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Re: HSC 2015 4U Marathon Dw, they obviously don't use any games/sports in HSC questions without explaining relevant rules lol.

Re: HSC 2015 4U Marathon Oh sorry guys, yeah I doubt you can find a nice surdic expression for p. Characterisation as the root of a certain polynomial is fine :). The main point was to find a way to handle to concept of deuce, questions with that theme (a very elementary random walk with...

Re: HSC 2015 4U Marathon Yep, that's the fun part :).

Re: HSC 2015 4U Marathon Player A is serving to Player B in a tennis match. He wins each point with probability 0 < p < 1. Given that both players are equally likely to win a service game if the score is 0-30, find: a) the value of p b) the probability that A wins a service game from 0-0.

Haha am going to keep trying to improve, give me time. I took 2 games off the #1 player (out of 8) and he is probably top 15ish in Aus. This game is so amazing. It's not strictly a league, there are just monthly local tournaments as well as bigger out-of-state events and majors etc. Rankings...

Boom, 2nd place. After this weeks rankings updates I will be ranked 2nd in the ACT!

Final bit of training for the next local melee tournament tomorrow. My sheik is feeling pretty crispy :).

Re: HSC 2015 4U Marathon - Advanced Level $Given that \\$p(z)=z^3+az^2+bz+c$\\ has all roots on the unit circle, show that \\$q(z)=z^3+|a|z^2+|b|z+|c|$ \\ also has all roots on the unit circle. $

Re: HSC 2015 4U Marathon - Advanced Level Apologies, the method I had in mind does not quite work when you follow it through. It is still quite an easy problem though. 1. Observe that the problem is trivial for n=2, with equality iff one of the sequences is constant. 2. Suppose \sigma is...

Re: HSC 2015 4U Marathon - Advanced Level Interesting that you find the rearrangement inequality harder than the other one! Complete opposite to me.

Re: HSC 2015 4U Marathon - Advanced Level Great solution to the first one, very efficient. Will read the second one a little more carefully later, but it sounds like it is probably right. My method was to expand \sum_{j}(x_{j}-x_{\sigma(j)})(y_{j}-y_{\sigma(j)})\geq 0 after...

Re: HSC 2015 4U Marathon - Advanced Level And an easier one: Prove that \sum_{k=1}^n x_ky_{\sigma(k)}\leq \sum_{k=1}^n x_ky_k for increasing sequences (x_k),(y_k) and an arbitrary permutation \sigma of the first n positive integers.)

Re: HSC 2015 4U Marathon - Advanced Level For positive real x,y,z, show that: \frac{xyz}{x^3+y^3+xyz}+\frac{xyz}{z^3+y^3+xyz}+ \frac{xyz}{x^3+z^3+xyz}\leq 1

Finished! They are so much easier now than when I last did them lol. With 36 you just have to: a) Get used to ness' quirky movement so you don't kill yourself by accident. Get familiar with his best kill moves (back air, back throw, forward smash). Back air is my favourite for this event...

It's been ages since I played the event matches, but this post reminds me how fun they were. Going to redo them now and get back to you :).

Re: HSC 2015 4U Marathon - Advanced Level If u is cos(2x), this equation is cubic in u with zero constant coefficient.

Re: HSC 2015 4U Marathon LHS > 3\arctan(2) > 3\arctan(\sqrt{3}) = \pi =RHS.

Re: HSC 2015 4U Marathon Well if there is a rational polynomial q(x) of degree < 3 with that root (which we call s), then there must exist such a polynomial m(x) (m for minimal) which divides x^3+3x+1. Why? By the division algorithm, x^3+x+1=q(x)d_1(x)+r_1(x) q(x)=r_1(x)d_2(x)+r_2(x)...

Re: HSC 2015 4U Marathon - Advanced Level It's just an anticlockwise spiral. You could use calculus to tell you what the gradient of the start of the curve at (0,0) is.

Entered one of the monthly Sydney melee tournaments whilst I was up for Christmas/New Year. Placed 4th out of around 40, you can check out the top 8 matches here: http://www.twitch.tv/sydneysmash/b/606442425 I am on at 56:30, 1:21, and 1:30, rocking the ACT tag. (Apart from the 1:21 set where...