Consider the following argument. If compilation of a computer program produces error messages, then the program is not correct. Compilation of this program does not produce error messages. ∴ This program is correct. Which of the following choices correctly describes whether the argument is valid or invalid and includes a correct justification? Valid, universal modus tollens. Valid, universal modus ponens. Invalid, converse error. Invalid, inverse error.

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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?