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Re: HSC 2013 2U Marathon Oh does that work hahaha... I assumed it was a typo but i didn't know which part.

Re: HSC 2013 2U Marathon Wolfram says no real solution; I couldn't do it :(

Thank you both! :)

What is the difference between domain and natural domain? Is there any significance such that a question ask you to find the natural domain which would be different to finding the 'domain'?

Schools that are rank ~300 constantly get a few 95+ each year; just try your best - the school is not the limiting factor here :)

What does that mean? I see it a lot, but I fail to see the algebra manipulation. I learnt to read/comprehend "ln a = b" as "e to power b equals a" - there is no use of math ("raise both sides by e") here but simply definition.

I don't know how to explain this well but, ln (ln x) = 1 simply means e^1 = (ln x) - from log definitions (kinda) and furthermore, x = e^e

I've had many different passions whilst growing up (the world is interesting) but I am now starting to zone in on engineering (computer). I remember in grade 4, we were required to pick an occupation off the blackboard along with another student. We then had to prepare a "speech" as to why (the...

Why do amorphous polymers tend to be transparent whilst crystalline polymers tend to be translucent/opaque? It seems counter intuitive.

Justify that step your solution. Why would you 'flip' it?

Your handwriting makes mine look almost illegible haha :P Here's mine, with a slightly different approach (y = kx^2 and no parameters). I think you get redundant in some places, or maybe mine is too short.

Do show :) I don't think my way is optimal and there are many approaches to this question!

Re: On a scale of 1 to 10, how much effort would you say you've put into your studies How can one have study/prep > 0 when procrastination = 10

Vowels and consonants occupy the same positions in the word hence we only need to consider the number of arrangements inside the two groups themselves. I.e. (Permutations of vowels in group of vowels) x (Permutations of consonants in group of consonants)

Well, your goal is to show that OA = OB And to do this: find eqns of lines RP and RQ and sub x = 0 to find A,B I'll guide you further if you're still stuck.

I will begin writing it; check back in a week :)

ಠ_ಠ

Oh, that's good to know :)

It does not :) You can quickly obtain the complex number that is 1/z where z = x + iy by rationalising the denominator and you'll see it comes out NOT to be z|

I believe so, since the principal argument of z is defined for -pi < theta <= pi