Question

Quantities $r$ and $s$ vary inversely. When $r$ is $1200,$ $s$ is $0.35.$ What is the value of $s$ when $r$ is $2400$? Express your answer as a decimal to the nearest thousandths.

Answer 1

Answer:

The value of s is 0.175.

Explanation:

Given,

r and s vary inversely,

That is,

$r\propto \frac{1}{s}$

$\implies r=\frac{k}{s}$

Where, k is the constant of proportionality,

We have, r = 1200 if s = 0.35,

$\implies 1200 = \frac{k}{0.35}$

$\implies k=1200\times 0.35 = 420$

Thus, the equation that shows the relation between r and s is,

$r=\frac{420}{s}$

$\implies s=\frac{420}{r}$

If r = 2400,

$s=\frac{420}{2400}=0.175$