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This is a set of equations I got from using the Lagrange multiplier theorem. What would be a quick way of solving them? \begin{align*}2x&=\lambda(4x-4y)\\ 2y&=\lambda(10y-4x)\\ 0&=2x^2-4xy+5y^2-54\end{align*}

Re: UNSW chit chat thread 2016 That's the only answer I remember cause it turned out to be $0 for me Everything else I purposely forgot Praying for scaling

Re: UNSW chit chat thread 2016 ...wow

Re: UNSW chit chat thread 2016 It was supposed to be my free HD. So much for that idea.

Re: UNSW chit chat thread 2016 You actually found it alright...

Ahh the progression refers to the sequence itself. Got it

What's the difference between calling it a geometric "series" as opposed to a geometric "progression"? Or is there none

Re: UNSW chit chat thread 2016 Take a hint. Not everyone will know. Quit the spam.

Re: UNSW chit chat thread 2016 You make me jealous I haven't even started my exams yet

A coin with probability p of coming up heads is tossed until the rth head appears. The probability that the number of tosses required is n (n>=r) is given by... This was a multiple choice question, but technically if I saw it I can just, without much further thought, think oh duh negative...

...Shuuya. Wow. Was I meant to care about your respect

How does this solution work? I remember reading about it somewhere but I don't recall where and it just appears as magic..

Re: HSC 2017 4U Marathon This is a marathon. They purposely throw in questions that can get overcomplicated. 100% of the time they are doable using just HSC techniques however if it were the HSC exam you'd be guided step by step

Re: HSC 2017 Maths (Advanced) Marathon When you see terms and sums and what not you should be thinking series.

Do you want to stay at uni that much longer?

I'm pretty sure this is still under the wing of probability and statistics... Anyway, I could handle the simple algebra they omitted to finish off the question. I'm just not sure as to how they generated that first expression; for some reason it did not follow for me despite the hint they...

Re: University Statistics Discussion Marathon \text{Prove that the sum of two binomials with the same probability parameter is still a binomial.}

Re: UNSW chit chat thread 2016 If you're meant to be the better one at coding then shouldn't you be the one knowing how to do everything on the go and not google google google?

That awesome feeling when this makes sense now..

Re: MATH1231/1241/1251 SOS Thread I could probably research it up but I feel as though InteGrand's answers are more comprehensible... \text{Prove that }i^i=\exp \frac{-\pi}{2}