Chapter 11.6, Problem 14PPE

To determine

Equation for the inverse variation.

Answer to Problem 14PPE

  $y=\frac{7.7}{x}$

Explanation of Solution

Given Information:

The variable y varies inversely with x. The value of y is 3.5 when x is 2.2 .

Calculation:

Given that the variable y varies inversely with x. So we have

  $\begin{array}{l}y\propto \frac{1}{x}\\ y=\frac{k}{x}\\ yx=k\mathrm{.......}\left(i\right)\end{array}$

Here k is the constant of proportionality.

Also given that the value of y is 3.5 when x is 2.2 . So, on substituting values of x and y in above equation (i), we get

  $\begin{array}{c}yx=k\\ \left(3.5\right)\cdot \left(2.2\right)=k\\ 7.7=k\\ k=7.7\end{array}$

So, with this value of k , above equation (i) becomes

  $\begin{array}{c}yx=7.7\\ y=\frac{7.7}{x}\end{array}$