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Re: HSC 2013 4U Marathon Let angle BOF=x. Now, angle AOD=x (triangles AOB and AOD are congruent) Hence, angle BOD=2x Hence, angle OBF=90-x Hence, angle ABF=x (tangent is perpendicular to radius drawn to point of contact) Now, triangle ABD is similar to triangle ACE Hence, angle ACE=x since...

Re: HSC 2013 4U Marathon This may help:

Re: HSC 2013 4U Marathon lol, he was trolling.

that's right man be proud.

Re: 2013 HSC physics marathon When a satellite fires its propulsion system, a thrust is generated as a reaction force which arises as a result of the outward force of gases exiting the exhaust when fuel is burnt in the engine. The forces are equal in magnitude by Newton's third law and...

Re: 2013 HSC physics marathon lol, chemistry died.

Re: HSC 2013 4U Marathon realise, diggin' the sig bro.

Re: HSC 2013 4U Marathon It's as if this thread is invisible to everyone besides the usual bosers. Usually you'd have some other randoms participate in marathon threads.

Re: HSC 2013 4U Marathon lol, are we like the only 4U maths students in the state? For part iii), use the fact that lim[n->infinity] sin(x)/x is equal to the limit of the product of the cosine functions as n->infinite. Let x=pi/2, rearrange for pi and use the identity cos(2x)=2cos^2(x)-1 to...

Re: HSC 2013 4U Marathon Oh okay.

Re: HSC 2013 4U Marathon This question is kind of weird because as goldy said lim[n->infinity] [sin(x)]/x = sin(x)/x.

Re: HSC 2013 4U Marathon What about cos(x/2), where does that go? It doesn't vary with n, that's why I'm still confused.

Re: HSC 2013 4U Marathon lim[n->infinity] sin(x/2^n)/(x/2^n)=1 which essentially comes from the lim[x->0] sin(x)/x =1 with the substitution u=x/2^n. The cosines approach 1. Actually, I'm still not sure of this. Some of the cosines are independent of n.

Re: HSC 2013 4U Marathon Wait no it's 1 lol.

Re: HSC 2013 4U Marathon Not sure actually either..

Re: HSC 2013 4U Marathon What about the 2^n?

re: HSC Chemistry Marathon Archive lol, was off by the word 'higher'. Don't know how to forgot to include that.

re: HSC Chemistry Marathon Archive New question. A 0.2845 g sample of impure sodium carbonate required 24.65 mL of an HCl solution for titration. A 0.2204 g sample of pure sodium carbonate required 20.06 mL of the HCl solution of the same concentration. What is the percentage of sodium...

Re: HSC 2013 4U Marathon Very nice question Sy.

re: HSC Chemistry Marathon Archive Oh right, okay thanks for that. Also, special thanks to you and deswa for offering everyone constructive criticism, should help us a lot :).