Design a PDA to accept each of the following languages. You may use either PDAs that accept by final state or ones that accept by empty stack, whichever is more convenient. a) The set of all binary strings with more 1's than 0's. b) The ternary language in Q1(a). For each PDA, please show the transition digram instead of a sequence of transitions.

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?