'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?

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Answer 1 · 2017-03-14T07:00:22

$L=6$

As $L$ varies jointly as $a$ , we can say $Lpropa$

and square root of $b$ means that $Lpropsqrtb$

and we can combine the two as $Lpropasqrtb$ , which means

$L=kxxaxxsqrtb$ , where $k$ is a constant.

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

$72=kxx8xxsqrt9=24k$ i.e. $k=72/24=3$ and

$L=3asqrtb$

Hence, when $a=1/2$ and $b=36$

$L=2xx1/2xxsqrt36=2xx1/2xx6=6$