A jogger travels a route that has two parts. The first is a displacement A→ of 2.55 km due south, and the second involves a displacement B→ that points due east. The resultant displacement A→ + B→ has a magnitude of 4.15 km. (a) What is the magnitude of B→, and (b) what is the direction of A→ + B→ as a positive angle relative to due south? Suppose that A→ - B→ had a magnitude of 4.15 km. (c) What then would be the magnitude of B→, and (d) what is the direction of A→ - B→ relative to due south?

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