Explanation Formula used: Instantaneous Rate of Change: As h → 0 , the limit of the ratio of the change in f ( x ) to the change in x is the instantaneous rate of change of f ( x ) with respect to is given by the formula f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h . Area of a circle of radius r is given by A = π r 2 . Calculation: It is given that the metal plate is of circular shape with radius r and two radius are r = 240 m and r = 480 m . Substitute r = r + h in A ( r ) = π r 2 and obtain the value of A ( r + h ) as follows: A ( r + h ) = π ( r + h ) 2 = π h 2 + π r 2 + 2 π h r Thus, the value of A ( r + h ) is π h 2 + π r 2 + 2 π h r . Substitute A ( r ) = π r 2 , A ( r + x ) = π h 2 + π r 2 + 2 π h r and obtain the value of A ( r + h ) − A ( r ) as follows: A ( r + h ) − A ( r ) = π h 2 + π r 2 + 2 π h r − π r 2 = π h 2 + 2 π h r The value of A ( r + h ) − A ( r ) is π h 2 + 2 π h r . Divide A ( r + h ) − A ( r ) by h and obtain the value of A ( r + h ) − A ( r ) h as shown below: A ( r + h ) − A ( r ) h = π h 2 + 2 π h r h = π h + 2 π r Thus, the value of A ( r + h ) − A ( r ) h is π h + 2 π r

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Author: Evans

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Chapter 23.4, Problem 36E

To determine

The difference in the rate of change of area A of the circular oil spill for r=240 m and r=480 m.

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Chapter 23.4, Problem 35E

Chapter 23.4, Problem 37E

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Chapter 23 Solutions

EBK BASIC TECHNICAL MATHEMATICS

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Do not multiply factors...Ch. 23.6 - Prob. 2PE Ch. 23.6 - Prob. 1E Ch. 23.6 - Prob. 2E Ch. 23.6 - Prob. 3E Ch. 23.6 - Prob. 4E Ch. 23.6 - Prob. 5E Ch. 23.6 - Prob. 6E Ch. 23.6 - Prob. 7E Ch. 23.6 - Prob. 8E Ch. 23.6 - Prob. 9E Ch. 23.6 - Prob. 10E Ch. 23.6 - Prob. 11E Ch. 23.6 - Prob. 12E Ch. 23.6 - Prob. 13E Ch. 23.6 - Prob. 14E Ch. 23.6 - Prob. 15E Ch. 23.6 - Prob. 16E Ch. 23.6 - Prob. 17E Ch. 23.6 - Prob. 18E Ch. 23.6 - Prob. 19E Ch. 23.6 - Prob. 20E Ch. 23.6 - Prob. 21E Ch. 23.6 - Prob. 22E Ch. 23.6 - Prob. 23E Ch. 23.6 - Prob. 24E Ch. 23.6 - Prob. 25E Ch. 23.6 - Prob. 26E Ch. 23.6 - Prob. 27E Ch. 23.6 - Prob. 28E Ch. 23.6 - Prob. 29E Ch. 23.6 - Prob. 30E Ch. 23.6 - Prob. 31E Ch. 23.6 - Prob. 32E Ch. 23.6 - Prob. 33E Ch. 23.6 - Prob. 34E Ch. 23.6 - Prob. 35E Ch. 23.6 - Prob. 36E Ch. 23.6 - Prob. 37E Ch. 23.6 - Prob. 38E Ch. 23.6 - Prob. 39E Ch. 23.6 - Prob. 40E Ch. 23.6 - Prob. 41E Ch. 23.6 - Prob. 42E Ch. 23.6 - Prob. 43E Ch. 23.6 - Prob. 44E Ch. 23.6 - In Exercises 33–58, solve the given problems by...Ch. 23.6 - Prob. 46E Ch. 23.6 - Prob. 47E Ch. 23.6 - Prob. 48E Ch. 23.6 - Prob. 49E Ch. 23.6 - Prob. 50E Ch. 23.6 - Prob. 51E Ch. 23.6 - Prob. 52E Ch. 23.6 - Prob. 53E Ch. 23.6 - Prob. 54E Ch. 23.6 - Prob. 55E Ch. 23.6 - Prob. 56E Ch. 23.6 - Prob. 57E Ch. 23.6 - Prob. 58E Ch. 23.7 - Prob. 1PE Ch. 23.7 - Prob. 2PE Ch. 23.7 - Prob. 3PE Ch. 23.7 - Prob. 4PE Ch. 23.7 - Prob. 1E Ch. 23.7 - Prob. 2E Ch. 23.7 - Prob. 3E Ch. 23.7 - Prob. 4E Ch. 23.7 - Prob. 5E Ch. 23.7 - Prob. 6E Ch. 23.7 - Prob. 7E Ch. 23.7 - Prob. 8E Ch. 23.7 - Prob. 9E Ch. 23.7 - Prob. 10E Ch. 23.7 - Prob. 11E Ch. 23.7 - Prob. 12E Ch. 23.7 - Prob. 13E Ch. 23.7 - Prob. 14E Ch. 23.7 - Prob. 15E Ch. 23.7 - Prob. 16E Ch. 23.7 - Prob. 17E Ch. 23.7 - Prob. 18E Ch. 23.7 - Prob. 19E Ch. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 21E Ch. 23.7 - Prob. 22E Ch. 23.7 - Prob. 23E Ch. 23.7 - Prob. 24E Ch. 23.7 - Prob. 25E Ch. 23.7 - Prob. 26E Ch. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 28E Ch. 23.7 - Prob. 29E Ch. 23.7 - Prob. 30E Ch. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 32E Ch. 23.7 - Prob. 33E Ch. 23.7 - Prob. 34E Ch. 23.7 - Prob. 35E Ch. 23.7 - Prob. 36E Ch. 23.7 - Prob. 37E Ch. 23.7 - Prob. 38E Ch. 23.7 - Prob. 39E Ch. 23.7 - Prob. 40E Ch. 23.7 - Prob. 41E Ch. 23.7 - Prob. 42E Ch. 23.7 - Prob. 43E Ch. 23.7 - Prob. 44E Ch. 23.7 - Prob. 45E Ch. 23.7 - Prob. 46E Ch. 23.7 - Prob. 47E Ch. 23.7 - Prob. 48E Ch. 23.7 - Prob. 49E Ch. 23.7 - Prob. 50E Ch. 23.7 - Prob. 51E Ch. 23.7 - Prob. 52E Ch. 23.7 - Prob. 53E Ch. 23.7 - Prob. 54E Ch. 23.7 - Prob. 55E Ch. 23.7 - Prob. 56E Ch. 23.7 - Prob. 57E Ch. 23.7 - Prob. 58E Ch. 23.8 - Prob. 1PE Ch. 23.8 - Prob. 1E Ch. 23.8 - Prob. 2E Ch. 23.8 - In Exercises 3–22, find dy/dx by differentiating...Ch. 23.8 - Prob. 4E Ch. 23.8 - Prob. 5E Ch. 23.8 - Prob. 6E Ch. 23.8 - Prob. 7E Ch. 23.8 - Prob. 8E Ch. 23.8 - Prob. 9E Ch. 23.8 - Prob. 10E Ch. 23.8 - Prob. 11E Ch. 23.8 - Prob. 12E Ch. 23.8 - Prob. 13E Ch. 23.8 - Prob. 14E Ch. 23.8 - Prob. 15E Ch. 23.8 - Prob. 16E Ch. 23.8 - Prob. 17E Ch. 23.8 - Prob. 18E Ch. 23.8 - Prob. 19E Ch. 23.8 - Prob. 20E Ch. 23.8 - Prob. 21E Ch. 23.8 - Prob. 22E Ch. 23.8 - Prob. 23E Ch. 23.8 - Prob. 24E Ch. 23.8 - Prob. 25E Ch. 23.8 - Prob. 26E Ch. 23.8 - Prob. 27E Ch. 23.8 - Prob. 28E Ch. 23.8 - Prob. 29E Ch. 23.8 - Prob. 30E Ch. 23.8 - Prob. 31E Ch. 23.8 - Prob. 32E Ch. 23.8 - Prob. 33E Ch. 23.8 - Prob. 34E Ch. 23.8 - Prob. 35E Ch. 23.8 - Prob. 36E Ch. 23.8 - Prob. 37E Ch. 23.8 - Prob. 38E Ch. 23.8 - Prob. 39E Ch. 23.8 - Prob. 40E Ch. 23.8 - Prob. 41E Ch. 23.8 - Prob. 42E Ch. 23.8 - Prob. 43E Ch. 23.8 - Prob. 44E Ch. 23.9 - Prob. 1PE Ch. 23.9 - Prob. 2PE Ch. 23.9 - Prob. 1E Ch. 23.9 - Prob. 2E Ch. 23.9 - Prob. 3E Ch. 23.9 - Prob. 4E Ch. 23.9 - Prob. 5E Ch. 23.9 - Prob. 6E Ch. 23.9 - Prob. 7E Ch. 23.9 - Prob. 8E Ch. 23.9 - Prob. 9E Ch. 23.9 - Prob. 10E Ch. 23.9 - Prob. 11E Ch. 23.9 - Prob. 12E Ch. 23.9 - Prob. 13E Ch. 23.9 - Prob. 14E Ch. 23.9 - Prob. 15E Ch. 23.9 - Prob. 16E Ch. 23.9 - Prob. 17E Ch. 23.9 - 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Prob. 63RE Ch. 23 - Prob. 64RE Ch. 23 - If $5000 is invested at interest rate i,...Ch. 23 - The temperature T (in °C) of a rotating machine...Ch. 23 - Prob. 67RE Ch. 23 - Prob. 68RE Ch. 23 - Prob. 69RE Ch. 23 - Prob. 70RE Ch. 23 - Prob. 71RE Ch. 23 - Prob. 72RE Ch. 23 - Prob. 73RE Ch. 23 - Prob. 74RE Ch. 23 - Prob. 75RE Ch. 23 - Prob. 76RE Ch. 23 - Prob. 77RE Ch. 23 - Prob. 78RE Ch. 23 - Prob. 79RE Ch. 23 - Prob. 80RE Ch. 23 - Prob. 81RE Ch. 23 - Prob. 82RE Ch. 23 - Prob. 83RE Ch. 23 - Prob. 84RE Ch. 23 - Prob. 85RE Ch. 23 - Prob. 86RE Ch. 23 - Prob. 87RE Ch. 23 - Prob. 88RE Ch. 23 - Prob. 89RE Ch. 23 - Prob. 90RE Ch. 23 - Prob. 91RE Ch. 23 - Prob. 92RE Ch. 23 - Prob. 93RE Ch. 23 - Prob. 94RE Ch. 23 - Prob. 95RE Ch. 23 - Prob. 96RE Ch. 23 - Prob. 97RE Ch. 23 - Prob. 98RE Ch. 23 - In Exercises 53–98, solve the given problems. 99....Ch. 23 - Prob. 1PT Ch. 23 - Prob. 2PT Ch. 23 - Prob. 3PT Ch. 23 - Prob. 4PT Ch. 23 - Prob. 5PT Ch. 23 - Prob. 6PT Ch. 23 - Prob. 7PT Ch. 23 - Prob. 8PT Ch. 23 - 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The difference in the rate of change of area A of the circular oil spill for r = 240 m and r = 480 m .

The difference in the rate of change of area A of the circular oil spill for r=240 m and r=480 m.

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