Tow astronauts of equal mass are attached to each other by a taught, mass-less tether in space away from the effects of gravity. They are in orbit about their center-of-mass with a period for one complete revolution of 60 s. If they each pull themselves along the tether such that they decrease their separation to one-third of their initial separation, what is their new period of revolution

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