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Get answer: A tank holds 1000 gallons of water, which drains from the bottom of the tank

Single Variable Calculus: Early Transcendentals | 8th Edition | ISBN: 9781305270336 | Authors: James Stewart ISBN: 9781305270336 484

Solution for problem 1 Chapter 2.1

Single Variable Calculus: Early Transcendentals | 8th Edition

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Single Variable Calculus: Early Transcendentals | 8th Edition | ISBN: 9781305270336 | Authors: James Stewart

Single Variable Calculus: Early Transcendentals | 8th Edition

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1
Problem 1

A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. t smind 5 10 15 20 25 30 V sgald 694 444 250 111 28 0 (a) If P is the point s15, 250d on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t 5, 10, 20, 25, and 30. (b) Estimate the slope of the tangent line at P by averaging the slopes of two secant lines. (c) Use a graph of the function to estimate the slope of the tangent line at P. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.)

Step-by-Step Solution:

Problem 1

A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes

t(min)

5

10

15

20

25

30

V(gal)

694

444

250

111

28

0

(a) If P is the point (15, 250) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t=5, 10, 20, 25, and 30.

(b) Estimate the slope of the tangent line at P by averaging the slopes of two secant lines.

(c) Use a graph of the function to estimate the slope of the tangent line at P. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.)

                                                               Step by Step Solution

Step 1 of 4

(a)

Consider the points are the points on the graph.

Then, the equation of the slope is,

Determine the slope of the secant line for the time t=5 as,

For the points,

Then, the slope is,

Determine the slope of the secant line for the time t=10 as,

For the points,

Then, the slope is,

Step 2 of 4

Chapter 2.1, Problem 1 is Solved
Step 3 of 4

Textbook: Single Variable Calculus: Early Transcendentals
Edition: 8
Author: James Stewart
ISBN: 9781305270336

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Get answer: A tank holds 1000 gallons of water, which drains from the bottom of the tank