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it's just using the result (x + y + z)/3 >= (xyz)^[1/3] substituting a/b, b/c, c/a for x, y, z, so the RHS cancels to become 1, and you just multiply the 3 across.

hopefully this helps, i think graphical methods are valid (you probably had the same answer as me in 3)

Oh well, thanks. the battle continues ....

hey, you shut up .... i just hate them so much

i'm sure there are mistakes somewhere, but here's my first attempt. particularly unsure about question 2

my old enemy, permutations and combinations... i think, although i'm unsure, that you have to consider a word with: - no e's - 1 e - 2 e's I don't think that you can say "3 different letters, therefore 7x6x5 ways" because there are 2 e's in choosing the first letter whereas only 1 of...

Quote: " ... any chance of u showing me" Yes. I have plenty of time, so here is the working out. I suppose this is a fairly unusual year 11 question ... anyway it's just like shafqat and chillin said.

not from another source, nor am i very skilled. Just used microsoft equation editor, then saved the equation box as an image in png form, then attached it to the post.

I think this is valid

This is a link from Buchanan's site, it has worked solutions to questions from cambridge, and they are arranged in topic and in levels of difficulty, or something, so it might be useful: http://members.optusnet.com.au/hoahie/4unit/

just wondering if anyone knows whether or not this is accepted in the HSC, because it makes things a lot easier sometimes. It goes something like 'if a plane of area A is rotated around an axis R [where the axis does not cut the area] then the volume is given by V = 2piRA'. Note this only applys...

thanks, nice solution I'm happy now

sorry about the triple post, my bad, it kept saying that the internet timed out or something ... anyway: "the point P representing z (= x + iy) in the Argand diagram lies on the line 6x + 8y = R where R is real. Q is the point representing (R^2)/z. Prove that the locus of Q is a circle and...

wow. That's awesome. Thank you so much.

please help me: "find the roots of z^6 + 1 = 0 and hence resolve z^6 + 1 into real quadratic factors; deduce that cos3x = 4(cosx - cos[pi/4])(cosx - cos[pi/2])(cosx - cos[{5pi}/6])

This comes from Patel's book: "Find the roots of z^6 + 1 = 0 and hence resolve z^6 + 1 into real quadratic factors; deduce that cos3x = 4(cosx - cos[pi/6])(cosx - cos[pi/2])(cosx - cos[{5pi}/6])" Please help

This comes from Patel's book: "Find the roots of z^6 + 1 = 0 and hence resolve z^6 + 1 into real quadratic factros; deduce that cos3x = 4(cosx - cos[pi/6])(cosx - cos[pi/2])(cosx - cos[{5pi}/6])" Please help

My teacher couldn't do this, and I don't know where to begin. How do I simplify i to the i?