Please help with the following math problems. Show work.

57. A 6-foot-tall man walks at the rate of 4 fu/sec away from the base of a street light 12 feet above the ground. At what rate is the length of his shadow changing when he is 20 feet away from the base of the light? 12 20 EXERCISE 57 58. CHEMISTRY In an adiabatic chemical process, there is no net change (gain or loss) of heat. Suppose a container of oxygen is subjected to such a process. Then if the pressure on the oxygen is P and its volume is V. it can be shown that pyle = C, where C is a constant. At a certain time, V = 5 m', P = 0.6 kg/m , and P is increasing at 0.23 kg/m per sec. What is the rate of change of V? Is V increasing or decreasing? 59. BOYLE'S LAW Boyle's law states that when gas is compressed at a constant temperature, the pressure P and volume V of a given sample satisfy the equation PV = C. where C is constant. Suppose that at a certain time the volume is 40 in', the pressure is 70 lb/in', and the volume is increasing at the rate of 12 in /sec. How fast is the pressure changing at this instant? Is it increasing or decreasing? 60. REFRIGERATION An ice block used for refrigeration is modeled as a cube of side s. The block currently has volume 125,000 cm* and is melting at the rate of 1.000 em' per hour