fuck math it ruined me throughout high school
Given are five line segments (or equivalently any five positive numbers aka lengths) so that any three of them can be put together to make a (nondegenerate) triangle. Prove that at least one of those triangles must be acute.
triangle inequality
what does the law of cosines tell you about acute triangles?
I forget most of the non-simple math I learned back in school already and I only graduated 2 years ago 
5
Over for retardcels
Math sucks, hated my bitch of a math teacher and It was difficult for me
Assuming psychological theories are even statistically falsifiable
Answer requires pretty much no physics.
a) Note that L/a and N must have the same parity, for L/a + N = 2N_+ (*). If L/a = 2k and N = 2m, then we must have that N_+ = m + k and N_- = m - k (solve (*) for N_+). \Omega is therefore (2m choose m + k) = (2m choose m - k) = (2m)! / ( (m + k)! * (m - k)! ).
Answer requires pretty much no physics.
I'm too lazy to deal with the case where both L/a and N are odd.
b) first of all, it's Stirling with two i's. Using log properties:
ln(\Omega) \simeq 2m*ln(2m) - 2m - (m + k)*ln(m + k) + (m + k) - (m - k)*ln(m - k) + (m - k)
= 2m*ln(2) - m*ln( (m + k) * (m - k) / m^2 ) + k*ln( (m - k) / (m + k) ) = N*ln(2) - m*ln( 1 - k^2 / m^2) + k*ln( 1 - 2k / (m + k) )
now using that ln(1 - x) \simeq -x for small x and the fact that N >> L/a AKA m >> k
ln(\Omega) \simeq N*ln(2) - m*( k^2 / m^2 ) - 2k^2 / m = N*ln(2) - m*( 3k^2 / m^2 ) = N*( ln(2) - 3k^2 / (2m^2) )
which is not quite the desideratum
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Assuming psychological theories are even statistically falsifiable
If a>b> c>d>e
In this case I've reached de > 1/3(D2+e2). Must be some other piece of info I'm not using
I remember everyone always mogging me with maths in school
I can't help you if I don't know how you got there
You should have greater than or equal to signs (right triangles are not acute). Try adding them up to make 2(d^2 + e^2) ≤ a^2 < (d + e)^2.
Isn't that why I shouldn't have >= signs? None of these are acute.
so we have 2de > d^2 + e^2. I guess this removes the possibility that any triangle involving those two is right angled
Exactly. By way of contradiction you assume none of the triangles are acute.
Rearranging the inequality yields that d^2 − 2de + e^2 < 0. Can you factor the expression on the left-hand side?
Ah. Ic. Noice. I was this close jfl
Yup you had the right idea from the get-go.
Fuark, low IQ shitskin genes won't let me master mathematical shit.
What 2 + 2?
Interesting watch. Based on the video I get the sense that Newtonian mechanics is a collection of mathematical ideas rather than a proper mathematical model. Differential equation can be quite finicky, however, so determinism of Newtonian mechanics hinges on details too finicky for a mere set of ideas. In short, I get the sense that determinism of Newtonian mechanics is a fundamentally ill-posed problem.
It's like asking whether God exists without specifying what God ought to be up front. I think it's contentious precisely because the terms ain't clear-cut.
No AI.
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this problem looks like tedium more than anything else
This was asked in a college entrance examination. With no calculator allowed and only pen and paper.
ew. I guess I'd write tan as sin over cos and start using prosthaphaeresis, but I don't feel like it.
Lazy boy. Poor, starving chinese students had to solve this in a dingy examination hall with feather-ink pens and sitting cross-legged with no shoes and socks in hope of putting food on their families table.
Nigga I'm doing a PhD in math. Let me have time off.
No. You have to solve this now. No one cares about your useless math PhD.
Billons must calculate
This thread exposes every East-Asiancel on the forum.
Today I was walking through college and I couldn't help but notice all the JBW couples so I decided to come up with my own hypothetical scenario where JBW is absolute law. Here's how it goes:
Let 'x' represent the white population (male + foid), let 'y' represent the non-white population (male + foid). Now, let 'a' represent the fraction of white men who can get white foids. The following rules exist:
1. Since JBW is absolute law, any white man can get non-white foids.
2. Only White men who are in the 'a' fraction can get white foids.
3. Non-white men cannot get any foids due to JBW.
4. There is a one to one correspondence between males and foids, ie. one male can pair with one foid only and all 'pairables' pair up.
5. Assume number of males and foids are the same.
6. Pairing takes place every 'iteration' (ie. generation).
7. When a white man pairs with a non-white foid, 2 non white children (either male or foid 50/50 chance) is born.
8. When a white man pairs with a white foid, 1 white child (either male or foid 50/50 chance) is born.
9. It takes 1 interation for a newly born child to be eligible for breeding.
10. It takes 4 iterations for a newly born child to 'die' (ie. removed from the population).
Assuming the initial white and non-white populations are 'x0' and 'y0' respectively, and they are newly born children:
I. Model 'x' and 'y' as functions of 'n', 'n' is the iteration number.
II. Would there be a net population collapse or blow up? How will this depend on the initial values 'x0' and 'yo' and the parameter 'a'?
Let 'x' represent the white population (male + foid), let 'y' represent the non-white population (male + foid). Now, let 'a' represent the fraction of white men who can get white foids. The following rules exist:
1. Since JBW is absolute law, any white man can get non-white foids.
2. Only White men who are in the 'a' fraction can get white foids.
3. Non-white men cannot get any foids due to JBW.
4. There is a one to one correspondence between males and foids, ie. one male can pair with one foid only and all 'pairables' pair up.
5. Assume number of males and foids are the same.
6. Pairing takes place every 'iteration' (ie. generation).
7. When a white man pairs with a non-white foid, 2 non white children (either male or foid 50/50 chance) is born.
8. When a white man pairs with a white foid, 1 white child (either male or foid 50/50 chance) is born.
9. It takes 1 interation for a newly born child to be eligible for breeding.
10. It takes 4 iterations for a newly born child to 'die' (ie. removed from the population).
Assuming the initial white and non-white populations are 'x0' and 'y0' respectively, and they are newly born children:
I. Model 'x' and 'y' as functions of 'n', 'n' is the iteration number.
II. Would there be a net population collapse or blow up? How will this depend on the initial values 'x0' and 'yo' and the parameter 'a'?
for the reproduction rules to make sense, x and y have to be natural numbers, but the fraction a of white men needn't be whole number.
edit -- Rule 6 cannot hold in general. If I start with 1 white male and 1 white female, after one iteration there'll be three wypipos by rule 8.
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Incest is allowed
Nigger this is pretty damn obvious
0<=a<=1 this is also obvious nigger
as soon as there are 3 wypipos there cannot be an equal number of men and women...
My point is that if, say, you have 3 white men and a = ¼ then ¾ white men are allowed to breed with white women. How am I supposed to make sense of ¾ white men?
Ah, equal number of men and foids applies to intial conditions my bad
Nigger that's how probabilities work
ah ok
first of all, no. Secondly, you didn't specify that the fraction of white men that gets to breed white women is probabilistic.
Nigger in any model involving copious amount of people. it should be pretty damn obvious. Sounds like you're just trying to pussy out of actually crunching it
I'm trying to understand what exactly the problem is before solving it. I like Markov chains, so I'll have a whack at your problem later.
Kay, good luck brocel
Guess I'll make a prediction for the heck of it. I think everyone will eventually die out with probability 1.
Same. Also kinda aligns a bit with what's happening irl in western countries at least
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