6. [-/1 Points] DETAILS LARCALC11 2.6.017.MI. At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 12 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 22 feet high? (Hint: The formula for the volume of a cone is V = P h.) ft/min Need Help? Read it Watch it Master It7. [-/2 Points] DETAILS LARCALC11 2.6.020. A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet. min 12 1- 3 fit theft (a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.7 feet deep? ft/min (b) If the water is rising at a rate of 3/8 inch per minute when h = 2.0, determine the rate at which water is being pumped into the trough. ft3/min Need Help? Read It 8. [-/5 Points] DETAILS LARCALC11 2.6.021. A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. (a) What is the velocity of the top of the ladder when the base is given below? 15 feet away from the wall ft/sec 20 feet away from the wall ft/sec 24 feet away from the wall ft/sec b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 15 feet from the wall. ft /sec c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 15 feet from the wall. rad/sec Need Help? Read It