Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
4th Edition
ISBN: 9781337687805
Author: James Stewart
Publisher: Cengage Learning
Question
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Chapter 2.6, Problem 46E
To determine

To Find: the rate at which the water is flowing out of the tank as function of t .For times t=0,10,20,30,40,50,60 and the flow rate and the amount of water remaining in the tank.at what time flow rate is the greatest and the least.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:

The volume V of water remaining in the tank after t minutes is given as:

  Vt=100,0001−160t2

  0≤t≤60

Concept used:

Find the derivative of V with respect to t .

Calculation:

Differentiate V with respect to t .It will give the rate at which water is flowing out of tank with time t .

  dVtdt=2⋅100,0001−160t−160dVtdt=−100,0031−160t                ......(1)

This is function which gives the water flowing out with respect to t .

Substitute t=0 into the equation (1) it gives:

  dVtdtt=0=−1000031−160⋅0    dVtdtt=0=−100003dVtdtt=0=−3333.33

At t=0 water flowing out of tank at the rate 3,333.33 gallon per minute.

Substitute t=10 into the equation (1) it gives:

  dVtdtt=10=−1000031−160⋅10    dVtdtt=0=−1000031−16dVtdtt=0=−−10000356dVtdtt=0=−250009dVtdtt=0==2777.7

At t=10 water flowing out of tank at the rate 2,777.77 gallon per minute.

Substitute t=20 into the equation (1) it gives:

  dVtdtt=10=−1000031−160⋅20    dVtdtt=0=−1000031−13dVtdtt=0=−−10000323dVtdtt=0=−200009dVtdtt=0==2222.2

At t=20 water flowing out of tank at the rate 2,222.22 gallon per minute.

Substitute t=30 into the equation (1) it gives:

  dVtdtt=10=−1000031−160⋅30    dVtdtt=0=−1000031−12dVtdtt=0=−−10000312dVtdtt=0=−100006dVtdtt=0=−1666.6

At t=30 water flowing out of tank at the rate 1666.6 gallon per minute.

Substitute t=40 into the equation (1) it gives:

  dVtdtt=10=−1000031−160⋅40    dVtdtt=0=−1000031−23dVtdtt=0=−−10000313dVtdtt=0=−100009dVtdtt=0=−1111.1

At t=40 water flowing out of tank at the rate 11111.1 gallon per minute.

Substitute t=50 into the equation (1) it gives:

  dVtdtt=10=−1000031−160⋅50    dVtdtt=0=−1000031−56dVtdtt=0=−−10000316dVtdtt=0=−1000018dVtdtt=0=−555.55

At t=50 water flowing out of tank at the rate 555.55 gallon per minute.

Substitute t=60 into the equation (1) it gives:

  dVtdtt=10=−1000031−160⋅60    dVtdtt=0=−1000031−1dVtdtt=0=−−1000030dVtdtt=0=0

At t=60 water ran out completely and tank will be empty.

The flow rate is greatest at t=0 and lowest at t=60 .

The tank will empty in an hour.

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Chapter 2.6, Problem 45E
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Chapter 2 Solutions

Single Variable Calculus: Concepts and Contexts, Enhanced Edition

Ch. 2.1 - A Lank holds 1000 gallons o f water, which drains...Ch. 2.1 - A cardiac monitor is used to measure the heart...Ch. 2.1 - The point P(2, 1) lies on the curve y = 1/(1 x)....Ch. 2.1 - The point P(0.5, 0) lies on the curve y = cos x....Ch. 2.1 - If a ball is thrown into the air with a velocity...Ch. 2.1 - If a rock is thrown upward on the planet Mars with...Ch. 2.1 - The table shows the position of a motorcyclist...Ch. 2.1 - The displacement (in centimeters) of a particle...Ch. 2.1 - The point P(1, 0) lies on the curve y = sin(l0/x)....Ch. 2.2 - Prob. 1E
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Prob. 9ECh. 2.3 - Evaluate the limit, if it exists. limx3x2+3xx2x12Ch. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - If 4x 9 f(x) x2 4x + 7 for x 0, find limx4f(x)Ch. 2.3 - If 2x g(x) x4 x2 + 2 for all x, evaluate...Ch. 2.3 - Prove that limx0x4cos2x=0.Ch. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.4 - Write an equation that expresses the fact that a...Ch. 2.4 - Prob. 2ECh. 2.4 - (a) From the graph of f , state the numbers at...Ch. 2.4 - Prob. 4ECh. 2.4 - Sketch the graph of a function f that is...Ch. 2.4 - Sketch the graph of a function f that is...Ch. 2.4 - Sketch the graph of a function f that is...Ch. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - 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Trace or copy the graph of the given function .f....Ch. 2.7 - Trace or copy the graph of the given function .f....Ch. 2.7 - Trace or copy the graph of the given function .f....Ch. 2.7 - Prob. 11ECh. 2.7 - Prob. 12ECh. 2.7 - Prob. 13ECh. 2.7 - Prob. 14ECh. 2.7 - Prob. 15ECh. 2.7 - Prob. 16ECh. 2.7 - Prob. 17ECh. 2.7 - Prob. 18ECh. 2.7 - Prob. 19ECh. 2.7 - Prob. 20ECh. 2.7 - Prob. 21ECh. 2.7 - Prob. 22ECh. 2.7 - Prob. 23ECh. 2.7 - Prob. 24ECh. 2.7 - Prob. 25ECh. 2.7 - Prob. 26ECh. 2.7 - Prob. 27ECh. 2.7 - Prob. 28ECh. 2.7 - Prob. 29ECh. 2.7 - Prob. 30ECh. 2.7 - Prob. 31ECh. 2.7 - Prob. 32ECh. 2.7 - Prob. 33ECh. 2.7 - Prob. 34ECh. 2.7 - Prob. 35ECh. 2.7 - Prob. 36ECh. 2.7 - Prob. 37ECh. 2.7 - Prob. 38ECh. 2.7 - Prob. 39ECh. 2.7 - Prob. 40ECh. 2.7 - Prob. 41ECh. 2.7 - Prob. 42ECh. 2.7 - Prob. 43ECh. 2.7 - Prob. 44ECh. 2.7 - Prob. 45ECh. 2.7 - Prob. 46ECh. 2.7 - Prob. 47ECh. 2.7 - Prob. 48ECh. 2.7 - Prob. 49ECh. 2.7 - Prob. 50ECh. 2.7 - Prob. 51ECh. 2.7 - Where is the greatest integer function f(x) = [[ x...Ch. 2.7 - 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