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Re: HSC 2012 Marathon :) I typed the question correctly. :)

I've selected a news article as my related text however i can't find the author of the specific article. Would it be fine to make one up or could i just say written by the Sydney Morning Herald?

Re: HSC 2012 Marathon :) \int \frac{x^4}{1 + x^{10}}dx

Re: HSC 2012 Marathon :) The thought of sqrt(-1) being defined is ridiculous :P

Re: HSC 2012 Marathon :) This is MX1 thread lol Nevertheless... As all the coefficients are real, by the Conjugate Root Theorem, 1 - 2i is also a root. By factor theorem, (x - 1 + 2i)(x - 1 - 2i), i.e. (x^2 - 2x + 5) is a factor of P(x). Let P(x) = (x^2 - 2x + 5)(ax + b) As constant = -15...

Re: HSC 2012 Marathon :) haha True. Should have gave it without the result!

Re: HSC 2012 Marathon :) Mind if i go backwards? lol I_n = (n -1)I_{n - 1} + (n - 1)! = (n - 1)[(n - 1)! - (n - 2)!] + (n - 1)! = (n - 1)^2 (n - 2)! - (n - 1)! + (n - 1)! = (n - 1)(n - 1)! = \frac{(n - 1)n!}{n} = n(n - 1)! - (n - 1)! = n! - (n - 1)!

Re: HSC 2012 Marathon :) Factors of 2012 are 1, 2, 4, ... Same thing as before, a^2 - b^2 = 2012 = 2(1006) (a + b)(a - b) = 2(1006) a + b = 1006, a - b - 2 a = 504, b = 502 (a + b)(a - b) = 4n a + b = 2n, a - b = 2 a = n + 1, b = n - 1

Re: HSC 2012 Marathon :) If they're integers, Let a and b be two positive integers such that, a^2 - b^2 = 2011, a > b (a + b)(a - b) = 2011 But 2011 is a prime number, therefore a + b = 2011, a - b = 1 or a + b = 1, a - b = 2011 Clearly a + b cannot equal to 1 as a, b > 0 and they're both...

That is insane. Although i wish i could do that lol.

Find the gradient of each (+ or - b/a), then use tan\theta = |\frac{m_1 - m_2}{1 + m_1 m_2}|

I'm interested in learning cyclic factorisation/expansion. Carrot? :)

Come to think of it, carboxylic esters are actually slightly polar due to C = O bond. Perhaps the different position of the C = O bond in butyl ethanoate allows for more effective dipole-dipole interactions hence a slightly higher boiling point. I'm not sure though. Ask your teacher or wait for...

Re: HSC 2012 Marathon :) You use the expansions and mess around to get the expressions.

With carboxylic esters (the ones we look at in our syllabus), they're non-polar so the only IMF between the molecules are dispersion forces. Increased molecular weight increases dispersion forces meaning greater boiling point so greater chain length (whether it be he alkyl or alkanoate part)...

I don't know if you're allowed to do this or not but use infinite as the upper limit after substitution. It gets you the answer lol.

ppm = mg/kg (milligrams/kilogram) (difference of powers by 10^6 to give 'parts per million') Now, 8.20ppm = 8mg/kg = (8 x 10^-3)g/1000g Dividing top and bottom by 1000 = (8 x 10^-6)g/g Multiplying top and bottom by 9 = (72 x 10^-6)g/9g = (7.2 x 10^-5)g/9g Therefore 7.2 x 10^-5 g of Al in...

Barely any grads who do chem/bio D:

Really? I find their questions throw me off lol.

Lol and looking at the avatar he's got me good. http://community.boredofstudies.org/member.php?u=1611013679 (this was all i could think of and it was p lame ^_^)