a. Answer The dimensions are Base is 10 ft, height is 5 ft. Explanation Calculation: S = 4 x h + x 2 V = 500 = h x 2 h = 500 x 2 Solve the volume equation for h and substitute into the other equation. S = 4 x h + x 2 S = 4 x ( 500 x 2 ) + x 2 = 2000 x + x 2 S ′ = − 2000 x 2 + 2 x = − 2000 x 2 + 2 x 3 0 = 2 x 3 − 2000 2 x 3 = 2000 x 3 = 1000 x = 10 Plug x back into the height equation. h = 500 ( 10 ) 2 = 5 Base is 10 ft, height is 5 ft. Thus, the dimensions are Base is 10 ft, height is 5 ft. b. To determine How you took weight into account. Answer Use the surface area of the tank as a stand in because the weight is directly dependent on the surface area. Increase one will increase the other, minimize one will minimize the other. Explanation Calculation: Use the surface area of the tank as a stand in because the weight is directly dependent on the surface area. Increase one will increase the other, minimize one will minimize the other.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.4, Problem 11E

To determine

Find the dimension to use the shop.

Expert Solution

Answer to Problem 11E

The dimensions are Base is 10 ft, height is 5 ft.

Explanation of Solution

Calculation:

S=4xh+x2V=500=hx2h=500x2

Solve the volume equation for h and substitute into the other equation.

S=4xh+x2S=4x(500x2)+x2 =2000x+x2S′=−2000x2+2x =−2000x2+2x30=2x3−20002x3=2000x3=1000x=10

Plug x back into the height equation.

h=500(10)2 =5

Base is 10 ft, height is 5 ft.

Thus, the dimensions are Base is 10 ft, height is 5 ft.

To determine

How you took weight into account.

Expert Solution

Answer to Problem 11E

Use the surface area of the tank as a stand in because the weight is directly dependent on the surface area. Increase one will increase the other, minimize one will minimize the other.

Explanation of Solution

Calculation:

Use the surface area of the tank as a stand in because the weight is directly dependent on the surface area. Increase one will increase the other, minimize one will minimize the other.

Chapter 5.4, Problem 10E

Chapter 5.4, Problem 12E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

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