A 100 g steel ball falls from a height of 1.8 m on to a metal plate and rebounds to a height of 1.25 m. Finda the p. e. of the ball before the fall (g = 10 m/s2),b its k. e. as it hits the plate, c its velocity on hitting the plate, d its k. e. as it leaves the plate on the rebound, e its velocity of rebound.

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit