Chapter 12.8, Problem 8WE

To determine

To calculate: How does $m$ changes when both $r$ and $s$ are doubled, when both $r$ and $s$ are tripled.

Answer to Problem 8WE

The value of $m$ is tripled.

Explanation of Solution

Given information:

How does $m$ changes when both $r$ and $s$ are doubled, when both $r$ and $s$ are tripled.

Where $m$ varies directly as the square of $r$ and inversely as $s$ .

Calculation:

Consider that $m$ changes when both $r$ and $s$ are doubled, when both $r$ and $s$ are tripled.

Where $m$ varies directly as the square of $r$ and inversely as $s$ .

As $y$ varies directly as $x$ , then the variation is direct and its equation is in the form $y=kx$ .

Recall that the $m$ ,varies directly as the square of $r$ and inversely as $s$, then:

  $m=k\frac{r^2}{s}$

When both $r$ and $s$are doubled, the equation becomes:

  $\begin{array}{c}m=k\frac{{\left(2r\right)}^2}{2s}\\ m=\frac{k4r^2}{2s}\\ m=\frac{2k{r}^2}{s}\\ m=2\left(\frac{k{r}^2}{s}\right)\end{array}$

Here the original variation, the value of $m$ is $2$ times:

Then the second thing is:

When both $r$ and $s$are tripled, the variation becomes:

  $\begin{array}{c}m=\frac{k{\left(3r\right)}^2}{3s}\\ m=\frac{9k{r}^2}{3s}\\ m=\frac{3k{r}^2}{s}\\ m=3\left(\frac{k{r}^2}{s}\right)\end{array}$

Hence the value of $m$ is tripled.

Thus, the value of $m$ is tripled. $$