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Re: HSC 2013 4U Marathon Ok thats good, thank you.

Re: HSC 2013 4U Marathon Woah, I can't picture anything with that information heh. Any chance of a diagram?

Hmm, I think you should check with someone else, I haven't heard of penalising for that, but you should ask someone else just in case.

I personally have no regrets with my subject selection, its a big workload but I reckon it will be worth it.

Min value of |z| where arg(z+i) = pi/4 is |z|=1/sqrt(2)

What regrets do you have about your current subject selection? Go. Open to non-2013ers too of course

I was able to get this now, after some integration, taylor forms of ln and some big stuff, I arrive at this identity, which technically we could find via observation but I got it anyway. \sum_{k=1}^{\infty} \frac{\sin k\theta}{k(k+1)} = \sum_{k=1}^{\infty} \frac{\sin k \theta}{k} -...

Re: HSC 2013 4U Marathon You got this right? \sum_{k=1}^{n} \cos k \theta = \frac{\cos \theta -1 + \cos n\theta - \cos (n+1)\theta}{2-2\cos \theta} \sum_{k=1}^{n} \sin k \theta = \frac{\sin \theta + \sin n\theta - \sin(n+1)\theta}{2-2\cos \theta} Then differentiation :)

======================== Alright new problem: I want to find \sum_{k=1}^{\infty} \frac{\sin k \theta}{T_k} Where I can pick an appropriate value of theta such as pi/2 or something. Now, here T_k=1+2+...+k = \frac{k}{2}(k+1) So the problem simplifies to finding: \sum \frac{\sin k...

Re: The p00n thread They need to rebalance weather man, faking hate that -> do you play competitively?

Re: HSC 2013 4U Marathon very simple question but explores something quite cool, how we can have infinite volume but the area of the cross-section is infinite. Similar to: http://en.wikipedia.org/wiki/Gabriel's_Horn

Re: HSC 2013 4U Marathon $i) Find the area underneath the curve$ \ \ \ \ f(x)=\frac{1}{x} \ \ \ \ \fbox{1} $For$ \ \ \ 1\leq x \leq n $ii) Find the volume created when rotating the area underneath$ \ \ f(x) \ \ $ by $ \ \ 2\pi \ \ $radians$ \ \ \ \ \fbox{1} $iii) Compare the two...

Yeah definitely, but it is essentially the same as a Prisoner's dilemma. I can see how being a friend could change the outcome, but how would repetition change it?

Nope, I'm not that fast lol I guess that will keep me occupied for the next few days I won't go through them as fast. And my Economics teacher showed us that when he was talking about Economics in Uni and he talked about how its always best to pick Steal in that game -> it is what gave me...

Wait how fast are we supposed to be going through this? I just noticed the Week 1 for 1-(1-10) o_o I just watched the whole weeks worth dammit... Should I just go over problems now for the rest of the week or something?

Correct

It should be 0% but N-award for non-completion if at all...

Re: HSC 2013 4U Marathon Alternatively, n^2-3n+2=(n-2)(n-1) And notice that if it were to be prime, one bracket must be equal to 1, the other whatever it might be (as long as its positive) (3-2)(3-1) = 1 \cdot 2 = 2 = \ \ $prime$ We could do the same for the other bracket where n=2, but...

Always look for shortcuts where ever possible: f(x)=x\sqrt{3x-4} = \sqrt{x^2(3x-4)} = \sqrt{3x^3-4x^2} This makes differentiating easier: f'(x)= \frac{1}{2}(9x^2-8x) (3x^3-4x^2)^{\frac{-1}{2}} f'(x)=\frac{9x^2-8x}{2\sqrt{4x^3-4x^2}} unfortunately we can't take the same shortcut...

Re: HSC 2013 4U Marathon A short but not necessarily easy one: $A prime number is a number where the only factors are 1 and itself, 1 is not prime$ $How many values of n is$ \ \ n^2-3n+2 \ \ $ a prime number?$