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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?

Write a program that keeps asking the user for new values to be added to a list until the user enters 'exit' ('exit' should not be added to the list). these values entered by the user are added to a list we call 'initial_list'. then write a function that takes this initial_list as input and returns another list with 3 copies of every value in the initial_list. finally, inside print out all of the values in the new list. for example: input: enter value to be added to list: a enter value to be added to list: b enter value to be added to list: c enter value to be added to list: exit output: a b c a b c a b c note how 'exit' is not added to the list. also, your program needs to be able to handle any variation of 'exit' such as 'exit', 'exit' etc. and treat them all as 'exit'.