"This is an ex-parrot!"
Dawn: I think a date should be in a real fancy restaurant, then champagne at a night club with a floor show, then ballroom dancing. Joyce: Unfortunately, we're not dating in a movie from the thirties.
'Get It Done'
Spike's Bitches 26: Damn right I'm impure!
[NAFDA] Spike-centric discussion. Lusty, lewd (only occasionally crude), risque (and frisque), bawdy (Oh, lawdy!), flirty ('cuz we're purty), raunchy talk inside. Caveat lector.
Susan W. - Oct 05, 2005 6:27:48 pm PDT #6703 of 10001
Good Trouble and Righteous Fights
Gris - Oct 05, 2005 6:32:38 pm PDT #6704 of 10001
Hey. New board.
How do you inscribe a triangle within a parabola? One point in the peak, one at each x-axis crossing? (assuming it's a parabola with exactly two real solutions)
Heh. Math geekery.
Emily - Oct 05, 2005 6:50:18 pm PDT #6705 of 10001
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
Oh, sorry, did I say that? It's meant to be a parabolic segment and its inscribed triangle, so I've said, basically, wherever the line is which cuts off the segment, move the segment so that line is at the x-axis and the segment is above it (so yes, the points of the triangle will be at the x crossings and at the vertex).
Gris - Oct 05, 2005 7:16:24 pm PDT #6706 of 10001
Hey. New board.
T:P is 3:4 right? That's a fun problem.
My method is below, all whitefonted for those that hate math (infidels!): Yeah, all parabolic segments can be defined by an upside-down (negative a) parabola with one of the solutions at (0,0) (so c=0). Then our parabola is of the form y = ax^2 + bx, with a < 0. Our key triangle points are the solutions to y=0: (0,0) and (-b/a, 0) and the peak, which is directly between them and turns out to be (-b / 2a, -b^2 / 4a) (can be found just by plugging x = -b/2a, the midpoint, or using derivative first to be sure). T = 1/2 * b * h, then, is b^3 / 8a^2
To find the area of the parabola segment, just need to integrate ax^2 + bx from 0->-b/a, which isn't too bad, and gives b^3 / 6a^2, so T:P = 3:4
I think this may have been a problem on the AP calc exam my senior year, actually. I've def' seen it somewhere. Figuring out the representation trick you did is definitely the crucial step.
Emily - Oct 05, 2005 7:27:53 pm PDT #6707 of 10001
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
Okay, so where were you two days ago when this would have saved me six pages?!
Also, why isn't it online anywhere? I googled parabola area inscribed triangle, but they all want to talk about Diophantus's proof, which is lovely but not what I need!
Sean K - Oct 05, 2005 7:30:06 pm PDT #6708 of 10001
You can't leave me to my own devices; my devices are Nap and Eat. -Zenkitty
OMG, CASH! You're all such pretty people!
meara - Oct 05, 2005 7:37:52 pm PDT #6709 of 10001
I like Cash's hair.
Emily - Oct 05, 2005 7:38:54 pm PDT #6710 of 10001
"In the equation E = mc⬧, c⬧ is a pretty big honking number." - Scola
My mother just forwarded my grandmother's obituary. It reads kind of strange to me, but I guess it may just be inescapably weird to read a summary like that of someone you know. I found this particularly weird:
Her husband, parents, brother, and an infant grandson preceded her in death.
I know it's traditional, but... it's weird. Also, depressing. Which, in an obituary, is sort of gilding the lily, don't you think?
(The obituary I can find online -- maybe a different paper? -- just says "She was preceded in death by an infant grandson" which, actually, may be worse.)
beth b - Oct 05, 2005 8:06:25 pm PDT #6711 of 10001
oh joy! Oh Rapture ! I have a brain!
Cash - you look so elegant ! No wonder Buffista babies are so cute.
Hey VW - hopeing things are going well enough so you can stay home. A step back is ok... we can help hold you up.
and I am jealous because you have a frosty.
dw - Oct 05, 2005 8:32:52 pm PDT #6712 of 10001
Silence means security silence means approval