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Curve? Not point?
Well, rearrange them so they look like their more-known forms. Also, try making agraph of these 2.
yes the intersection of a plane and the other surface hehe.
z=x^2-1 and y=x-1
they look like this: http://assets.openstudy.com/updates/attachments/4f6ea09fe4b0772daa08c3f9-brinethery-1332650156119-tripleintegralproblem.pdf
WAT. I CANT DO THT.
i better do my vecotrs work tho
other people, be my savior!
i was thinking systems...but to do it a third equation is needed...is integration applicable?
Well I don't want to find a point. I want to find a curve. so I just need a pair of equations. But i can figure out a way of getting the equation of the curve.
which math lesson is this? maybe i'll have an idea on how to solve it from there.
Well I was studying triple integrals.
ohh...then this really has something to do with integration...which i am weak at :p sorry
Well the integration part is clear, the problem is to get the cuve of intersection of those surfaces =/
z = 1-x^2 y = 1-x -> x = 1-y z = 1-(1-y)^2 z = 1 - 1+2y-y^2 z = 2y-y^2
Thanks amistre that is one of the results i got. But this one confuse me too:\[z=1-x^2=(1+x)(1-x)=y(1+x)\]
I graphed \[z=y(1+x)\]and I got a weird surface. That confused me.
and the equation \[z=2y-y^2\] it's a surface too. I don't know how does a curve's equation looks like.
the "curve" is the intersection of the plane and the cylindar; but id have to plot them to see it better
yep, thats the setup i had on my paper :)
So the idea I have on my mind is that the intersection between those two surfaces is a space curve. but none of the equations I have got is a space curve.
I can interpret z = 2y - y^2 and x = 0. as a curve. But I'm not sure.
the projection onto the zy plane is 2y-y^2 i wonder if instead of trying to solve for xyz we introduce a x(t), y(t) and z(t)
x=1-t y = t z=2t-t^2
but with x = t
http://www.wolframalpha.com/input/?i=polar+r%3D%3C1-t%2Ct%2C2t-t%5E2%3E this aint it but its a cool mistake nonetheless
ahh that it's in polar coordinates. How do I do to specify cartesian coordinates?
i dunno yet, wolfram hates me
I got it hehe: http://www.wolframalpha.com/input/?i=parametric+plot+%28t%2C+1-t%2C1-t%5E2%29
Ohh that looks better
that looks like it :)
Well thank you amistre64!