8. A rectangular aquarium having a length of 3 meters, a width of 2 meters, and a height of 2 meters is filled to the top with a mixture of water and sediment. The density of the liquid at a distance of y meters from the top of the tank is p(y) = 1000 + 6y² kilograms per m³. 2 (a) A student has been asked to calculate the work done in emptying the tank. She claims that she can calculate the work by multiplying the total weight of the water in the tank and then multiplying by 2 meters. Explain, using a few sentences, why this method will not give a correct answer. Please not that you are not being asked to correct her error; you are being asked why her solution is incorrect. You will be graded on how clearly, completely, and convincingly you explain why the student's solution method doesn't work.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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8. A rectangular aquarium having a length of 3 meters, a width of 2 meters, and a height
of 2 meters is filled to the top with a mixture of water and sediment. The density
of the liquid at a distance of y meters from the top of the tank is p(y) = 1000 + 6y²
kilograms per m³.
3.
(a) A student has been asked to calculate the work done in emptying the tank.
She claims that she can calculate the work by multiplying the total weight of
the water in the tank and then multiplying by 2 meters. Explain, using a few
sentences, why this method will not give a correct answer. Please not that you
are not being asked to correct her error; you are being asked why her solution
is incorrect. You will be graded on how clearly, completely, and convincingly
you explain why the student's solution method doesn't work.
2.
Transcribed Image Text:8. A rectangular aquarium having a length of 3 meters, a width of 2 meters, and a height of 2 meters is filled to the top with a mixture of water and sediment. The density of the liquid at a distance of y meters from the top of the tank is p(y) = 1000 + 6y² kilograms per m³. 3. (a) A student has been asked to calculate the work done in emptying the tank. She claims that she can calculate the work by multiplying the total weight of the water in the tank and then multiplying by 2 meters. Explain, using a few sentences, why this method will not give a correct answer. Please not that you are not being asked to correct her error; you are being asked why her solution is incorrect. You will be graded on how clearly, completely, and convincingly you explain why the student's solution method doesn't work. 2.
(b) Set up and evaluate an integral that gives the work needed to empty the tank. Please show your work,
and include the correct units with your answer.
(Note: This refers back to the same tank and information given at the beginning of Problem 8.)
Transcribed Image Text:(b) Set up and evaluate an integral that gives the work needed to empty the tank. Please show your work, and include the correct units with your answer. (Note: This refers back to the same tank and information given at the beginning of Problem 8.)
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