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Write a script called 'prob1.m' that solves for the variables y, and z in terms of a user inputed x. The variables y and z are defined as follows:
y = x - 30 when 0 < x < 100
= 0.20*x + 800 when x > 100
= -50 otherwise
z = -1 when x < 0
= 0 when x = 0
= 1 when x > 0
Your script should prompt the user to input a value of x (use the input function). Next it should compute the values of y and z (surpress the output at first). Finally it should explicitly display the values of x, y, and z. From with the 'hw4.m' script call 'prob1.m'.
1. Use mathematical induction to prove Whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
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