Function Name: poly Parameters: list of ints, int Returns: int Description: A polynomial of degree n with coefficients a0,a1,a2,a3, . . . ,an is the function p(x) = (a0 * x0) + (a1 * x1) + (a2 * x2) + (a3 ∗ x3) + . . . + (an ∗ xn) This function can be evaluated at different values of x. For example: If p(x) = 1+2x1+ x2, then p(2) = 1+2 ∗ 2+22 = 9. If p(x) = 1+x2+x4, then p(2) = 21 and p(3) = 91. Write a function poly() that takes as input a list of coefficients a0, a1, a2, a3, . . . , an of a polynomial p(x) and a value x. The function will return poly(x), which is the value of the polynomial when evaluated at x.

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The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?