a. Answer The relation between the variables h and r is r = 0.4 h . Explanation Given r h = 4 20 . Calculation: From the given, r h = 4 20 r = 0.4 h Thus the relation between the variables h and r is r = 0.4 h . b. To determine To find the water level dropping when h = 6 f t . Answer The water level dropping d h d t = − 0.276 when h = 6 f t . Explanation Given r h = 4 20 . Calculation: From the given, d V d t = − 5 , r = 0.4 h Plug r = 0.4 h value in V = 1 3 π r 2 h V = 0.16 3 π h 3 Derivative with respect to t on both sids. d V d t = 0.16 π h 2 d h d t − 5 = 0.16 π ( 6 ) 2 d h d t d h d t = − 0.276 Thus, the water level dropping d h d t = − 0.276 when h = 6 f t .

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

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

See similar textbooks

Question

Chapter 5, Problem 62RE

To determine

To find the relation between the variables h and r.

Expert Solution

Answer to Problem 62RE

The relation between the variables h and r is r=0.4h.

Explanation of Solution

Given rh=420.

Calculation:

From the given, rh=420

r=0.4h

Thus the relation between the variables h and r is r=0.4h.

To determine

To find the water level dropping when h=6ft.

Expert Solution

Answer to Problem 62RE

The water level dropping dhdt=−0.276 when h=6ft.

Explanation of Solution

Given rh=420.

Calculation:

From the given, dVdt=−5,r=0.4h

Plug r=0.4h value in V=13πr2h

V=0.163πh3

Derivative with respect to t on both sids.

dVdt=0.16πh2dhdt−5=0.16π(6)2dhdtdhdt=−0.276

Thus, the water level dropping dhdt=−0.276 when h=6ft.

Chapter 5, Problem 61RE

Chapter 5, Problem 63RE

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

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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