(Numerical analysis) a. The following is an approximate conversion formula for converting Fahrenheit to Celsius temperatures:

C e l s i u s   =   ( F a h r e n h e i t   −   30 )   /   2

Using this formula, and starting with a Fahrenheit temperature of 0 degrees, write a C++ program that determines when the approximate equivalent Celsius temperature differs from the exact equivalent value by more than 4 degrees. (Hint: Use a while loop that terminates when the difference between approximate and exact Celsius equivalents exceeds 4 degrees.)

b. Using the approximate Celsius conversion formula given in Exercise 8a, write a C++ program that produces a table of Fahrenheit temperatures, exact Celsius equivalent temperatures, approximate Celsius equivalent temperatures, and the difference between the exact and approximate equivalent Celsius values. The table should begin at 0 degrees Fahrenheit, use 2-degree Fahrenheit increments, and terminate when the difference between exact and approximate values is more than 4 degrees.