Chapter 8.2, Problem 4ST

a.

To determine

To find: Constant of variation .

Answer to Problem 4ST

The constant of variation, k is $15$ .

Explanation of Solution

Given information:

The following variation:

y varies inversely as x.

  $y=45$ when $x=\frac{1}{3}$ .

Calculation:

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

  $xy=k$

where k is a constant.

Substituting the given values of x and y in the above equation,

  $\begin{array}{l}xy=k[\text{Given]}\\ 45\left(\frac{1}{3}\right)=k[\text{Substitute]}\\ k=15[\text{Multiply]}\end{array}$

b.

To determine

To find: Value of x when $y=30$ .

Answer to Problem 4ST

When $y=30$ , $x=\frac{1}{2}$ .

Explanation of Solution

Given information:

The following variation:

y varies inversely as x.

  $y=45$ when $x=\frac{1}{3}$ .

Calculation:

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

  $xy=k$

where $k=15$ (calculated in part a).

Therefore, an equation of the inverse variation is $xy=15$ .

To find x when $y=30$ , substitute in $xy=15$ .

  $\begin{array}{l}xy=15[\text{Equation]}\\ x\left(30\right)=15[\text{Substitute]}\\ x=\frac{15}{30}[\text{Divide both sides by 30]}\\ x=\frac{1}{2}[\text{Simplify]}\end{array}$