Chapter 11.6, Problem 5P

Suppose/varies inversely with x. Write an equation for the inverse variation.

$y=\frac{2}{5}whenx=\frac{4}{5}$

To determine

To find : an equation for the inverse variation

Answer to Problem 5P

The equation is $k=\frac{8}{15}$

Explanation of Solution

Given information : Y varies inversely with x , $y=\frac{2}{3}$ when $x=\frac{4}{5}$

Calculation :

Y varies inversely with x

  $\begin{array}{l}y\alpha \frac{1}{x}\\ y=\frac{k}{x}\\ y=\frac{2}{3}\\ x=\frac{4}{5}\\ k=xy\\ k=\frac{2}{3}\times \left(\frac{4}{5}\right)\\ k=\frac{8}{15}\end{array}$