This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise An upright cylindrical tank with radius 8 m is being filled with water at a rate of 2 m³/min. How fast is the height of the water increasing? Part 1 of 3 If h is the water's height, the volume of the water is V = ²h. We must find dv/dt. Differentiating both sides of the equation gives dh dt Part 2 of 3 dv/dt = πr² x Part 3 of 3 Substituting for r, this becomes dv/dt = 64 So dh/dt = |h 64T X m/min. Therefore, the height of the water is increasing at Submit Skip (you cannot come back) 64 π dh/dt. m/min (rounded to four decimal places).
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise An upright cylindrical tank with radius 8 m is being filled with water at a rate of 2 m³/min. How fast is the height of the water increasing? Part 1 of 3 If h is the water's height, the volume of the water is V = ²h. We must find dv/dt. Differentiating both sides of the equation gives dh dt Part 2 of 3 dv/dt = πr² x Part 3 of 3 Substituting for r, this becomes dv/dt = 64 So dh/dt = |h 64T X m/min. Therefore, the height of the water is increasing at Submit Skip (you cannot come back) 64 π dh/dt. m/min (rounded to four decimal places).
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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Transcribed Image Text:This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped
part, and you will not be able to come back to the skipped part.
Tutorial Exercise
An upright cylindrical tank with radius 8 m is being filled with water at a rate of 2 m³/min. How fast is the height of the water increasing?
Part 1 of 3
If h is the water's height, the volume of the water is V = ²h. We must find dv/dt. Differentiating both sides of the equation gives
dh
dt
Part 2 of 3
dv/dt = πr² x
Part 3 of 3
Substituting for r, this becomes dv/dt = 64
So dh/dt =
|h
64T
X
m/min.
Therefore, the height of the water is increasing at
Submit Skip (you cannot come back)
64 π dh/dt.
m/min (rounded to four decimal places).
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