Ryan and Carson attended their church's youth retreat at Camp Paradise this past fall. On Saturday afternoon they took a walk out to the harbor and watched incoming waves from Lake Michigan rock the boating piers up and down. Ryan and Carson observed that the piers made a complete up and down vibration cycle in 6.6 seconds. The piers were positioned a distance of 24 meters apart. When one pier was at a high position, the neighboring pier was at a low position and there was exactly one wave crest between them. Determine the wavelength, frequency and speed of the waves.

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