Question

Word problemo *_*

Answer 1

@tHe_FiZiCx99

Answer 2

do you know what the transverse and conjugate axes mean?

Answer 3

No

Answer 4

You got @whpalmer4 lol you don't need me, he's a waay better teacher :P

Answer 5

Oh great ;D

Answer 6

okay, the transverse axis connects the vertices of the hyperbola. the conjugate axis is perpendicular to the transverse axis

Answer 7

Okay..

Answer 8

let's arbitrarily define the center of the hyperbola to be at (0,0). it could always be moved somewhere else later, if necessary, but I don't see any need to do that in the problem statement.

Answer 9

a hyperbola will have the formula

(x^2/a^2) - (y^2/b^2) = 1 if the transverse axis is aligned with the x-axis

and

(y^2/a^2) - (x^2/b^2) = 1 if the transverse axis is aligned with the y-axis

let's go with the second one. I think if we have the two glass plates "hinged" at the top, then the hyperbola formed by the edge of the fluid is going to be shaped like a bowl or a hill (opens up or down). that means the transverse axis is parallel to the y-axis.

Answer 10

I wish the OpenStudy staff could get the drawing and equation tools working :-(

Answer 11

Okay...

Answer 12

a is half the length of the transverse axis, and b is half the length of the conjugate axis, in our formula above

a = 30/2 = 15
b = 50/2 = 30

what do you get if you plug those numbers into the formula?

Answer 13

(Y^2/225)-(X^2/900)=1

Answer 14

That's right. I believe that is the answer, if I've understood the problem correctly.

Answer 15

Really..that is it?!?!
OH GOODNESS I GIVE UP ON MATH! XD

Answer 16

The hyperbola represented by that equation looks like this

Answer 17

@thisSucks AND @AravindG CAN YOU JUST DOUBLE CHECK THIS PLEASE ;D

@whpalmer4 THANK YOU SO MUCH FOR YOUR HELP AND EXPLANATION!

Answer 18

oops, just spotted one mistake. 50/2 = 25, not 30 :-)

what is the new, improved formula?

Answer 19

b = 25

Answer 20

too much blood in my caffeine stream this morning :-)

Answer 21

(Y^2/225)-(X^2/625)=1
Lol! xD I SHOULD HAVE CAUGHT THAT TOO!

Answer 22

Yes, you should have, and I'm trying very hard to conceal my profound disappointment that you did not ;-)

Here's a new picture:

Answer 23

Hey xD
Am sorry,but my mind is everywhere at the moment
Lol thank you for catching that,how embarrassing

Answer 24

if you look, you can see that it is 30 from vertex to vertex, so that's our transverse axis of length 30. harder to see the conjugate axis as you need to draw the asymptotes, but when I hold a ruler up to my screen along where the asymptotes should be, it looks to cross the x axis at -25 or +25

Answer 25

Yes,I see that

Answer 26

so that would be a conjugate axis of 50, which a last rereading of the problem says is what we want. usually a good idea to reread the problem after solving it, just to be positive you solved that same problem :-)

Answer 27

and didn't make any dumb mistakes like dividing 50 in half and getting 30 :-)

Answer 28

I never did like hyperbolas, by the way. Must have fallen asleep in class that day :-)

Answer 29

THANK YOU SO MUCHHHHHHHHHHHHHHHHHHHHHHHHH
And clearly you had your eyes open ;D

Answer 30

I am curious about this problem now — might have to find some small pieces of glass and corn syrup and see for myself!

Answer 31

xD Well tomorrow I shall ask my teacher and I will update you!

Answer 32

you do that, thanks!

Answer 33

:) thank you!

Answer 34

ah, here's a picture!

http://demo.physics.uiuc.edu/lectdemo/scripts/demo_descript.idc?DemoID=483

Answer 35

I was thinking the clamped together part was at the top, not the side, but this makes more sense. I wonder if it means that we should switch x and y in the solution...leaning toward thinking that it does. That gives us a picture like this:

Answer 36

hmm, on second thought, scratch that. the edge of the fluid isn't going to curve back out to the right as it gets higher (assuming we had a less viscous liquid that could move further up)