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Re: HSC 2014 4U Marathon ?, chat is bugged

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Re: HSC 2014 4U Marathon I'm not sure if this is right (haven't touched complex in a while) arg(z-2)+arg(z+2)=pi arg((z-2)(z+2))=pi arg(z^2-4)=pi Thus, the complex number z^2-4 must be purely real Let z=x+iy z^2-4 = (x^2-y^2-4)+2ixy Demand: Im(z)=0 2xy=0 xy=0 Pair of intersecting lines (x=0 ; y=0)

So if P(z) is a real polynomial, then complex roots occur in conjugate pairs. Thus z=-i is also a root. Let the final root of P(z) be (alpha) Product of the Roots = (i)(-i)(1+√2)(alpha)= -1 (alpha)=1-√2 Therefore the roots are z=i, -i, 1+√2, 1-√2 Sum of roots = -a a = -2 Sum of roots (3 at a...

I do business studies and economics and by far economics is one of the most challenging yet rewarding subjects. Economics is very conceptual but once you understand how everything works and links up its more or so the gratification that you achieve that's satisfying. As for any humanities...

Re: HSC 2014 4U Marathon It is a hyperbola that has had its x-y axis rotated 45 degrees anti-clockwise. The equation of this hyperbola on the new X-Y axis is 11y^2-7x^2=2 (I think) and cuts the x-y axis at y=-1 and y=1. Learned something new today :p

Re: HSC 2014 4U Marathon Not sure if rotation of axes of conic sections are within the constraints of the 4U syllabus

Re: HSC 2014 4U Marathon Nice question, took me while to figure the pattern :p

Re: HSC 2014 4U Marathon :d

Re: HSC 2014 4U Marathon By inspection x=6 ->4! = 24

Re: HSC 2014 4U Marathon ahh i see now, I thought my first approach was wrong lol..

Re: HSC 2014 4U Marathon So what I should of done: Multiple top and bottom by sqrt(x^2+4x+7)-x, You get lim(n->-infinity) 4x+7/(sqrt(x^2+4x+7)-x), Divide everything by x, lim(n->-infinity) [4+7/x]/[-sqrt(1+4/x+7/x^2)-1] (for x negative) =-2

Re: HSC 2014 4U Marathon dw I got it, typesetting solution :D

Re: HSC 2014 4U Marathon Can u explain what I'm doing wrong, I divide by x and bring the x inside the sqrt. By simplifying, you get lim(n->-infinity)[sqrt(1+4/x+7/x^2)+1] and you get 2. Now i go to check with my calculator by subbing in a large value, it tells me its worth -2 zzz

Re: HSC 2014 4U Marathon what i meant was -1 <= sec(a) < sec(b) <= 1 (within the domain) which is undefined unless a=b=0 i tried editing but it still doesnt show, some bug in the system

Re: HSC 2014 4U Marathon -1<=sec(a)<sec(b)<=1? which is undefined except a=b=0

Re: HSC 2014 4U Marathon idk i thought there had to be some condition with the sec function

Re: HSC 2014 4U Marathon consider the sec function and the condition given

Re: HSC 2014 4U Marathon na not even close man, there's about 1000 other people in this state that are better than me

Re: HSC 2014 4U Marathon oh yes, you got me there haha :D reminds me of a past hsc curve sketching question