Question

If y varies directly as x^2 and y=12 when x=2, find y when x=5. Help please!

Answer 1

okay, if \(u\) varies directly with \(v\), then we can write \[u = kv\]

Here you have \(y\) varying directly with \(x^2\). What will the relationship look like, given what I just stated?

Answer 2

\(k\) is the constant of variation, btw.

Answer 3

You wrote u=kv...

Answer 4

@whpalmer4

Answer 5

Yes, I'm aware of that :-)

If you have "thing 1" varying directly with "thing 2",

"thing 1" = k* "thing 2"

Answer 6

Yes, but it's the x^2 that's tripping me up. Would direct variation work the same way?

Answer 7

"thing 1" is y
"thing 2" is x^2

Answer 8

So I'd get y=k(x^2)?

Answer 9

it can be a considerably more complicated expression than \(x^2\), but it still works the same way: \(u = k * v\) if \(u\) varies directly with \(v\)

yes! \[y = kx^2\]Now, you know a pair of \((x,y)\) that go together. Use them to find the value of \(k\)...

Answer 10

I just don't know how... I don't know the step that comes after y=kx^2.

Answer 11

@whpalmer4

Answer 12

" y=12 when x=2"

plug those numbers into your new formula and solve for \(k\)

Answer 13

And what I get will be my correct answer?

Answer 14

no, but it will be a necessary step to finding the final answer.

Answer 15

\[12 = k(2)^2\]\[12 = k*4\]\[k =\]

Answer 16

When I come up with it I'll put it on here.

Answer 17

I got the answer of y=30. Is this correct?

Answer 18

Uh, no. Can you show me what you got for \(k\)?

Answer 19

I got 6=k :/

Answer 20

\[12 = k(2)^2\]\[12 = k*4\]\[k=\]

Answer 21

it looks like you're forgetting to square \(x\)...

Answer 22

both in finding \(k\) and then in finding the value of \(y\) that goes with the new value of \(x\)

Answer 23

at least you're consistent — we just have to fix one problem and then you'll be doing it right :-)

Answer 24

Oh, k=3?

Answer 25

yes!
so the new, improved value of \(y\) when \(x=5\) is?

Answer 26

So the second answer would be y=15?

Answer 27

I was afraid you would answer that. the equation is \[y = kx^2 = k*x*x\]

Answer 28

\[y = 3*5*5 = \]

Answer 29

75!

Answer 30

yes

Answer 31

Thank you so much for your help and patience, I appreciate it so much!

Answer 32

what would the value of \(y\) be if \(x = -1\)?

Answer 33

3?

Answer 34

yes, very good!

I made a graph of the curve that you have here, and put on crossing lines at the various points we visited.

Answer 35

You are unbelievable helpful. Thank you!!!

Answer 36

You're welcome!