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Re: 2015 permutation X2 marathon how come we don['t account for when it's like _C_C_C_C_C_CC_ ?

What is the reasoning for that?

Re: 2015 permutation X2 marathon is this valid? if not, why? A ** I ** I ** O ** O ** where the stars are the possible ways letters can go into (C,M,B,N,N,T) Since there's 10 spots for letters to go into: 10C6 And since you can shift the vowels as a group until the last O touches the last...

I'd say: 3 unit maths > 3 unit english > Chemistry > Economics > Legal > Music 2

You should first know what sin^-1 x and cos^ -1 x looks like already. Then for sine inverse: y = asin^{-1}(bx) + x_{0} $ Step 1. $ Domain: -1 \leq bx \leq 1 \frac{-1}{b} \leq x \leq \frac{1}{b} $ Step 2. $ Range: \frac{-\pi}{2} \leq sin^( $linear $) \leq \frac{\pi}{2} a* \frac{-...

same thing except you don't divide by 'a' which is the constant term under the sqrt so: \int \frac{1}{\sqrt{a^2 - b^{2}x^{2}}} dx = \frac{1}{b} sin^{-1}{\frac{bx}{a}} + $ C $ always divide by number in front of x

$ If your function is in the form of $ \frac{1}{a^2 + b^{2}x^{2}} $ Then $ \int \frac{1}{a^2 + b^{2}x^{2}} dx = \frac{1}{ab}tan^{-1}(\frac{bx}{a}) $ tan inverse $ ( $ square root of $ b^2 x^2 $ divide by square root of a^2 $ ) $) all over 'a' and number in front of x 'b' $ $ Hence...

Re: HSC 2015 4U Marathon $ Using induction, show that for each positive integer n there are unique positive integers $ p_{n} $and $ q_{n} $ such that $ (1+\sqrt2)^{n} = p_{n} + q_{n} \sqrt2 $ Show also, that $ {p_{n}}^{2} - 2{q_{n}}^{2} = (-1)^{n}

Re: MX2 2015 Integration Marathon nice solution, I had this in mind: $ Using x^{logy} = y^{logx} $ (log2)^{log(x)} = x^{log(log2)} $ Hence, $ I = \int_0^1 x^{log(log2)} dx = [\frac{x^{log(log2) + 1}}{log(log2)+1}]_0^1 = \frac{1}{log(log2) + 1)}

Re: MX2 2015 Integration Marathon $ let $ cot^{-1}(x) = \alpha cot \alpha = x \therefore $ I $ = \int (cos[tan^{-1}(sin \alpha )])^2 dx $ I $ = \int (cos[tan^{-1}(\frac{x}{\sqrt{1+x^2 }})])^2 dx $ let $ tan^{-1}(\frac{x}{\sqrt{1+x^2 }}) = \theta tan \theta =...

Re: HSC 2015 4U Marathon Interesting method. The one I had in mind was letting S = ... Then do S - S/a = ...

Re: HSC 2015 4U Marathon Was suppose to be k/(a^(k-1)) oops

Re: HSC 2015 4U Marathon $ New question $ \sum_{k=1}^{\infty}\frac{k}{a^{k-1}}

thanks anyone else?

this is post-trials school rank 300-400 last year overall ranks: Person 1: English advanced: 20/69 Math Ext 1: 5/30 Math Ext 2: 4/12 Economics 2/21 Physics 6/48 Person 2: English advanced: 27/69 Math Ext 1: 4/30 Math Ext 2: 2/12 Chemistry: 1/35 Physics: 2/48

Re: HSC 2015 3U Marathon Is the answer [6C0 * 4C4 + 6C1 * 4C3 + 6C2 * 4C2] all over 10C4

Re: HSC 2015 3U Marathon y = \frac{4}{\pi}sin^{-1}x \pi y = 4sin^{-1}x \frac{\pi y}{4} = sin^{-1}x sin(\frac{\pi y}{4}) = x $ Taking the sine of both sides $

Re: MX2 2015 Integration Marathon oops fixed

Re: MX2 2015 Integration Marathon $ let $ u = (1-\frac{1}{x})^{n} ... dv = dx du = \frac{n}{x^2}(1-\frac{1}{x})^{n-1} ... v = x \therefore I_n = [x(1-\frac{1}{x})^{n}]_1^2 - n \int_1^2 \frac{1}{x}(1-\frac{1}{x})^{n-1} dx I_n = 2^{1-n} - n \int_1^2 (1-\frac{1}{x})^{n-1} -...

just ask ms sapra