Question

find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.

Answer 1

k = ⅔

d. y = ⅔xz; y(6, 3) = 12

Explanation:

y ∝ x and y ∝ z, so

y ∝ xz and

(1) y = kxz Divide each side by xz

k = y/(xz) Let x = 1, z =4, y = ⁸/₃

= (⁸/₃)/(1 × 4)

= ⁸/₃ × ¼ Cancel 4s

(2) k = ⅔ Substitute into (1)

y = ⅔xz Let x = 6, z = 3

y = ⅔ × 6 × 3 Cancel 3s

y = 2 × 6

y = 12

y(6, 3) = 12