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Asked by Yeeun

P is inversely proportional to the square of Q(P,Q > 0). When P=3, Q=4. Find an equation for P in terms of Q and find the exact value of Q when P=8?

An inverse proportionality means that the two variables are related in a manner like: P=b/Q^2 or P(Q^2)=b where b is a constant of proportionality. If you now substitute the known values for P and Q you will get the value of b: 3*(4^2)=3*16=48. Therefore b=48. So the equation of P in terms of Q is: P=48/Q^2. To find Q when P is 8, you should now solve the equation for Q, so you get: Q^2=48/8=6 therefore Q=sqrt(6). Notice here you take only the positive value of the square root as P,Q are both positive.

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Fotios Tsitsos
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