Negatively charged particle is released from rest at point b and accelerates until it reaches point a. the mass and charge of the particle are 4.0 106 kg and 2.0 105 c, respectively. only the gravitational force and the electrostatic force act on the particle, which moves on a horizontal straight line without rotating. the electric potential at a is 36 v greater than that at b; in other words, va vb 36 v. what is the translational speed of the particle at point a?

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