Asearchlight rotates at a rate of 3 revolutions per minute. the beam hits a wall located 12 miles away and produces a dot of light that moves horizontally along the wall. how fast (in miles per hour) is this dot moving when the angle θ between the beam and the line through the searchlight perpendicular to the wall is π3? note that dθ/dt=3(2π)=6π.

speed of dot = mph.

note: watch the units! this problem asks for the answer in miles per hour, not in miles per minute!

b. a conical water tank with vertex down has a radius of 12 feet at the top and is 27 feet high. if water flows into the tank at a rate of 10 ft3/min, how fast is the depth of the water increasing when the water is 18 feet deep?

the depth of the water is increasing at ft/min.

c. a street light is at the top of a 13 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path. how fast is the tip of her shadow moving when she is 30 ft from the base of the pole?