Chapter 12, Problem 82CLR

To determine

To find: The value of a when $b=20$ and $c=5$ .

Answer to Problem 82CLR

The value of a is 4.

Explanation of Solution

Given:

The value of a varies directly with b and inversely as the square of c .

Also, $a=10$ when $b=8$ and $c=2$ .

Calculation:

Since a varies directly with b,

  $\begin{array}{c}a\propto b\\ a=pb\end{array}$.........(1)

Since a varies inversely as the square of c,

  $\begin{array}{c}a\propto \frac{1}{c^2}\\ a=\frac{q}{c^2}\end{array}$.............(2)

From equations (1) and (2), $a=\frac{kb}{c^2}$ where $k=pq$ .

Substitute 10 for a , 8 for b and 2 for c in the relation $a=\frac{kb}{c^2}$ to find the value of k .

  $\begin{array}{c}a=\frac{kb}{c^2}\\ 10=\frac{k8}{2^2}\\ 10=2k\\ k=5\end{array}$

So, the relation becomes $a=\frac{5b}{c^2}$ .

For $b=20$ and $c=5$ , the value of a is,

  $\begin{array}{c}a=\frac{5b}{c^2}\\ =\frac{\cancel{5}\times 20}{\cancel{5}\times 5}\\ =4\end{array}$