Chapter 8.2, Problem 4WE

To determine

To find: Value of p when $q=16$ .

Answer to Problem 4WE

When $q=16$ , $p=18$ .

Explanation of Solution

Given information:

The following variation:

p varies inversely as the square root of q.

  $p=12$ when $q=36$ .

Calculation:

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

  $p\sqrt{q}=k$

where k is a constant.

Substituting the given values of p and q in the above equation,

  $\begin{array}{l}p\sqrt{q}=k[\text{Given]}\\ 12\cdot \sqrt{36}=k[\text{Substitute]}\\ 12\cdot 6=k[\text{Find square root]}\\ k=72[\text{Multiply]}\end{array}$

Therefore, an equation of the inverse variation is $p\sqrt{q}=72$ .

To find p when $q=16$ , substitute in $p\sqrt{q}=72$ .

  $\begin{array}{l}p\sqrt{q}=72[\text{Equation]}\\ p\sqrt{16}=72[\text{Substitute]}\\ p\left(4\right)=72[\text{Find square root]}\\ p=18[\text{Divide both sides by 4]}\end{array}$