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

Answer:

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.

Step-by-step 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:

$y=k \cdot \frac{x}{\sqrt{z}}$

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

$4=k \cdot \frac{2}{\sqrt{4}}$

$4=k \cdot \frac{2}{2}$

$4=k(1)$

$4=k$

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

$y=4 \cdot \frac{x}{\sqrt{z}}$

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

$y=4 \cdot \frac{6}{\sqrt{9}}$

$y=4 \cdot \frac{6}{3}$

$y=4 \cdot 2$

$y=8$