Question

It is given that x varies directly as y and inversely as the square of z, and that x = 10 when y = 4 and z = 14. What is x when y = 14 and z = 7?

Answer 1

Typo on last sentence. Supposed to be: what is x when y = 16 and z = 7

Answer 2

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Answer 3

x = k (y/z^2) where k is a constant
then find the k by substituting x = 10, y = 4 and z = 7

after you got the k value,
x = k (16/49)

Answer 4

Variation... roughly speaking, direct variation involves division while inverse variation involves multiplication...

So since x varies directly with y, divide x by y, and since x varies inversely with the *square* of z, then multiply x by \(z^2\)

And all that should remain constant:
\[\Large \frac{\color{red}x\color{blue}z^2}{\color{green}y}= k\]

Answer 5

Now, you need to find the value of k.
Use the second bit of your problem: "...and that x = 10 when y = 4 and z = 14"