A frog is sitting on a lily pad when it sees a delicious fly. He darts out his tongue at a speed of 3.90 m/s to catch the fly. The tongue has a mass of 0.410 g, and the rest of the frog plus the lily pad have a mass of 12.5 g. What is the recoil speed of the frog and the lily pad? Ignore drag forces on the pad due to the water.

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