Answer:
[tex]y=448[/tex]
Step-by-step explanation:
To solve this problem, we'll use the concept of joint variation and inverse variation.
Given that y varies jointly as x and the square of z and inversely as n. We can express this mathematically as...
[tex]y \propto \dfrac{xz^2}{n}[/tex]
Add a direct Proportion constant, "k," to get rid of the proportion sign.
[tex]y \propto \dfrac{xz^2}{n}\\\\\Longrightarrow y =k\dfrac{xz^2}{n}[/tex]
Now using the fact that y=80 when x=9, z=4, and n=18. We can find the value of "k."
[tex]y =k\dfrac{xz^2}{n}\\\\\Longrightarrow 80=k\dfrac{(9)(4)^2}{18} \\\\\Longrightarrow 80=k\dfrac{(9)(16)}{18} \\\\\Longrightarrow 80=k\dfrac{144}{18} \\\\\Longrightarrow 80=8k\\\\\Longrightarrrow \boxed{k=8}[/tex]
Thus, we have...
[tex]y =\dfrac{10xz^2}{n}[/tex]
Now we can plug in x=37,z=7, and n=35 to find y.
[tex]y =\dfrac{8xz^2}{n}\\\\\Longrightarrow y =\dfrac{10(32)(7)^2}{35}\\\\\Longrightarrow y =\dfrac{10(32)(49)}{35}\\\\\Longrightarrow y =\dfrac{15680}{35}\\\\\therefore \boxed{\boxed{y=448}}[/tex]
