Explanation Given information: The water level is raising at a rate only 0.05 min/ft when the water is 12 ft deep. Calculation: The water flow into the tank at a rate of 80 f t 3 / min . Let A is the rate of water flowing out from the tank, r is the radius of tank, and y is the height of tank, Then the volume of water present in tank, V = 1 3 π r 2 y .................. ( 1 ) and tan ( θ ) = r y = 20 40 ⇒ r = y 2 . Where, d V d t = ( 80 − A ) f t 3 / min Differentiate equation (1) with respect to time from both sides. V = 1 3 π r 2 y .................. ( 1 ) d V d t = d d t ( 1 3 π r 2 y ) d V d t = d d t ( 1 3 π ( y 2 ) 2 y ) [ ∵ r = y 2 ] d V d t = 1 3 × 4 π d d t ( y 3 ) d V d t = ( 3 y 2 ) 3 × 4 π d y d t d V d t = y 2 π 4 d y d t Substitute d V d t = ( 80 − A ) f t 3 / min and when y = 12 and d y d t = 0

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.7, Problem 48PS

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To find the rate of water flowing out from the tank.

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Chapter 3.7, Problem 47PS

Chapter 3.7, Problem 49PS

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Problem 3. A driver on a desert road discovers a hole in the gas tank leaking gas at the constant rate of 4 gallons per hour. This driver, having no way to plug the hole, decides to drive for as long as the gas supply allows. The gauge reading indicates the tank is three-fourths full, which means that the tank contains 14 gallons. The car consumes gas at the rate of 18 miles per gallon at 40 mph. For each 5 mph below 40 mph add one-half mile per gallon to this rate; for each 5 mph above 40 mph, subtract one mile per gallon from this rate. If the driver chooses the best constant speed in order to get the maximum driving distance, find the maximum distance that the 14 gallons will allow. Assume that gas consumption is a continuous function of speed.

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Chapter 3 Solutions

Calculus

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To find the rate of water flowing out from the tank.

Solution Summary: The author calculates the rate of water flowing out of the tank at 2.25ft3/mathrmmin.

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To find the rate of water flowing out from the tank.

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Chapter 3 Solutions