In a local bar, a customer slides an empty beer mug on the counter for a refill. The bartender does not see the mug, which
slides off the counter and strikes the floor 1.40m from the base
of the counter. If the height of the counter is 0.860m, (a) with
what speed did the mug leave the counter and (b) what was the
direction of the mug’s velocity just before it hit the floor?

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