In Fig. 3, an annular copper cylinder of radii Router = 40 cm, Rinner = 20 cm and mass M = 5 kg rolls from rest a D = 10 m distance down a Ф = 30° incline. Assume that the incline and the horizontal surface have the same fictional coefficient. a/ Compute the speed of the center of mass of the cylinder at the end of
the incline.
b/ How long does the cylinder reach to the bottom of the incline?
c/ If the annular copper cylinder and a solid wood cylinder having the same radius Router and mass release

together from rest at the initial location, which cylinder reaches the bottom first? Why?

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