A train is traveling at a speed of 80\,\dfrac{\text{km}}{\text{h}}80 h km 80, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction when the conductor applies the brakes. The train slows with a constant acceleration of magnitude 0.5\,\dfrac{\text{m}}{\text{s}^2}0. 5 s 2 m 0, point, 5, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction. We want to find the distance the train travels from the time the conductor applies the brakes until the train comes to a complete stop. Which kinematic formula would be most useful to solve for the target unknown?

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