Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.8 - Modeling Using Variation - Exercise Set - Page 425: 38

Answer

Yes, it can resist because it can bear $360\ \text{pounds}$.

Work Step by Step

According to the given statement; $\begin{align} & F\propto \text{Velocit}{{\text{y}}^{2}} \\ & F\propto \text{Area} \\ & F=k\times \text{Area}\times \text{Velocit}{{\text{y}}^{2}} \end{align}$ Substitute the values of velocity, area and force to find k using Window 1 data. $\begin{align} & F=k\times \text{Area}\times \text{Velocit}{{\text{y}}^{2}} \\ & 150=k\times \left( 4\times 5 \right)\times {{30}^{2}} \\ & 150=k\times \left( 20 \right)\times 900 \\ & k=\frac{150}{20\times 900} \end{align}$ So, $k=\frac{1}{20}$ Now, $F=\frac{\text{Area}\times \text{Velocit}{{\text{y}}^{2}}}{20}$ Now, substitute the values of velocity, area and force to find k using Window 2 data. $\begin{align} & F=\frac{\text{Area}\times \text{Velocit}{{\text{y}}^{2}}}{20} \\ & F=\frac{\left( 3\times 4 \right)\times {{60}^{2}}}{20} \\ & F=360\ \text{pounds} \\ \end{align}$ As the hurricane force is $300\ \text{pounds}$ which less than the window 2 bearing force, it can stand against the hurricane.
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