Question

y varies directly as x and inversely as the square of z. y=20 when x=50 and z=5. Find y when x=3 and z=6.

Answer 1

Answer:

y = $\frac{5}{6}$

Step-by-step explanation:

Given that y varies directly as x and inversely as the square of z then the equation relating them is

y = $\frac{kx}{z^{2} }$ ← k is the constant of variation

To find k use the condition y = 20 when x = 50 and z = 5, then

k = $\frac{yz^2}{x}$ = $\frac{x20(25)}{50}$ = 10, thus

y = $\frac{10x}{z^{2} }$ ← equation of variation

Given x = 3 and z = 6, then

y = $\frac{10(3)}{36}$ = $\frac{30}{36}$ = $\frac{5}{6}$