Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 8 - Rational Functions - 8-1 Inverse Variation - Practice and Problem-Solving Exercises - Page 503: 15

Answer

$xy=250$ When $x=10$, the value of $y$ is $25$. Refer to the graph below.
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Work Step by Step

Recall: An inverse variation is represented by the equation $xy=k$, where $k$ is the constant of variation. As the value of $x$ increases, the value of $y$ decreases. The equation that models the direct variation can be determined by solving the value of $k$: This can be done by taking any ordered pair $(x, y)$ then substituting the values of $x$ and $y$ into the inverse variation formula $xy=k$. Since $x=2.5$ when $y=100$, substitute these into the formula $xy=k$ to obtain: \begin{align*} xy&=k\\\\ 2.5(100)&=k\\\\ 250&=k\end{align*} Therefore, the equation that models the inverse variation is $xy=250$. To find the value of $y$ when $x=10$, substitute $10$ to $x$ in the equation above to obtain: \begin{align*} xy&=250\\\\ 10(y)&=250\\\\ y&=\frac{250}{10}\\\\ y&=25 \end{align*} Use a graphing utility to obtain the graph above.
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