# Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set: 72

$\color{blue}{y=\frac{0.0015}{x^2}}$.

#### Work Step by Step

RECALL: (1) When $y$ varies directly as $x$, the variation is direct and is represented by the equation $y=kx$ where $k$ is the constant of variation. (2) When $y$ varies inversely as $x$, the variation is inverse and is represented by the equation $y=\frac{k}{x}$ where $k$ is the constant of variation. $y$ varies inversely as the square of $x$ so the equation is $y=\frac{k}{x^2}$ with $k$=constant of variation. To find the value of $k$, substitute the given values into $y=\frac{k}{x^2}$ to obtain: $$y=\frac{k}{x^2} \\0.15=\frac{k}{0.1^2} \\0.15 =\frac{k}{0.01} \\0.15(0.01)=k \\0.0015=k$$ Thus, the equation of the variation is: $\color{blue}{y=\frac{0.0015}{x^2}}$.

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.