Explanation Given: The fuel economy of a certain hybrid electric car at a speed between 50 mi / hr or 100 mi / hr can be calculated by formula F = 0.005 v 2 − 1.25 v + 96 and the resulted fuel economy is 39 miles per gallon. Definition used: Standard quadratic equation : “An equation in which the variable appears to the second power, but to no higher power, is called a quadratic equation. A standard quadratic equation can be expresses as, a x 2 ︸ + b x ︸ + c ︸ = 0 ↓ ↓ ↓ [ x 2 -term ] [ x -term ] [ Constant term ] That is every quadratic equation must have x 2 -term, but the x -term or constant tem may be missing.” Procedure used: 1. Identify the values of a , b and c by comparing the given equation with the standard quadratic equation a x 2 + b x + c = 0 . 2. Substitute the values of a , b and c into the quadratic equation formula x = − b ± b 2 − 4 a c 2 a . 3. Simplify the equation for x . 4. Check the solution by back substituting the values of x in the original equation. Calculation: The given fuel economy of a certain hybrid electric car at a speed between 50 mi / hr or 100 mi / hr can be calculated by formula F = 0.005 v 2 − 1.25 v + 96 . Here a vehicle has to maintain the fuel economy for 39 miles per gallon. Where F is the fuel economy of a vehicle. Substitute F = 39 in the above formula as follows. F = 0.005 v 2 − 1.25 v + 96 39 = 0.005 v 2 − 1.25 v + 96 0.005 v 2 − 1.25 v + 96 − 39 = 0 0.005 v 2 − 1.25 v + 57 = 0 Here the quadratic equation is 0.005 v 2 − 1.25 v + 57 = 0 . Step 1: Identify the values of a , b and c by comparing the given equation with the standard quadratic equation a v 2 + b v + c = 0

11th Edition

ISBN: 8220106960455

Author: CARMAN

Publisher: PEARSON

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Chapter 11, Problem 20CPS

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To find: The speed to maintain the fuel economy of the vehicle of 26 miles per gallon.

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Chapter 11, Problem 19CPS

Chapter 11, Problem 21CPS

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Chapter 11 Solutions

EBK MATHEMATICS FOR THE TRADES

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The speed to maintain the fuel economy of the vehicle of 26 miles per gallon.

Solution Summary: The author calculates the fuel economy of a certain hybrid electric car by formula F=0.005v2-1.25v+96 and the result is 39 miles per gallon.

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To find: The speed to maintain the fuel economy of the vehicle of 26 miles per gallon.

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Chapter 11 Solutions