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Re: MX2 2016 Integration Marathon Carrotsticks, do you know who Paradoxica reminds me of? A guy called hayabusaboston lol, do you remember him? They're like exactly the same lol.

Re: HSC 2016 4U Marathon - Advanced Level Let's see if one of the BOS members can crack it

Re: HSC 2016 4U Marathon - Advanced Level A difficult question which one of my students asked me the other day: $Consider the concentric ellipses$\ \frac{x^2}{a^2}+\frac{y^2}{b^2} $and$ \frac{x^2}{c^2}+\frac{y^2}{d^2}, $ where $ b<a<c $ and $ b<d<c. $The tangent at $E(x_0,y_0)$ intersects with...

Re: HSC 2016 4U Marathon - Advanced Level uhhhh Cauchy Schwarz isn't needed to solve that question mate.

Re: HSC 2016 4U Marathon - Advanced Level Sy, can you post some difficult questions like you usually do? I know that you stepped the difficulties down a little for your last couple of questions lol

Re: HSC 2016 4U Marathon - Advanced Level I know that this is a mere typo, but ur last statement about a,b, and c being necessarily rational isn't quite right. Perhaps a different notation would fix the problem :D Just really nit picking here

Re: HSC 2016 4U Marathon - Advanced Level $oh okay, you just want the second bit$\\ii)\ Let L= \sqrt{s(s-a)(s-b)(s-c)}.\ $(x-alt_a)(x-alt_b)(x-alt_c)=0.-->$ x^3-2L(1/a+\1/b+1/c)x^2+4L^2(1/ab+1/ac+1/bc)x-{8L^3/abc}=0.$moving things over,we get that$...

Re: HSC 2016 4U Marathon - Advanced Level Which part do you specifically need help with(as in first part or second part)? I'll type up as soon as I come back from work

Re: HSC 2016 4U Marathon - Advanced Level oh nvm, just realised sy already posted solutions for the polygon and average distance question, no need to post those ones up then. If a 2016ers needs soln for the altitude q, I can type them up.

Re: HSC 2016 4U Marathon - Advanced Level does any 2016ers need solutions for sy's past 3 questions before his most recent? I can quickly type them up if requested!

Re: HSC 2016 MX2 Combinatorics Marathon for b) should be something like 26^12-(8C1*26^7-answer from part a) couldve made errors, literally walking home from the station with no pen or paper

Re: HSC 2016 4U Marathon - Advanced Level any interesting questions?

Integrand never said anything about if p1=p2 and q1=q2, then LHS = RHS (from sy's post). He's saying that if LHS=RHS then p1=p2, and q1=q2. Search up if and only if type arguments on wiki for details on this. Your second line makes it seem like he wasn't talking about this. You have completely...

Re: HSC 2016 4U Marathon - Advanced Level Yep yep I screwed up hahaha

Re: HSC 2016 4U Marathon - Advanced Level Tell me if I'm going full weirdo mode but isn't this factorization only true if q is odd? I'm talking about the part where you factorised (t+h)^q-t^q

Re: HSC 2016 4U Marathon - Advanced Level Consider P(x)-Q(x)= R(x), this has infinite roots, and the only polynomial with infinite roots is R(x)=0. Thus, R(z) is also =0 for all complex numbers z, and hence P(x)=Q(x) for all complex numbers as well

Re: HSC 2016 4U Marathon - Advanced Level Do you have a difficult problem to share with us?

Re: HSC 2016 4U Marathon - Advanced Level Notice that the derivative of lnx /x is (1-lnx)/x^2, which <0 if x>e, so f(x)= lnx /x is a strictly decreasing function for x>e. Thus if y>x>e, there is no positive integer solutions for x^y=y^x (since this rearranges to form lnx/x=lny/y). So we only...

Re: HSC 2016 4U Marathon - Advanced Level Can you or sy or someone post a difficult problem?

Re: HSC 2016 4U Marathon - Advanced Level Exactly my point. Drongoski was right all along