'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

$L = 6$ $L=6$

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

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

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

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

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

$72 = k \times 8 \times \sqrt{9} = 24 k$ $72=kxx8xxsqrt9=24k$ i.e. $k = \frac{72}{24} = 3$ $k=72/24=3$ and

$L = 3 a \sqrt{b}$ $L=3asqrtb$

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

$L = 2 \times \frac{1}{2} \times \sqrt{36} = 2 \times \frac{1}{2} \times 6 = 6$ $L=2xx1/2xxsqrt36=2xx1/2xx6=6$