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 and Y=2, Z=7.

I have a table set up with the X's, Y's, and one Z but don't know where to go from there.. @mathmale

Answer 1

"varies jointly" tells us that y is directly proportional to the values of both x and y. Symbolically, y=k*x*y, where k is just a constant of proportionality which we must find.

We're told that z=7 when x=2 and y=2. substitute these three values into y=k*x*y, and then solve the resulting equation for k. Again, k is our constant of proportionality.

Answer 2

Okay so I would be written as 2 = 7*2*2 ?

Answer 3

*it

Answer 4

If z= k * x * y, and z=7, x=2 and y=2,
7 = k * 2 * 2. Nicole, please solve this for k.

Answer 5

Oh, I see. Sorry.

Answer 6

So, z = ( ? )x*y

Answer 7

k = 7/4 ?

Answer 8

Yes, and so, if x= 4 and y = 8, z = ??

Answer 9

16?

Answer 10

Sorry, 56?

Answer 11

56 is right.

Answer 12

Okay, now that I have the equation used and the answer to Z, is that the problem solved? Or is there more?

Answer 13

Yes, it is solved. You have Z=7/4(X)(Y), and found Z when x=2 and y=4. That is all that the question requires.

Answer 14

Okay, thank you to both of you! Would you be willing to help me more?

Answer 15

sure!

Answer 16

Cool.

Graph each equation. Identify the x- and y-intercepts and the asymptotes of the graph.

y = 1/x

I can put up pictures as we go for the graph.

Answer 17

Do I just do a fill in table for x?

Answer 18

You could.
Vertical asymptotes are whenever the denominator is 0 (here, x=0)
Horizontal asymptotes are harder to describe...

Answer 19

Nicole, BT is right on target, and I'm glad you two are working together. The function y=1/x is important and often seen in math. I'd suggest you memorize its shape, just as you would memorize the shape of the basic parabola