if y varies inversely as x² and x varies directly as z. find the relationship connecting y and z if c is a constant

y = c/z²

Step-by-step explanation:

(1) y ∝ 1/x²or

y = a/x² where a is a constant

x ∝ z or x = bz, where b is a constant

Substitute x into (1)

y ∝ a / (bz) ² = a / (b²z²) = (a/b²) / z²

a is a constant and b is a constant, so a/b² is a constant.

Let c = a/b². Then

y = c/z²