Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 8 - Radical Functions - 8.4 Solving Radical Equations - 8.4 Exercises - Page 653: 34

Answer

$23^{\circ} \mathrm{C}$

Work Step by Step

Given \begin{equation} c=340.3 \sqrt{\frac{T+273.15}{288.15}}. \end{equation} Set $c = 345$ to find the temperature at sea level. \begin{equation} \begin{aligned} 345&=340.3 \sqrt{\frac{T+273.15}{288.15}}\\ \frac{345}{340.3}&=\sqrt{\frac{T+273.15}{288.15}}\\ (1.013811)^2& =\left( \sqrt{\frac{T+273.15}{288.15}}\right)^2\\ 1.0278134& = \frac{T+273.15}{288.15}\\ 288.15\cdot 1.0278134-273.15&\approx T\\ 23& \approx T. \end{aligned} \end{equation} The temperature at sea level is about $23^{\circ} \mathrm{C}$.
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