Question

Write the function that models each relationship. find z when x=4 and y=8. z varies jointly with x and y.?
when x=2 y=2 and z=7

Answer 1

@whpalmer4

Answer 2

Joint variation means \[z = k x y \]Plug in the values you know and solve for \(k\). Then use the updated equation to find the desired value of \(z\)

Answer 3

so when i find out what k is then do i leave z and plug in k x=4 and y=8?

Answer 4

Yes, if \(k\) turns out to be 3 (it isn't), you would evaluate
\[z = (3)(4)(8)\]

Answer 5

oh ok and then that would be are answer

Answer 6

You don't actually have to find \(k\) to solve this problem, as it turns out.

Answer 7

That would be OUR answer, yes :-)

Answer 8

ok but im going to find k because i know how to do it now and it will not hurt to find it :)

Answer 9

after you find \(z\) I'll show you how you could have it without finding \(k\)

Answer 10

yes, I agree, you should find \(k\) — doing it the other way will allow us to check our work, which is usually a good thing.

Answer 11

ok let me find z

Answer 12

will k =1.75?

Answer 13

and will z=56

Answer 14

@whpalmer4 are you still there???

Answer 15

Yes to both!

Answer 16

awesome i did it right so happy!!!

Answer 17

Here's how you could have found it without finding \(k\) first:

\[z = kxy\]because this is joint variation. We know that \(z = 7\) if \(x = 2, y = 2\). We want to find \(z\) when \(x = 4, y = 8\). We are doubling \(x\), so that causes a doubling of \(z\). \(x = 4, y = 2, z = 7*2 = 14\). Now we are quadrupling \(y\), so that causes a quadrupling of \(z\). \(x = 4, y = 8, z = 14*4 = 56\) Piece of cake :-)

Answer 18

ok i get it thank you so much for your help!!!! i have to go. thank you again!!!

Answer 19

You're welcome!