Explanation Given the equation of the efficiency of a screw as E = 100 T ( 1 − f T ) T + f . Rewrite the given equation of the efficiency of the screw as follows. E = 100 T ( 1 − f T ) T + f = 100 T − 100 f T 2 T + f = 100 T T + f − 100 f T 2 T + f Substitute f = 0.25 in the above equation. E = 100 T T + f − 100 f T 2 T + f = 100 T T + 0.25 − 100 ( 0.25 ) T 2 T + 0.25 = 100 T − 25 T 2 T + 0.25 Differentiate E with respect to T as shown below. d E d T = d d T ( 100 T − 25 T 2 T + 0.25 ) = ( 100 − 50 T ) ( T + 0.25 ) − ( 100 T − 25 T 2 ) ( T + 0.25 ) 2 In order to obtain maxima and minima put d E d T = 0 . ( 100 − 50 T ) ( T + 0.25 ) − ( 100 T − 25 T 2 ) ( T + 0.25 ) 2 25 − 25 T 2 − 12.5 T = 0 T 2 + 1 2 T − 1 = 0 Use the quadratic formula x = − b ± b 2 − 4 a c 2 a and solve the above equation. From equation T 2 + 1 2 T − 1 = 0 , note that a = 1 , b = 1 2 and c = − 1 . Substitute a = 1 , b = 1 2 and c = − 1 in above expression. T = − 1 2 ± ( 1 2 ) 2 − 4 ( 1 ) ( − 1 ) 2 ( 1 ) = − 1 2 ± 1 4 + 4 2 = − 0

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 24.7, Problem 41E

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The acute angle that makes the efficiency E the greatest.

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Chapter 24.7, Problem 40E

Chapter 24.7, Problem 42E

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Chapter 24 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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Ch. 24.1 - Prob. 9E Ch. 24.1 - Prob. 10E Ch. 24.1 - Prob. 11E Ch. 24.1 - Prob. 12E Ch. 24.1 - In Exercises 11–14, find the equations of the...Ch. 24.1 - Prob. 14E Ch. 24.1 - Prob. 15E Ch. 24.1 - Prob. 16E Ch. 24.1 - Prob. 17E Ch. 24.1 - Prob. 18E Ch. 24.1 - Prob. 19E Ch. 24.1 - Prob. 20E Ch. 24.1 - Prob. 21E Ch. 24.1 - Where does the normal line to the parabola y = x —...Ch. 24.1 - Prob. 23E Ch. 24.1 - Prob. 24E Ch. 24.1 - A certain suspension cable with supports on the...Ch. 24.1 - Prob. 26E Ch. 24.1 - Prob. 27E Ch. 24.1 - Prob. 28E Ch. 24.1 - Prob. 29E Ch. 24.1 - Prob. 30E Ch. 24.2 - In Example 1, let x1 = 0.3, and find x2. 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