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Re: 2015 permutation X2 marathon Yeah, only 5 of the 8 gaps between the consonants will be filled by vowels, leaving blank spaces in the other gaps. This means that consonants with a blank space between them will be together, so it includes the cases where 2-3 consonants are together (I hope...

Re: 2015 permutation X2 marathon Because that only provides the case where all 5 vowels are together, not when there are 2-4 vowels together.

Re: 2015 permutation X2 marathon I'm just gonna leave the name out, in case you decide to remove it. First, we arrange the consonants, which there are 7 of: 7! Then, we place the 5 vowels in the gaps between the consonants, including at the beginning and end of the consonants. There are...

"conical pile" From that, we can say that the pile is in the shape of a cone, with altitude (height) h and diameter h. Using the volume of a cone: \begin{align*} V &= \frac{\pi r^2 h}{3}\\ V &= \frac{\pi [\frac{h}{2}]^2 h}{3} \\ V &= \frac{\pi h^3}{12} \end{align*}

Re: 2015 HSC Economics Marathon hahaha, no worries, just thought I'd make sure!

Re: 2015 HSC Economics Marathon It should increase, because the amount of people employed decreases while the amount of people unemployed stays the same. So the proportion of unemployed people to the labour force increases, i.e. unemployment rate increases (like in my example: 2 from 8, or...

Re: 2015 HSC Economics Marathon For the first question, I'll use a theoretical situation to describe it: Suppose you have an economy with a working age population of 10 people: 6 are employed, 2 are unemployed. Therefore the labour force has 8 people and the unemployment rate will be 25%. If...

\begin{align*}\frac{3sec^2 3x}{tan 3x} &= 3sec^2 3x \ cot3x \\ &= 3 \left (\frac{1}{cos^2 3x} \right ) \left ( \frac{cos3x}{sin3x} \right ) \\ &= \frac{3}{sin3xcos3x}\end{align*}

Re: HSC 2015 4U Marathon Hopefully, this suffices (still no LATEX): http://i.imgur.com/QJNbrGy.jpg?1 Couple of fixes: *r is the length of the semi-major/semi-minor axis (in final answer) *gradients are equal

Re: HSC 2015 2U Marathon dy/dx = 3x^2 + 2x y = (3x^3)/3 + (2x^2)/2 + C y = x^3 + x^2 + C At the point (2, 13): 13 = 8 + 4 + C C = 1 Therefore, y = x^3 + x^2 + 1 ----------------------------------------------------------------------------- NEW QUESTION: The relation defining the inside...

Re: HSC 2015 2U Marathon Still haven't learnt how to use LATEX, haha http://i.imgur.com/cLHkVpU.jpg?1 (Haven't learnt Probability or Series in depth, so hopefully this is right)

Re: HSC 2015 4U Marathon I managed to get an answer to it, but there are probably better ways to do it http://imgur.com/CqsLJB6 (still new to this, haha)

Hey guys, I'm Jack! I'm doing: 4U Maths Adv English (please kill me now) Physics Economics Goal: Aiming for 96.3 for UNSW Commerce, but not really fussed Looking forward to a great year with you guys! Good luck everyone!