Question

Express the statement as an equation. Use the given information to find the constant of proportionality.

W is inversely proportional to the square of r. If $r=6$, then$W=10$

Short answer

Equation that represents the statement is $W=\frac{k}{r^2}$.

.Constant of proportionality is 360.

Step-by-step solution

Step 1. Understanding Inverse variation.

The relation between two variables is inversely proportional when,

$y=\frac{k}{x}$or $xy=k$

Here $k\ne 0$, y is inversely proportional to x and vice versa.

Step 2. Write the equation.

The relation between variables is inversely proportional hence,

$W=\frac{k}{r^2}$

Where k is constant of proportionality.

Step 3. Plug the values given in the equation to determine the value of the constant of proportionality.

Given values:

$\begin{array}{l}r=6\\ W=10\end{array}$

Putting values we get,

$\begin{array}{l}10=\frac{k}{6^2}\\ k=10\times 36\\ k=360\end{array}$