ECE 1620 - Assignment #2 - Due: 28 Jan 2022

• Each program must start with a comment containing your name and a brief (e.g. one line) description of the program.

• Programs must compile with no warnings or errors.

• For each problem, write a function in the form:

    double name_of_your_function( double name_of_your_input)
    {
      // ... local variables, computations ...
  
      return the_answer;
    }
  

• In the main program, use the function to compute a result, and display the function input and result values. Create an input variable and initialize it with a value of your choosing in the main program.

• Use separate names for functions and variables. For example, if you have a variable named area then you can not also have a function with the same name, so name the function farea or just f or something different.

• For programs which need the value of π, define it as a symbolic constant using atan near the top of your program, i.e.

  #define PI (4*atan(1))
  

Example: convert miles to kilometers

1. a2/p1.c - Fahrenheit to Celsius

   Write a function to convert degrees Fahrenheit to degrees Celsius.

   Degrees Celsius is degrees Fahrenheit, minus 32, times 5/9.

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2. a2/p2.c - Surface Area of Sphere

   Write a function to compute the surface area of a sphere of radius r.

   The area is 4πr².

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3. a2/p3.c - Birthday Collisions

   Write a function to compute the probability of a collision (i.e. duplicate value) when 5 values are selected randomly from a set of n possibilities. The probability of at least one collision is 1 minus the probability of no collisions:

   

   Test using n=365.

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4. a2/p4.c - Polynomials

   Write a function to evaluate the following rational polynomial (from page 39) using nested form to minimize the number of multiplications:

   

Nested form for polynomial evaluation (Horner's Rule), to minimize number of multiplications:

  Math:  p = a x3 + b x2 + c x + d

     C:  p = a*x*x*x + b*x*x + c*x + d;

         p = (a*x*x + b*x + c)*x + d; // factor out one x

         p = ((a*x + b)*x + c)*x + d; // factor out another x -> nested form

The evaluation of long expressions should be broken into several statements.

If we try to evaluate the expression in one statement, it becomes too long to be easily read:

  f = (x*x*x - 2*x*x + x - 6.3)/(x*x + 0.05005*x - 3.14);

We could break the statement into two lines:

  f = (x*x*x - 2*x*x + x - 6.3)/
      (x*x + 0.05005*x  - 3.14);

Another solution is to compute the numerator and denominator separately:

  numerator = x*x*x - 2*x*x + x - 6.3;
  denominator = x*x + 0.05005*x - 3.14;
  f = numerator/denominator;

The variables x, numerator, denominator, and f must be floating-point variables (i.e. double) in order to compute the correct value of f.