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Prove\ that\ \sum_{k=0}^{n} ^{n}C_{k}\ 2^{3k}=3^{2n} Also are we allowed to use induction or?

Ohh thanks for the help ^^ But just one question what did you mean in: BUT we haven't yet used the fact that OQ is parallel to the tangent at P. This gives the condition that Not sure what you did there.

P is a point on the ellipse x^2/a^2 + y^2/b^2 =1 with centre O. line drawn from O, parallel to the tangent to the ellipse at P, meets the ellipse at Q. Prove that the area of the triangle OPQ is independent of the position P. Found this question quite tough :/ Any help is appreciated ^^

Lol whoops my bad =='

Ahh.... I knew I did something wrong :/ @ littlesmallworld Should be 1 unit not 8

Hopefully not wrong.

Remember to note that <img src="http://latex.codecogs.com/gif.latex?|z|=\sqrt{x^2&plus;y^2}&space;\\&space;So&space;|z|^2=x^2&plus;y^2&space;\\&space;\therefore=(x&plus;iy)(x-iy)" title="|z|=\sqrt{x^2+y^2} \\ So |z|^2=x^2+y^2 \\ \therefore=(x+iy)(x-iy)" />

MX2 and Chem ^^'

A bit late, but thanks for the help everyone! Awesome response Tashe.

Hey guys, Just out of curiosity say for this dot point: Perform a first-hand investigation, gather information and analyse data to calculate initial and final velocity, maximum height reached, range and time of flight of a projectile for a range of situations by using simulations, data...

Can't afford to miss this ^^

No worries because it does make sense! Thanks~

Bit stuck on these two questions. The first one I can do just don't know how to find the values of arg. 1) Find the modulus and argument of each of the complex numbers z1=2i and z2=1+sqrt(3)i. Mark on an Argand diagram the points P, Q, R and S representing, z1, z2, z1+z2, and z1-z2...

I believe you mean compare to kJ/mol right? and heat of combustion? Well kJ/mol is measured by one mole of a substance. For example 1 mol of methanol = about 32 g, ethanol is about 46 g etc. However this isn't a fair comparison in the sense that one mole of a substance is dependent on its MM...

We're up to Newton's universal gravitation in physics.

It shouldn't directly assess your prelim content, but the syllabus does state that your prelim content is assumed knowledge. You sure its not like skills or knowledge picked up from prelim and applied to HSC?

Ohh okay thanks for the help! And for the second part I meant to say (w^2)^2=w. My mistake...

Its usually a test where you teacher allows you to bring one sheet of paper with anything into the exam room. At least that's what my school does.

Hi all, bit confused on how to answer because my teacher rushes a LOT! Any help would be great! <img src="http://latex.codecogs.com/gif.latex?$1)\&space;Find\&space;the\&space;fourth\&space;root\&space;of\&space;1&plus;i\sqrt3&space;\\$" title="$1)\ Find\ the\ fourth\ root\ of\ 1+i \sqrt3...

Ooh crap yeah it was a typo. Supposed to be i instead of 1. Thanks for help... I kind of get it. So since z/z-i is real, you let it equal x and sub it into the form z=x+iy?