Answer:
y = [tex]\frac{5}{6}[/tex]
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 = [tex]\frac{kx}{z^{2} }[/tex] ← k is the constant of variation
To find k use the condition y = 20 when x = 50 and z = 5, then
k = [tex]\frac{yz^2}{x}[/tex] = [tex]\frac{x20(25)}{50}[/tex] = 10, thus
y = [tex]\frac{10x}{z^{2} }[/tex] ← equation of variation
Given x = 3 and z = 6, then
y = [tex]\frac{10(3)}{36}[/tex] = [tex]\frac{30}{36}[/tex] = [tex]\frac{5}{6}[/tex]
