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High School Math Calculus CALCULUS-W/XL ACCESS

The rate of the water at time t .

The rate of the water at time t .

Solution Summary: The author calculates the rate of the water at time t based on the formula used.

CALCULUS-W/XL ACCESS

CALCULUS-W/XL ACCESS

6th Edition

ISBN: 9781418300197

Author: Finney

Publisher: PEARSON

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Question

Chapter 2.4, Problem 25E

a.

To determine

To calculate: The rate of the water at time t .

a.

Expert Solution

Answer to Problem 25E

The rate is dydt=t12−1 .

Explanation of Solution

Given information:

The function is y=61−t122 and time is t=12

Concept used:

The formula used is ddxxn=nxn−1 .

Calculation:

The function is y=61−t122 .

Differentiate the function with respect to time t .

dydt=ddt61−t122=621−t122−1−112=−1−t12dydt=t12−1

Conclusion: The rate is dydt=t12−1 .

b.

To determine

To calculate: The value of rate when it is fastest and slowest.

b.

Expert Solution

Answer to Problem 25E

The value of rate when it is fastest is dydt=−1 and value of rate when it is slowest is dydt=0 .

Explanation of Solution

Given information:

The function is y=61−t122 .

Concept used:

The formula used is ddxxn=nxn−1 .

Calculation:

The function is y=61−t122 .

Differentiate the function with respect to time t .

dydt=ddt61−t122=621−t122−1−112=−1−t12dydt=t12−1

The rate will be fastest when t=0

dydt=012−1=0−1=−1

The rate will be slowest when t=12

dydt=1212−1=1−1=0

Conclusion: The value of rate when it is fastest is dydt=−1 and value of rate when it is slowest is dydt=0 .

c.

To determine

To calculate: The comparison between the graphs of y and dydt

c.

Expert Solution

Explanation of Solution

Given information:

The function is y=61−t122 .

Calculation:

The function is y=61−t122 .

Differentiate the function with respect to time t .

dydt=ddt61−t122=621−t122−1−112=−1−t12dydt=t12−1

The graphs of y and dydt in the same graph is as shown below.

CALCULUS-W/XL ACCESS , Chapter 2.4, Problem 25E

Conclusion: The particle will be in rest when t=3.2 , t=0.9 .

Chapter 2.4, Problem 24E

Chapter 2.4, Problem 26E

Chapter 2 Solutions

CALCULUS-W/XL ACCESS

Ch. 2.1 - Prob. 1QR Ch. 2.1 - Prob. 2QR Ch. 2.1 - Prob. 3QR Ch. 2.1 - Prob. 4QR Ch. 2.1 - Prob. 5QR Ch. 2.1 - Prob. 6QR Ch. 2.1 - Prob. 7QR Ch. 2.1 - Prob. 8QR Ch. 2.1 - Prob. 9QR Ch. 2.1 - Prob. 10QR

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.2 - Prob. 1QR Ch. 2.2 - Prob. 2QR Ch. 2.2 - Prob. 3QR Ch. 2.2 - Prob. 4QR Ch. 2.2 - 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Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 67RE Ch. 2 - Prob. 68RE Ch. 2 - Prob. 69RE Ch. 2 - Prob. 70RE Ch. 2 - Prob. 71RE Ch. 2 - Prob. 72RE Ch. 2 - Prob. 73RE Ch. 2 - Prob. 74RE Ch. 2 - Prob. 75RE Ch. 2 - Prob. 76RE Ch. 2 - Prob. 77RE Ch. 2 - Prob. 78RE Ch. 2 - Prob. 79RE Ch. 2 - Prob. 80RE Ch. 2 - Prob. 81EP Ch. 2 - Prob. 82EP Ch. 2 - Prob. 83EP

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