Question

Y varies directly with x and inversely with the source root of z if y =4 when x=z and z=4 what is y when x=6 and z=9

Answer 1

8

I made a couple of assumptions so you might want to make sure I made the right assumptions.

I assumed you meant square root of z; not source of z.

I also assumed you meant x=2 not x=z.

Explanation:

y varies directly with means y=k times something where k is a constant.

Inversely means to divide by whatever it says it varies inversely with.

So we have:

`y=k \cdot (x)/(√(z))`

We are given y=4 and x=2 and z=4, which means:

`4=k \cdot (2)/(√(4))`

`4=k \cdot (2)/(2)`

`4=k(1)`

`4=k`

So the constant is k which means the equation for any (x,y,z) is:

`y=4 \cdot (x)/(√(z))`

We want to know y when x=6 and y=9:

`y=4 \cdot (6)/(√(9))`

`y=4 \cdot (6)/(3)`

`y=4 \cdot 2`

`y=8`