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What are you doing for your PhD?

Re: HSC 2014 4U Marathon In how many ways can the word: CARROTSTICKS be arranged in a line so that the two Rs (which are indistinguishable) are separated by at least one other letter?

Talk to sinyeta, assuming you did 4U.

Try this:

Re: HSC 2014 4U Marathon Meant this. Feel free to share the easier method :tongue:.

Re: HSC 2014 4U Marathon i) cosn\theta =cos^{n}-\binom{n}{2}sin^{2}\theta cos^{n-2}\theta +\binom{n}{4}sin^{4}\theta cos^{n-4}\theta...\\ =cos^{n}-\binom{n}{2}(cos^{n-2}\theta-cos^{n}\theta) +\binom{n}{4}(cos^{n-4}\theta-2cos^{n-2}\theta+cos^{n}\theta )...\\\Rightarrow...

I used cis2pi/3. But if you think about it... w^12 =(w^3)^4=1^4=1.

I went w^12=cis8pi (de Moivre). Then cis8pi= cis1440=cis360=1+0i=1

Re: HSC 2014 4U Marathon By using the binomial theorem on cos5theta and solving the equation 32x^5 -40x^3 +10x -1=0, find the exact form of cos\frac{\pi}{15}cos\frac{7\pi}{15}cos\frac{13\pi}{15}cos\frac{19\pi}{15}.

I've done a few. Some may be wrong. 1a. w is a cube root of unity, making w^3 =1. Clearly w=1 is a solution. The roots are equally spaced around the unit circle. Making w=1, cis2pi/3, cis-2pi/3= cos2pi/3 - sin2pi/3. 1b. w^2, w and 1 are cube roots of unity...

Re: HSC 2014 4U Marathon ^ I removed the brackets from Im to make it easier to do.

Re: HSC 2014 4U Marathon z satisfies |z-i|=Imz+1. Sketch/determine the locus of P(x,y) representing z. If A is the point (0,1) on the Argand diagram and B is the y-intercept of the tangent of the locus at P on the Argand diagram, show that angleAPB=angleABP.

True. There is a much older film version of it though :P

For this I sometimes find putting my phone and laptop at the other end of the house helps so I'm less likely to 'just quickly check something or take a break'. If you struggle to focus maybe try doing history or multimedia homework first so you are actually doing work then try moving onto your...

Even though it is frowned upon, studying the film rather than the novel may be ok...

It will make no difference whether it's part of a trilogy or not.

Don't pretend you don't know... =.=

Inb4cinnamonisafmsalt

Dat .95 tho

Some ideas (not sure if they're right): Visual techniques - use of cross cutting, eg. Contrasting Darren and Adam's reactions to the raid. - pathetic fallacy when Adam visited Villawood - Close ups of characters during moments of discovery; signifies importance of discovery Sound techniques...