Chapter 12.8, Problem 7WE

To determine

To calculate: How does $x$ change when both $u$ and $v$ are doubled, when $u$ is doubled and $v$ is halved.

Answer to Problem 7WE

The variation is the same as original.

Explanation of Solution

Given information:

How does $x$ change when both $u$ and $v$ are doubled, when $u$ is doubled and $v$ is halved.

Where $x$ varies jointly as $u$ and $v$ .

Calculation:

Consider that $x$ change when both $u$ and $v$ are doubled, when $u$ is doubled and $v$ is halved.

Where $x$ varies jointly as $u$ and $v$ .

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

Recall that the $x$ ,varies jointly as $u$ and $v$, then:

  $x=kuv$

When $u$ and $v$are doubled, the equation becomes:

  $\begin{array}{l}x=k\times 2u\times 2v\\ x=4kuv\end{array}$

Here the original variation, the value of $x$ is $4$ times as it grate:

Then the second thing is:

When $u$ is doubled and $v$ is halved, the variation becomes:

  $\begin{array}{l}x=k\times 2u\times 0.5v\\ x=kuv\end{array}$

Hence the variation is the same as original.

Thus, the variation is original. $$