Question

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

A varies inversely as r. If $\mathrm{r}=3$, then$\mathrm{A}=7$

Short answer

Equation that represents the statement is $\mathrm{A}=\frac{\mathrm{k}}{\mathrm{r}}$.

Constant of proportionality is 21.

Step-by-step solution

Step 1. Understanding Inverse variation.

The relation between two variables is inversely proportional when,

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

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

Step 2. Write the equation.

The relation between variables is inversely proportional hence,

$\mathrm{A}=\frac{\mathrm{k}}{\mathrm{r}}$

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:

$\begin{array}{l}\mathrm{A}=7\\ \mathrm{r}=3\end{array}$

Putting values we get,

$\begin{array}{l}7=\frac{\mathrm{k}}{3}\\ \mathrm{k}=7\times 3\\ \mathrm{k}=21\end{array}$