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: 38

Answer

The air temperature is $-20.7132$ $^{\circ}$F.

Work Step by Step

1. Write the wind chill temperature (WCT) formula from exercise $37$ $WCT=\begin{cases}T, 0\leq v \leq 3\\35.74 + 0.6215T − 35.75v^{0.16} + 0.4275T v^{0.16}, 3 < v\end{cases}$ 2. Wind speed $v=48$mi/h. since, $v>3$ $WCT=35.74 + 0.6215T − 35.75v^{0.16} + 0.4275T v^{0.16}$ 3. Now substitute values of wind speed and WCT in the formula. $-60=35.74 + 0.6215T − 35.75\times 48^{0.16} + 0.4275T\times 48^{0.16}$ 4. Isolate the terms with $T$ and solve for $T$ $0.6215T + 0.4275T\times 48^{0.16}=-60 + 35.75\times 48^{0.16} - 35.74$ $\implies T (0.6215 + 0.4275\times 48^{0.16})=-29.3237$ $\implies T(1.4157)=-29.3237$ $\implies T=-20.7132$ Hence, the air temperature is $-20.7132$ $^{\circ}$F.
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