Question

Z varies directly with x and inversely with y.

Answer 1

Answer:

z = $\frac{20}{9}$

Step-by-step explanation:

Given that z varies directly with x and inversely with y then the equation relating them is

z = $\frac{kx}{y}$ ← k is the constant of variation

To find k use the condition when x = 6 and y = 2, z = 15, thus

15 = $\frac{6k}{2}$ ( multiply both sides by 2 )

30 = 6k ( divide both sides by 6 )

5 = k

z = $\frac{6x}{y}$ ← equation of variation

When x = 4 and y = 9, then

z = $\frac{5(4)}{9}$ = $\frac{20}{9}$