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For n = 1, we're trying to prove 1 > 2(sqrt2 - 1) That is 3 > 2sqrt2, which is true because 9 > 8

Try sum of roots.

Preview file? That helps out sometimes.

As others have said, circle geometry is often asked under harder 3 unit. They can be tough, so here are a few pointers: -Know all theorems well, and do lots of practice. -If stuck, leave it and come back at the end. -Draw a really neat diagram, and preferably don't scribble over the exam...

Sure thing.

Let z = x + iy |x -8 + iy| = 2(x - 2) (x-8)^2 - y^2 = 4(x-2)^2 Sorry, my mistake. Fixed now. Thanks for completing solution.

Equate co-efficients of x.

Expand and equate co-efficients: 2x^2 + x + 1 = ax^2 - ax - 2 + bx - b + c So a = 2 1 = b - a so b = 3 c - b - 2 = 1 so c = 6

Integration 1. 4/15 (sqrt2 + 1) 2. 1/3 3. (6 + pi – 3sqrt3)/6 4. 2/sqrt3 tan^-1 (2tan @/2 + 1/ sqrt3) + c 5. 16/3 log |x-5/x-3| + c 6. -2log|x-1| + 3log(x^2 + x + 2) + c 7. 1/9 x^3 (3lnx – 1) + c 8. 1/6 (2pi – 3sqrt3) 9. sqrt( x^2 + 2x + 5) + log( x + 1 + x^2 + 2x +...

Binomial 1.a) 112 b) -65 2. x = 0, (5 + sqrt10) / 2, (5 - sqrt10) / 2 3.a) 25 choose 10. 7^15. (5x) ^10 b) 25 choose 15 . 7^10. 10^15 4. 1/(n+1) 5. 0, n is odd (-1)^n/2. n choose n/2

Dynamics 1. a) a = -16pi^2x b) v^2 = 16pi^2(400 – x^2) c) 6sqrt11 2.a) 2sqrt6 km/s b) 28000/3sqrt6 sec 3. c) 1/2sqrt kg . log3 secs

Rates 1. a) $942 b) 12.2238% 2. a) $1801.85 b) 71% c) 1500 3. c) 1/60 log 10 d) 2min 45 secs

De Moivre, volumes, recursion 2.d) 5 3. b) (z-1)(z^2 + z +1)(z^2 – 2zcos(2pi/9) + 1) (z^2 – 2zcos(4pi/9) + 1) (z^2 – 2zcos(8pi/9) + 1) 4. 1.81 cubic units 5. 2^(1/3) : sqrt( 2 ^ [2/3] – 1) 6. a) 10! (pi^10 / 10! – pi^8/8! + pi^6/6! – pi^4/4! + pi^2/2! – 2)

The answers are a bit long, so if anyone wants any answers for proofs, ask, and I’ll scan up Pender’s solutions for that question. Complex 1. a)22 + 13i b) -1/13(5 + 14i) c) Sqrt(17/13) 2. proof 3. a) circle, radius 2, centre (2,0). Shaded in. b) x – 2y – 3 = 0 c) arc of a...

to reply to the other post, usyd is very competitive as you need a minimum uai of 99.95, and there are only 10 places. But I think less people would put it as first preference because they don't think they have a chance, while with unsw they do.

Idyll is right in that at unsw its a combination of marks, rather than a hurdle system like uncle. If you get a really high uai + umat, then you don't have to do great in the interview to get in.

Public Enemy Welcome To The Terrordome 911 Is A Joke Bring The Noise Don't Believe The Hype Give It Up Shut 'Em Down Fight The Power By The Time I Get To Arizona Night Of The Living Baseheads Nighttrain ripped off a best of album, but a good representation...

oh good. understand now. :p

haven't heard it yet, i'll go to limewire now. i don't really download albums, just singles.