Answer:

q = 5/108

Step-by-step explanation:

q varies directly as r and inversely as cube of s

q = kr/s³ where k is the constant of variation

if q = 5, r = 1 and s = 1/2

q = kr/s³

5 = k ( 1 ) / ( 1/2 ) ³

5 ( 1/2 ) ³ = k ( 1 )

k = 5 ( 1/8 )

k = 5/8

if r = 2 and s = 3, find q.

q = kr/s³

q = ( 5/8 ) ( 2 ) / 3³

q = ( 10/8 ) / 27

q = 10/8 * ( 1/27 )

q = 10/216 ÷ 2/2

q = 5/108