Sand falls from a hopper at a rate of 0.5 cubic meters per hour and forms a conical pile beneath. Suppose the radius of the cone is always half the height of the cone.(a) Find the rate at which the radius of the cone increases when the radius is 2 meters. Give an exact answer.meters per hour(b) Find the rate at which the height of the cone increases when the radius is 2 meters. Give an exact answer.meters per hour

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Answered: Sand falls from a hopper at a rate of…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...

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A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?
The resistance of a copper wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. A copper wire with a diameter of 0.0126inch has a resistance of 64.9ohms per thousand feet. What length of 0.0201-inch-diameter copper wire will produce a resistance of 33.5ohms?
A piece shown by the shaded portion is to be cut from a square plate 128 millimeters on a side. a. Compute the area of the piece to be cut. Round the answer to the nearest square millimeter. b. After cutting the piece, determine the percentage of the plate that will be wasted.
A carbide milling cutter is used for machining a 27.25-inch length of stainless steel. The cutting time is 12.35 minutes, the cutting speed is 240 feet per minute, and the feed is 0.01 inches per revolution. What is the diameter of the carbide milling cutter? Round the answer to 2 decimal places.
Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.
Which A winch of radius 2 ft is used to lift heavy loads. If the winch makes 8 revolutions every 15 s, find the speed at which the load is rising.
Solve each problem. w is directly proportional to z. If w=-6 when z=2, find w when z=-3.

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