Question

z varies directly with x and inversely with y. When x=6 and y=2, z=15. Find z when x=4 and y=9

Answer 1

Can someone explain how to do this?

Answer 2

start out with z=

Answer 3

Then put the directly stuff on top and the inversely stuff on the bottom.

Answer 4

I made a proportion of 6/15 4/z

Answer 5

I tried to cross multiply and divide and got 10

Answer 6

Then multiply by k for the constant.

Answer 7

How do you determine the constant?

Answer 8

\[z=\frac{kx}{y}\]
\[\frac{zy}{x}=k\]
\[\frac{15(2)}{6}=\frac{9z}{4}\]

Answer 9

Here is how to find k
Replace z with 15, y with 2 and x with 6 and solve for k

Answer 10

2.2 repeating?

Answer 11

Is that what k equals?

Answer 12

\[15=\frac{6k}{2}\]
\[30=6k\]
\[5=k\]

Answer 13

Isn't it 15 times 2?

Answer 14

Yes. and 15 times 2 = 30

Answer 15

and isn't it 9k/4