p varies directly as the square of r and inversely as q and s and p = 40 when q = 5, r = 4 and s = 6

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p varies directly as the square of r and inversely as q and s and p = 40 when q = 5, r = 4 and s = 6, what is the equation of variation?

Two rules of variation:

1. Varies directly means we multiply
2. Varies inversely means we divide

There exists a constant k such that our initial equation of variation is:
p = kr^2/qs

With p = 40 when q = 5, r = 4 and s = 6, we have:
4^2k / 5 * 6 = 40
16k/30 = 40

Cross multiply:
16k = 40 * 30
16k = 1200

Using our equation calculator, we get:
k = 75

So our final equation of variation is:
p = 75r^2/qs