Question

Need help!

v varies directly as the square of x and inversely as the cube of y. Find v when x=3 and y=2, given that v=2 when x=4 and y=3

Answer 1

Explanation:

If two objects vary directly, we just divide those two objects.

If two objects vary indirectly, we multiply them.

So here we have

`\frac{v}{ {x}^(2) } {y}^(3) = k`

where k is a constant.

So let analyze when all variables Except k is given.

`(2)/(16) (27) = 3.375`

So k=3.375

`\frac{v}{ {3}^(2) } (2 {}^(3) ) = 3.375`

`(v)/(9) (8) = 3.375`

`(v)/(9) (8) = (27)/(8)`

`v8 = (243)/(8)`

`v = (243)/(64)`

`3.796875`