Search results

Re: MX2 2015 Integration Marathon interesting question, when x=0, f(0)=(1+\sqrt{1+4(0)})/2=1?

Re: HSC 2015 4U Marathon sorry have to bump again lol

Re: HSC 2015 4U Marathon are you sure? I think not all steps are reversible. if one thinks the logic is all good in that proof, can you please rewrite the proof step by step in correct order? The key point is: from \frac{z_2 -z_1}{z_3 -z_1} = \frac{z_3 - z_2}{z_1 -z_2} to z_2 - z_1 = w(z_3...

Re: HSC 2015 4U Marathon This is exactly what I would do.

Re: HSC 2015 4U Marathon it seems to me you proved that if ABC is equilateral then the given equation is true, but the question asks you to prove its converse: given the equation, prove ABC is equilateral.

Re: HSC 2015 4U Marathon - Advanced Level $ firstly, $ |c|=|z_1z_2z_3|=|z_1||z_2||z_3|=1. $ secondly $ |a|=|z_1+z_2+z_3|=|\bar{z_1}+\bar{z_2}+\bar{z_3}|=\left|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}...

Re: HSC 2015 4U Marathon NEW QUESTION A, B $ and $ C $ are the points that represent the complex numbers $ z_1, z_2 $ and $ z_3 $ on the Argand diagram. Prove that if $ \frac{z_2-z_3}{z_1-z_3}=\frac{z_1-z_3}{z_1-z_2}, $ then $ \triangle{ABC} $ is equilateral. $

Re: HSC 2015 4U Marathon limiting sum of GP, with r=-z^2/9, and take imaginary part

Re: HSC 2015 4U Marathon well done guys. next one: $ Show that the modulus of each root of the equation $ z^3+z+12=0 $ lie between $ 2 $ and $ \sqrt{6}.

Re: HSC 2015 3U Marathon yes quite so. and a comment, the function x/|x| (which usually called sign function or Heaviside function) has no definition and is discontinuous at x=1, this justfifies that y' does not exist at x=0. plus, guys, don't forget my last question, still there unanswered

Re: HSC 2015 4U Marathon NEXT QUESTION $ Find any straight lines that are tangent to the curve $ y=x^4+4x^3-2x^2 $ at two distinct points. $

Re: HSC 2015 3U Marathon NEXT QUESTION $ For what values of $ \theta, |(3\sin\theta-\cos\theta)+k(\cos\theta-2\sin\theta)|\leq1 $ is true for all real $ -1\leq k\leq1 ?

You must factorise the number 216. No better way because the variable appears on both the base and the index. 216=6*6*6=6^3=(2*3)^3. so x=3

In the case of n=m=1, which is very easy, do u guys think what the probability asked in the question should be? 1 or 1/2?

Re: HSC 2015 4U Marathon NEXT QUESTION $ (i) Factorise $ z^8+1 $ into real quadratic factors. $ $ (ii) Hence show that $ \cos4\theta=8\left(\cos^2\theta-\cos^2\frac{\pi}{8}\right)\left(\cos^2\theta-\cos^2\frac{3\pi}{8}\right).

Re: HSC 2015 4U Marathon NEXT QUESTION $ You may use $ \cos3\theta=4\cos^3\theta-3\cos\theta. $ Solve the equation $ 4x^3-9x-1=0. $ Leave your answer in exact trigonometric form. $

Re: HSC 2015 4U Marathon no

Re: HSC 2015 4U Marathon NEXT QUESTION $ Solve the equation $ x^4-8x^3+16x^2-8x+1=0. $ Leave your answer in exact form. $

Re: HSC 2015 4U Marathon I don't really know about the tennis rule, but I doubt 4qp^3 might be wrong, because if B win the first game over ?

Re: HSC 2015 3U Marathon NEXT QUESTION $ For what values of $ k, |(3\sin\theta-\cos\theta)+k(\cos\theta-2\sin\theta)|\leq1 $ is true for all real $ \theta ?