The value of y is [tex]\frac{8}{27}[/tex]
Explanation:
Given that y varies directly as x and inversely as the square of z.
Thus, it can be written as
[tex]y=\frac{kx}{z^2}[/tex]
Also, given that [tex]y=8[/tex] when [tex]x=16[/tex] and [tex]z=4[/tex]
Substituting these values in the above expression, we have,
[tex]8=\frac{k(16)}{4^2}[/tex]
[tex]8=\frac{k(16)}{16}[/tex]
[tex]8=k[/tex]
Thus, the value of the constant is 8
Now, we shall find the value of y.
The value of y can be determined by substituting [tex]x=3[/tex] , [tex]z=9[/tex] and [tex]k=8[/tex] in the expression [tex]y=\frac{kx}{z^2}[/tex]
Thus, we have,
[tex]y=\frac{8(3)}{9^2}[/tex]
Simplifying, we get,
[tex]y=\frac{24}{81}[/tex]
Dividing, we get,
[tex]y=\frac{8}{27}[/tex]
Thus, the value of y is [tex]\frac{8}{27}[/tex]
