Suppose r varies directly as the square of m, and inversely as s. If r = 16 when m=9 and s = 9, find r when m=27 and s = 9.

r = 144.

Step-by-step explanation:

r ∝ m^2 / s

r = k m^2/s where k is a constant

From the given values:

16 = k 9^2 / 9

16 = 9k

k = 16/9

So when m = 27 and s = 9:

r = 16/9 * 27^2 / 9

r = (16 * 27^2) / 81

r = 16*27 / 3

= 9*16

= 144,