HSC 2013-14 MX1 Marathon (archive) (1 Viewer)

Sy123 · Aug 9, 2013

Re: HSC 2013 3U Marathon Thread

HeroicPandas said:
I found a mistake in my working out for the RHS $(-1)^n \binom{2n}{n}$

If i equate coefficients of x^(2n) for [3], i get $\binom{2n}{2n}$

I'm pretty sure you get $(-1)^n \binom{2n}{n}$

The n+1th term in that binomial expansion in [3] is $\binom{2n}{n} (-1)^n (x^2)^n$

HeroicPandas · Aug 9, 2013

Re: HSC 2013 3U Marathon Thread

Sy123 said:
I'm pretty sure you get $(-1)^n \binom{2n}{n}$

The n+1th term in that binomial expansion in [3] is $\binom{2n}{n} (-1)^n (x^2)^n$

ahh i see, made a mistake on my very last term (wrong power lol)

JJ345 · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

Sy123 said:
I don't think so, I could be wrong but I'm getting what the question sasys.

I'm not getting the +g either for some reason. How did you solve it?

Sy123 · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

JJ345 said:
I'm not getting the +g either for some reason. How did you solve it?

Yep I redid and you are right if we take range as distance from projection (which is probably the more correct definition), I took range as distance from origin.

Kustom- · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

OMG I need help with this stupid question -_-

Prove:
sin(x) + sin(nx) = 2sin (nx/2 + x/2) x cos(nx/2 - x/2)

Please!!

Carrotsticks · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

Start with RHS then expand then prove LHS.

Kustom- · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

see I tried but didn't get toooo far... Im not sure how to expand 2sin(x/2) x sin(x/2) x sin(nx/2) x cos(nx/w)

Makematics · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

argh so tempting to use 4U sum to product rules for that haha

AnimeX · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

Makematics said:
argh so tempting to use 4U sum to product rules for that haha

sum to product rules? what are they?

Carrotsticks · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

Kustom- said:
see I tried but didn't get toooo far... Im not sure how to expand 2sin(x/2) x sin(x/2) x sin(nx/2) x cos(nx/w)

Are you sure that result is correct?

Makematics said:
argh so tempting to use 4U sum to product rules for that haha

I know right lol.

Sy123 · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

$$2 projectiles are fired from the origin at the same time with the same velocity with angles of projection$ \ \alpha \ $and$ \ \beta$

$\frac{\pi}{2} > \alpha > \beta > 0$

$$Prove that if the projectiles collide then the horizontal distance from the origin is maximised when$ \ \alpha + \beta = \frac{\pi}{2}$

Carrotsticks · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

Sy123 said:
$$2 projectiles are fired from the origin at the same time with the same velocity with angles of projection$ \ \alpha \ $and$ \ \beta$

$\frac{\pi}{2} > \alpha > \beta > 0$

$$Prove that if the projectiles collide then the horizontal distance from the origin is maximised when$ \ \alpha + \beta = \frac{\pi}{2}$

Well fuck me.... that was one of the questions I was considering for BOS Trial before I scrapped it.

Kustom- · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

nope, im not sure they are correct haha.. i expanded too 2sin(nx/2)cos(x/2) + cos(nx/2)2sin(x/2) x cos(nx/2)cos(x/2) + sin(x/2)sin(nx/2)
then from there did 2sin(nx/2)cos(nx/2) x cos(x/2)Cos(x/2) and got sin(nx)cos^2(x/2) and left with c0s(nx/2)2sin(x/2) x sin(x/2) sin(nx/2)

Sy123 · Aug 10, 2013

Re: HSC 2013 3U Marathon Thread

Carrotsticks said:
Well fuck me.... that was one of the questions I was considering for BOS Trial before I scrapped it.

o_o

This year or last year?

Sy123 · Aug 11, 2013

Re: HSC 2013 3U Marathon Thread

$$Prove for some integers$ \ m, n$

$1+ \frac{m}{1!} + \frac{m(m+1)}{2!} + \dots + \frac{m(m+1) \dots ( m+n-1)}{n!} = \frac{(m+n)!}{m! n!}$

braintic · Aug 11, 2013

Re: HSC 2013 3U Marathon Thread

Sy123 said:
$$Prove for some integers$ \ m, n$

$1+ \frac{m(m+1)}{2!} + \dots + \frac{m(m+1) \dots ( m+n-1)}{n!} = \frac{(m+n)!}{m! n!}$

Are you missing an m/(1!) ? (I don't know - I haven't done the question. But it looks like a term is missing.)

Menomaths · Aug 11, 2013

Re: HSC 2013 3U Marathon Thread

Imagine Sy's been getting other people to do his homework for him

Sy123 · Aug 11, 2013

Re: HSC 2013 3U Marathon Thread

braintic said:
Are you missing an m/(1!) ? (I don't know - I haven't done the question. But it looks like a term is missing.)

I got that question from Summation of Series - Jolley, series number 196.
I'm pretty sure the 1 cancels out which is why it's there

EDIT: Let me redo it I may have made a mistake

Menomaths said:
Imagine Sy's been getting other people to do his homework for him

hahahahaha

JJ345 · Aug 11, 2013

Re: HSC 2013 3U Marathon Thread

Sy123 said:
I got that question from Summation of Series - Jolley, series number 196.
I'm pretty sure the 1 cancels out which is why it's there

I showed the result but having the m/1! was necessary---> Are you sure there isn't a mistake? I may be wrong though.

Sy123 · Aug 11, 2013

Re: HSC 2013 3U Marathon Thread

Sorry you are right braintic, I am missing a m/1!, I apologise, fixing now.

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