Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 0 - Before Calculus - 0.1 Functions - Exercises Set 0.1 - Page 15: 40

Answer

The wind speed to the nearest mile per hour is 18 mi/h.

Work Step by Step

The formula for WCT if the wind speed is above 3 mi/h is: $WCT = 35.74 +0.6215T - 35.75v^{0.16} + 0.4275Tv^{0.16}$ Where WCT is the equivalent temperature in °F, T is the outside or air temperature in °F, and v is the wind speed. In the question, WCT = 5 °F, T = 20 °F, and v is unknown. Thus, replacing the values of the known parameters in the equation above, we have: $5 = 35.74 +0.6215\times20 - 35.75v^{0.16} + 0.4275\times20v^{0.16}$ $5 = 35.74 +12.43 - 35.75v^{0.16} + 8.55v^{0.16}$ Collecting like terms and rearranging, we have: $-5 +35.74+12.43 = 35.75v^{0.16} - 8.55v^{0.16}$ $43.17 = 27.2v^{0.16}$ Dividing both sides by the 27.2, we have: $\frac{43.17}{27.2} = \frac{27.2}{27.2}v^{0.16}$, $v^{0.16}$=1.587 $\sqrt[0.16] v^{0.16}=\sqrt[0.16] {1.587}$ $v = 17.94 $ The wind speed to the nearest mile per hour is 18 mi/h.
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