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: 39

Answer

$ T = 15^\circ F$

Work Step by Step

We need to find the air temperature to the nearest degree. Denote it $T$. We are given that $WCT = -10^\circ F$, $v = 48 \, mi/h $. Recall the definition of the WCT: $$ WCT = \left\{\begin{array}{lr} T, & 0\leq v\leq 3\\ 35.74 + 0.6215T − 35.75v^{0.16} + 0.4275T v^{0.16}, & v>3\\ \end{array}\right\} $$ We have that $v > 3$ and therefore we can write: $$ WCT = 35.74 + 0.6215T − 35.75v^{0.16} + 0.4275T v^{0.16} $$ Substitute for the value of the $WCT$ to get: $$ 35.74 + 0.6215T − 35.75v^{0.16} + 0.4275T v^{0.16} = -10 $$ Substitude for the value of $v$ to get: $$ 35.74 + 0.6215T − 35.75 \cdot (48^{0.16}) + 0.4275T \cdot (48^{0.16}) = -10 $$ Rewrite the equation as follows: $$ T \cdot \left(0.6215 + 0.4275 \cdot \left(48^{0.16}\right)\right) = -10 - 35.74 + 35.75 \cdot (48^{0.16}) $$ $$ T = \frac{-45.74 + 35.75 \cdot (48^{0.16})}{\left(0.6215 + 0.4275 \cdot \left(48^{0.16}\right)\right)} $$ And plugging it in a calculator yields $ T \approx 14.6^\circ F$. We are requested to find the air temperature to the nearest degree; thus the answer is $ T = 15^\circ F$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.