'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#