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Re: HSC 2014 4U Marathon - Advanced Level Shouldnt it have equality with n=1 anyways here is my attempt: $Suppose we have 2m balls, m of which are red and the remainder being blue$ $The probability of selecting n red balls without replacement is given by:$...

ooh ok that makes sense then thanks man!

oh okay is that the same for advanced streams like 1901 and 1902, cause its sounds a bit low? Im guessing around 200 people do it so less than 10 will get HD?

Hey, I was just wondering whats the mark distribution (roughly) for HD's, D's etc for first year maths is like?

Re: HSC 2014 4U Marathon I got 18/7?

Re: HSC 2014 4U Marathon This is what i did: $ By considering similar triangles , we can prove$ \dfrac{BQ}{AB}=\dfrac{PQ}{PC}\; $and$\; \dfrac{QC}{AC}=\dfrac{PQ}{PB} $Adding these two equations:$ \dfrac{BQ}{AB}+\dfrac{QC}{AC}=1=PQ\left(\dfrac{1}{PB}+\dfrac{1}{PC}\right) \therefore...

Re: HSC 2014 4U Marathon - Advanced Level The lowercase thing? I fixed it but is the answer right?

Re: HSC 2014 4U Marathon - Advanced Level $let \; \sum_{k=1}^n a_k=S_n S_n-S_{n-1}=\dfrac{n+1}{n-1}S_{n-1} S_n=\dfrac{2n}{n-1}S_{n-1}=\dfrac{(2n)(2n-2)(2n-4)...(4)}{(n-1)(n-2)(n-3)...1}S_1=2^n\,n \therefore a_n=S_{n}-S_{n-1}=2^{n-1}(n+1)

Re: MX2 Integration Marathon $Using$\; u=ln(lnx) \rightarrow du=\dfrac{dx}{xln(x)}\; $and$\; dv=dx \rightarrow v=x \therefore \int ln(lnx)dx=xln(lnx)-\int \dfrac{dx}{ln(x)} \int\left(\dfrac{1}{ln(x)}+ ln(lnx)\right)dx=xln(lnx)+c

Re: MX2 Integration Marathon \dfrac{d}{dx}xln(lnx)=\dfrac{1}{lnx}+ln(lnx) \therefore \int{\left (\frac {1}{lnx} + ln (ln (x))\right ) dx =xln(ln(x))+c $Other than this method we can apply IBP to $ \int ln(lnx)dx $ which will cancel out the other integral.$

Re: HSC 2014 4U Marathon - Advanced Level Nice solution bro :)

Re: HSC 2014 4U Marathon - Advanced Level Right i made a typo my bad, i fixed it the LHS was meant to be squared, thanks for pointing out the error

Re: HSC 2014 4U Marathon Well maybe its a dog house :p

Re: HSC 2014 4U Marathon Here you go, sorry if wording isn't clear enough

Re: HSC 2014 4U Marathon - Advanced Level $Prove$\sum_{k=0}^{n} \binom{4n}{2k}^2=\dfrac{1}{4}\binom{8n}{4n}+\dfrac{1}{4}\binom{4n}{2n}+\dfrac{1}{2}\binom{4n}{2n}^2

Re: HSC 2014 4U Marathon \\$A projectile is launched at the edge of a house,which has a roof slanted at an angle of$\; 45^{\circ}.$The projectile just touches the roof (on both the left and right side of the house) when fired at a speed$\; V$and at an angle$\; \theta\; $.The walls of the house...

Re: HSC 2014 4U Marathon - Advanced Level Oh right, I see it! Thanks for letting me know :) Il update it now

Re: MX2 Integration Marathon Had a feeling there would be recursion, took me a while to find it: \dfrac{\sin^2{nx}}{\sin^2{x}}=\dfrac{\sin^2{(n-1)x}}{\sin^2{x}}+\dfrac{\sin{(2n-1)}}{\sin{x}} $Let$ \...

Re: HSC 2014 4U Marathon - Advanced Level $Here is my attempt and again nice question $ $I'm assuming that x,y and t are independent variables$ \int_{0}^{x+y} f(t) \ dt = \int_0^x f(y) \cos t + f(t) \cos y \ dt+\int_0^y f(t)dt...

Is this question ur asking related to the method ur trying to use to prove 3d in math1902 assignment?