MATH!

[SeasonedSpice]

This is for all of y'all math geniuses.es.es. XD

ur parent function is: y=f(x)

now, what happens, or how is this function transformed when it is modified like this: y=2f(x)
and: y=f(2x)

[Kit-]

Vertical dilation and horizontal contraction.

[T0rajir0u]

dis sounds like hw 2 me

[GuidoHunter]

Your equation is ∂^2u/∂x^2=0
Your boundary conditions are ∂u/∂x(-L,t)=∂u∂x(L,t) and u(-L,t)=u(L,t) on a thin circular ring of circumference 2L.
Your initial condition is u(x,0)=f(x)

Find the function u.

--Guido

http://andy.mikee385.com

[Kilgamayan]

Let there be a geometric figure (not necessarily convex) with area less than 1. Prove you can place this figure on the coordinate plane so that no points with two integer coordinates belong to the figure.

EDIT: Hell, let's bust out the entire second CPS packet too.

1) Bob broke camp early and motored up-river to his favorite fishing hole. A mile upstream, his hat flipped overboard, but he didn't notice for another 5 minutes. As soon as he realized his hat was missing, he turned around and went after it. He recovered his hat just as it was passing the camp. Assuming Bob motored at full speed the whole way, how fast is the river flowing? The time it takes Bob to turn the boat around is negligible.

2) Can you find natural numbers m and n such that (m^2) - 3(n^2) = 8?

3) Let A be a collection of 100 integers. Can you select 15 integers in A such that the difference between any two of them is divisible by 7?

4) Prove that there exists an integer whose decimal representation consists entirely of 1s and which is divisible by 1999.

5) Say you want to color the real plane in such a fashion that no two points at unit distance have the same color. Can you do this with 2 colors? How about 3 colors?

[T0rajir0u]

Originally Posted by Kilgamayan

2) Can you find natural numbers m and n such that (m^2) - 3(n^2) = 8?

3) Let A be a collection of 100 integers. Can you select 15 integers in A such that the difference between any two of them is divisible by 7?

4) Prove that there exists an integer whose decimal representation consists entirely of 1s and which is divisible by 1999.

m^2 congruent to 8 mod 3 = 2 mod 3, impossible

we consider A mod 7; by pidgeonhole principle some residue class must contain ceiling(100/7) = 15 members

by fermat's little theorem (10^{1998} - 1)/9 is divisible by 1999 (which is prime) (ps the problem works for any integer relatively prime to 10 lulz)



other problems are gay and it's late

ps find integer solutions to x^3 + y^4 = 19^19

[Kit-]

Originally Posted by Kilgamayan

5) Say you want to color the real plane in such a fashion that no two points at unit distance have the same color. Can you do this with 2 colors? How about 3 colors?

2 colors: impossible, make an equilateral triangle with sides of length 1; at least two must share the same color.
3 colors: don't want to think right now rofl.

[Kilgamayan]

Originally Posted by T0rajir0u

(ps the problem works for any integer relatively prime to 10 lulz)

It was a problem from the 1999 Math Olympiad >_>

Originally Posted by T0rajir0u

other problems are gay and it's late

what

I expect you to get the river one no problem

In fact, I expect both the algebraic answer and logical answer from you

However I don't expect the first one from anyone since he gave it the first day of class and no one has done it yet

[duhh_]

me and math dont mix.

however, i do think i saw a site to help with stuff like that.

::begins going thru history::

[cetaka]

Originally Posted by Kilgamayan

5) Say you want to color the real plane in such a fashion that no two points at unit distance have the same color. Can you do this with 2 colors? How about 3 colors?

2 colors:
sup triangle

For 3 colors it's long and gay but still not that bad, you know that 2 points can't be 2 units apart that are the same color (easy contradiction, just try it), so draw random circles and stare at it for a couple minutes blabladone

[Kilgamayan]

That's not a proof at all >_>

I want to see something SUBSTANTIAL