Chapter 8.2, Problem 3WE

To determine

To find: Value of w when $v=3$ .

Answer to Problem 3WE

When $v=3$ , $w=12$ .

Explanation of Solution

Given information:

The following variation:

w is inversely proportional to the square of v.

  $w=3$ when $v=6$ .

Calculation:

The given variation can be expressed as an equation as follows:

  $w{v}^2=k$

where k is a constant.

Substituting the given values of w and v in the above equation,

  $\begin{array}{l}w{v}^2=k[\text{Given]}\\ 3{\left(6\right)}^2=k[\text{Substitute]}\\ 3\cdot 36=k[\text{Find square]}\\ k=108[\text{Multiply]}\end{array}$

Therefore, an equation of the inverse variation is $w{v}^2=108$ .

To find w when $v=3$ , substitute in $w{v}^2=108$ .

  $\begin{array}{l}w{v}^2=108[\text{Equation]}\\ w{\left(3\right)}^2=108[\text{Substitute]}\\ w\left(9\right)=108[\text{Find square]}\\ w=12[\text{Divide both sides by 9]}\end{array}$