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Okay, well first note that gcd(A,B)=B is equivalent to just saying that B divides A. (Let me know if you don't see why this is the case). So let's count the number of pairs of positive integers not exceeding N such that B|A. This is the same as letting B vary between 1 and N, and counting the...

Agree with your first paragraph, and in any case I would take a high average and above average variance over low average and low variance. I don't think that was the SCG match, I think it was an earlier match in the subcontinent. And that SCG match was pretty ugly because of all the umpiring fails.

Using dolphin for melee/pm and project64k for smash 64. Project M: http://smashboards.com/threads/project-m-3-02-online-via-dolphin-netplay-full-setup-optimization-guide-redesigned.346700/ Melee: http://smashboards.com/threads/dolphin-online-melee-netplay.335432/ Smash 64...

Melee is the best :D. Literally my favourite game of all time now. I go to tournaments from time to time. But 64 and PM are also pretty sick. Do any of you play online through your pc (with a usb controller / gc controller adapter?) If not, then you really should.

Breaking a bos hiatus to answer a question I always found interesting in high school. Your intuition is close with real exponentiation. First we assume a\geq 0. If (q_n) is a sequence of rationals tending to r\in\mathbb{R}, then we can define a^r=\lim_{n\rightarrow\infty}a^{q_n}. A little...

For most aspirations though, a REALLY strong HSC performance is unnecessary. Surely there is nothing wrong with cruising in high school, spending your time instead on properly learning stuff that actually is important to your particular field. (Of course, this sentiment only applies to students...

Cheers. It does seem pretty tailor made for inclusion-exclusion, which isn't TOO lengthy. If I can think of something faster later I will post.

What is the question?

It's 1440.

Haha sorry, I should have included quotation tags. Was referring to OP, not you! :).

Err no.

Why is it any of your business what other people's priorities/goals in life are? Definitely don't get why there should be any hate.

Too much routine computation (where you see exactly the same questions hundreds of times), not all that much creativity/intuition required. Marks can say more about how robotic you are at doing the same questions quickly and accurately than your understanding and how "good" you are at mathematics.

Maths was my best and probably my favourite. The latter says more about how I disliked most of my other subjects though. Mathematics in general is beautiful, but the actual HSC courses are a little dull.

?

I know a+b+c = 1 is an assumption, but why should this imply the inequality I quoted?

Can you explain this?

Well the question is misleading with the line "Find the complex number represented by R". As you have pointed out, there are two choices because if we reflect a triangle about one of its sides we get a similar triangle (in fact congruent), although it's orientation is reversed. If this...

Re: HSC 2014 4U Marathon - Advanced Level I am sure there are lots of ways, its just an algebraic manipulation so you always have lots of choices with these things.

Re: HSC 2014 4U Marathon - Advanced Level $For brevity of notation, we set:\\$y:=\tan(x),u:=\tan(\alpha),v:=\tan(\beta),s:=u+v,t:=uv.$\\ \\ Then the assumption translates to:\\ \\ $y^2=\frac{(y-u)(y-v)}{(1+uy)(1+vy)}\\ \Rightarrow t(y^4-1)+s(y^3+y)=0\\ \Rightarrow \frac{t}{s}=\frac{y}{1-y^2}.$...