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Re: HSC 2014 4U Marathon - Advanced Level Here is a nice probability question \\ $There are$ \ n \ $coins called$ \ C_1, C_2, \dots, C_n \ $and they are all biased so that the probability of$ \ C_k \ $landing heads is$ \ \frac{1}{2k+1} \\ \\ $Find the probability in terms of$ \ n \ $of...

Re: HSC 2014 4U Marathon Yep that's the idea

Re: MX2 Integration Marathon \\ \int_0^{\pi /2} \frac{dx}{\sin^4x + \cos^4x}

Re: HSC 2014 4U Marathon \\ (0,0), (a,11) \ $and$ \ (b,37), \ $are vertices of an equilateral triangle, find the value of$ \ ab

Re: HSC 2014 4U Marathon ಠ_ಠ

Re: HSC 2014 4U Marathon - Advanced Level Yep pretty similar to my solution! Quite interesting how numbers like 4 and 2 can come out of something that seems so simple

Re: MX2 Integration Marathon \\ \int_0^{\pi /4} \frac{dx}{1+ \sin^2 x}

Re: MX2 Integration Marathon

Re: HSC 2014 4U Marathon \\ $Find the exact form of$ \ \cos \frac{\pi}{10}

Re: HSC 2014 4U Marathon - Advanced Level \\ $Find all integer solutions$ \ (x,y) \ $where$ \ x^y = y^x \ $and$ \ x \neq y

I believe I have found a gene that determines how well you can see your surroundings Therefore, your observations of your surroundings is completely illusory since I've found a gene that explains it -- Not a very good argument now is it?

You have never observed large scale Darwinian evolution, so you say that Darwinian evolution (or whatever kind you profess) is the best explanation for the existence of similar DNA, fossils etc. Your distinction between "real" and "best" is rhetorical at best, you are not even clear with what...

What led you to that conclusion?"

Ok so let some atheist say: "The best explanation for there being rocks older than 6000 years and there being similar DNA across species is Darwinian evolution" Theist says: "Just because its the best explanation doesn't mean its true" Atheist says: "lolol dumb theist go believe in santa...

That's pretty unrealistic Especially since there are 10s of arguments for the existence of God in all their variations, and the number of arguments for atheism is basically "evil =(" which isn't actually an argument against God, and moreso against a specific rendition of God (and some others...

Well you still would have inclinations to either side, whether atheism or theism, I doubt you are dead center right in the middle between them, the evidence for both weight out exactly...

Re: HSC 2014 4U Marathon - Advanced Level 1 + z^k + z^{2k} + z^{3k} + \dots + z^{(n-1)k} = \frac{z^{nk}-1}{z^k-1}

Re: HSC 2014 4U Marathon - Advanced Level \\ a,b \ $are integers, if$ \ b \ $divides$ \ a $, show that$ \ 2^b - 1 \ $divides$ \ 2^a - 1

e = 1/0! + 1/1! + 1/2! + ... let e = p/q, S(n) = 1/0! + 1/1! + ... + 1/n! e - S(n) = 1/(n+1)! + 1/(n+2)! + .... < 1/(n+1)! (1 + 1/(n+1) + 1/(n+1)^2 + ...) = 1/((n)(n!)) e - S(n) > 0 0< n n! e - n n! S(n) < 1 Therefore n n! e - n n! S(n) is not an integer Since e = p/q, and...

Polytheism = Atheism + Supernatural pantheon of 'god's Where 'god' is actually a finite being like us Whereas serious religions, like Judaism, Chrisitanity and Islam, and beliefs like Deism affirm a perfect Being with Omnipotence, Omniscience etc. etc. So you have a lot more in common with...