'L varies jointly as a and square root of b, and L = 72 when a = 8 and b = 9. Find L when a = 1/2 and b = 36?

Mar 14, 2017

$L = 6$

Explanation:

As $L$ varies jointly as $a$, we can say $L \propto a$

and square root of $b$ means that $L \propto \sqrt{b}$

and we can combine the two as $L \propto a \sqrt{b}$, which means

$L = k \times a \times \sqrt{b}$, where $k$ is a constant.

As $L = 72$, when $a = 8$ and $b = 9$, it means

$72 = k \times 8 \times \sqrt{9} = 24 k$ i.e. $k = \frac{72}{24} = 3$ and

$L = 3 a \sqrt{b}$

Hence, when $a = \frac{1}{2}$ and $b = 36$

$L = 2 \times \frac{1}{2} \times \sqrt{36} = 2 \times \frac{1}{2} \times 6 = 6$