Two blocks, M1 and M2, are connected by a massless string that passes over a massless pulley as shown in the figure. M2, which has a mass of 23.0 kg, rests on a long ramp of angle =31.0∘. Friction can be ignored in this problem. Determine the mass 1 of block M1 for which the two blocks are in equilibrium (no acceleration).
If the actual mass of M1 is 5.00 kg and the system is allowed to move, what is the acceleration of the two blocks? A positive acceleration corresponds to M2 moving up the incline.
What distance does block M2 move in 2.00 s?

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