Question

Suppose r varies directly as the square of​ m, and inversely as s. if r equals 15r=15 when m equals 8m=8 and s equals 4s=4​, find r when m equals 16m=16 and s equals 4s=4.

Answer 1

Symbolically,

k*m^2
r= ---------
s

Now replace r with 15 and m with 8. Calculate the constant of proportionality k:
k(8)^2
15 = ---------- Solve this for k by dividing both sides of this equation by
4

4 4
------- . We get ------- * 15 = k, and this simplifies to 60/64 = 15/16.
8^2 8^2

Then your function r is

k*m^2 15 *m^2
r= --------- = -------------
s 16s

You are to find r when m equals 16 and s equals 4. This would be:

k*m^2 15 *m^2 15*16^2 15(16)
r= --------- = ------------- => r = -------------- = ------------ = 60 (answer)
s 16s 16*4 4