes two arguments, the length of the ladder and the distance at the base. Both are in feet. The function returns the distance up the wall reached by the ladder, also in feet. For example:
```
     > (ladder-height 10 6)
     8
     > (ladder-height 13 5)
     12
     > (ladder-height 20 3.5)     ; that's steep... be careful!!
     19.691368667515217
```
I have provided check-= expressions for these three examples in your template file.

According to The Joy of Cooking, when you are cooking candy syrups, you should cook them 1 degree cooler than listed in the recipe for every 500 feet of elevation you are above sea level. For example, the recipe for Chocolate Carmels calls for a temperature of 244° Fahrenheit. If you were making your Chocolate Carmels in Denver, the Mile-High City, you would want to cook the syrup at 233.44°.

Write a Racket function named candy-temperature that takes two arguments, the recipe's temperature in degrees Fahrenheit and the elevation in feet, and returns the temperature to use at that elevation. For example:
```
     > (candy-temperature 244 5280)    ;; Denver, baby!
     233.44
     > (candy-temperature 302 977.69)  ;; the highest point in Cedar Falls
     300.04462                         ;;     is approx. 298m above sea level
     > (candy-temperature 302 -1401)   ;; the Dead Sea 1401 ft below sea level
     304.802
```
I have provided check-= expressions for these three examples in your template file.

Generally, the dimensions of engineered components are not exactly the specified value, but rather within a certain tolerance of the specified value. The tolerance generally depends upon the application and the material being used. For example, a metal piece used in construction that is listed as 5 cm in length might actually be any length within 1 mm of 5 cm, that is, between 4.9 cm and 5.1 cm, inclusive.

Write a Racket procedure named in-range? that takes three numbers as arguments: two numbers to compare, and a tolerance, epsilon. in-range? returns true if its first two arguments are within epsilon of one another, and false otherwise. For example:
```
     > (in-range? 4.95 5.0 0.1)
     #t
     > (in-range? 4.95 5.0 0.01)    ;; not anymore!
     #f
     > (in-range? 5.0 4.95 0.1)     ;; works both ways
     #t
     > (in-range? 5.0 5.95 0.1)
     #f
     > (in-range? 5.5 5.95 0.5)
     #t
```
I have provided check-true and check-false expressions for all of these examples in your template file.

Deliverables

By the due time and date, submit the following files electronically:

homework02.rkt, your file of function definitions, and
interactions.txt, an Interactions session that demonstrates each of your functions on a new example or two.

No hard copy is required.

Be sure that your submission follows all of the submission requirements. Use Save Interactions As Text... to create the file of interactions that you submit, and change the file extension to txt.

Be sure to use the specified names for your files! This enables an autograder to find and run your code.

Eugene Wallingford ..... wallingf@cs.uni.edu ..... January 24, 2023