A 10 Superscript negative 910−9-F capacitor (11 nanofaradnanofarad) is charged to 5050 V and then disconnected. One can model the charge leakage of the capacitor with a RC circuit with no voltage source and the resistance of the air between the capacitor plates. On a cold dry day, the resistance of the air gap is 66times×10 Superscript 131013 Upper OmegaΩ; on a humid day, the resistance is 77times×10 Superscript 6106 Upper OmegaΩ. How long will it take the capacitor voltage to dissipate to half its original value on each day

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?