Let p1 be a convex polygon and p2 be an arbitrary polygon (not necessary convex) inside p1. the polygon separation problem is to find another polygon p3 to separate p1 and p2 (i. e., p3 is inside p1 and contains p2 in its interior) and minimize its number of edges. you may assume that p3 shares a vertex with p1. design a greedy algorithm to solve this problem and make your algorithm run as fast as possible. you should justify the correctness of your algorithm.

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.