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Re: HSC 2014 4U Marathon (i) Prove that for any point along the y-axis, there is exactly two normals that can drawn to the hyperbola xy=c^2 (ii) Hence, explain why it is impossible to have 3 normals drawn from an arbitrary point to the hyperbola in the x-y plane

Re: HSC 2014 4U Marathon

Re: MX2 Integration Marathon

Re: HSC 2014 4U Marathon (iii) Let u=tan(x) and you get the required result (iv) Hint for this part (v) Im guessing as n approaches infinity the integral approaches 0 with the use of part (iv)

Re: HSC 2014 4U Marathon (i) Can be proven using vectors, I've answered this before so I'll let someone else have a go (ii) Basic circle geometry; you get a(Ɵ)=sqrt[2(1-cos(Ɵ))] and b(Ɵ)=sqrt[2(1+cos(x))], hence a(Ɵ)/b(Ɵ) turns out to be tan(Ɵ/2). Integrating we obtain the required result...

As for the first one, the best way to prove these type of questions is by moving it all on one side and calling it f(x) and proving > or < 0. This can be done by inspecting stationary points. There always tends to be one minimum/maximum stationary point with y-ordinate 0. Hence, you can deduce...

Maths Extension 2 - Wed 22 Oct AM Business Studies - Thurs 23 Oct AM Economics - Fri 24 Oct AM Well... fuck :cry:

Re: MX2 Integration Marathon Yeah pretty much, was aiming to utilise the property int{(x=-a to x=a) f(x)dx} = int{(x=0 to x=a) f(x)+f(-x)dx}

Re: MX2 Integration Marathon -> question

As a 4u student, you should know how to derive them. It's not that hard lol

Re: MX2 Integration Marathon pretty much what i did :D, after simplifying you should get something like

Re: MX2 Integration Marathon Made this one up :D

Re: MX2 Integration Marathon -> Question

Re: HSC 2014 4U Marathon Yeah can also be done by complex numbers, that's how my teacher derived the formulae for the rectangular hyperbola

Re: HSC 2014 4U Marathon Here's what I followed to sketch that. It shows the process of deriving the angle of rotation plus the new coordinates on the shifted x-y axis, pretty doable in 4u tbh

A rise in domestic income increases the level of disposable income. Thus, consumers tend to demand greater imports as their purchasing power increases to greater enhance their standard of living. By the same token, if there is a upswing in the international business cycle (i.e. world growth)...

LMFAO

Re: HSC 2014 4U Marathon Here's a good work through complex numbers question (part (e) meant to be arrows --> on top)

Re: HSC 2014 4U Marathon Sketch the curve: 6cos(x^2-y^2)=pi

Re: HSC 2014 4U Marathon A+B = 2pi/3 ?