# F is inversely proportional to sqrtg when f=15, g=144. How do you work out g when f=90?

Nov 24, 2016

$g = 4$

#### Explanation:

As $f$ is inversely proportional to $\sqrt{g}$,

it means $f \propto \frac{1}{\sqrt{g}}$

i.e. $f = \frac{k}{\sqrt{g}}$, where $k$ is a constant

When $f = 15$, $g = 144$

Hence $15 = \frac{k}{\sqrt{144}} = \frac{k}{12}$

and $k = 12 \times 15 = 180$

Hence equation is $f = \frac{180}{\sqrt{g}}$ and when $f = 90$,

we have $90 = \frac{180}{\sqrt{g}}$

or $\sqrt{g} = \frac{180}{90} = 2$

and $g = 4$