[WANTED] Day[9] or mathuser

What curve?, there is no curves by what your saying, its only line segments.

the lines fill in the area beneath a curve. if all the lines that beetles drew were there at once there would be a curve over the area that the lines filled in. sorry for my vagueness

y intercept wouldn't be 1-x because they are at different speeds. or am i missing something?

u forgot the dead or alive part :O!

On September 29 2008 19:18 TBB wrote: y intercept wouldn't be 1-x because they are at different speeds. or am i missing something?

no youre adding something. the bugs are assumed to be traveling at the same speed as it isnt mentioned otherwise.

On September 29 2008 19:03 Subaru wrote: What curve?, there is no curves by what your saying, its only line segments.

the line segment that connects the two points is a tangent line, which means only at one point does it touch the curve.



seems like a trick question imo. to have a function of f(x,y) = x, 1-x, where every point from [0,1] is a tangent line doesnt make sense unless the curve is a function of the bugs movement in which case id have to find a pencil and paper and i dont feel like doing that

oh if one bug is alive and other is dead this is ez

Isn't it y = 1 - x ? I think you're really overthinking this

hyperbola?

it's a quarter circle

yeah so the equation of the curve is (x - 1)^2 + (y - 1)^2 = 1 for 0 <= x <= 1 and 0 <= y <= 1

i hate beetles so i take my shotgun and blow those fuckers up

=
problem solved.

kthxbai

Missing info: There was a pile of dead ethiopians at x=2?

On September 29 2008 22:04 thundza wrote: it's a quarter circle

actually... kinda a quarter circle, but not really. ask myth for more info.

woops, it's not a quarter circle, though it looks extremely close to it. talked to some better-at-math friends and it turns out that...

for time t = the time remaining that the bugs will continue to walk, and t in [0, 1], the slope of all the tangent lines is t/(t-1) and the y-intercept of all the tangent lines is t. therefore,

now, the curve defined by all these tangent lines is

so, to compute sup, we differentiate the tangent function with respect to t, getting

for which the critical points are at

or just 1 - sqrt(x) since t in [0,1]. so plug t = 1 - sqrt(x) into the curve and you will get

and the curve looks like this:

also it looks from the graph like this function is not symmetrical about the y=x line but if you plug in some numbers, it is

for x = 0.81, sqrt(x) = 0.9, so y = 0.81 - 1.8 + 1 = 0.01, and when x = 0.01, sqrt(x) = 0.1, so y = 0.01 - 0.2 + 1 = 0.81

same works for (0.04, 0.64) and (0.64, 0.04), etc.

eat it day[9] we don't need you, we just need tristan AND nick rauh

well you can set up a parametric equation that...

damnit corwin -_-

haha yeah my first thought too was just a quarter circle...

yeaaah so it turned out to be a least a little more complicated than i'd thought haha
awesome myth thanks =]

and thundza haha