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Interesting approach - would you say it used "hence" though

Re: HSC 4U Integration Marathon 2017 \int_{0}^{1}\frac{1}{(x+3)^2}\ln \left(\frac{x+2}{x+1}\right)\;\textrm{d}x

If there isn't a response in the next little while I might have to concede there was a typo. It came from a past paper from the 90's of a reputable school. Ive tried to guess the typo, but am interested to know if anyone has solved it. Thanks

So i am stuck on this question: Question 8 ii) "hence deduce..." Thanks for your help

big fan of 13d) - that one took some thought.

Re: HSC 2016 4U Marathon - Advanced Level \large \textrm{The shaded (parallel) cross section is an isosceles trapezium with height } h \textrm{ and parallel sides equal to } y \textrm{ and } z \textrm{ as shown}. \\\textrm{The rear face } ABCD \textrm{ is a square with side length of } a...

Re: MX2 2016 Integration Marathon Soz been out of the thread for a while - good to know its a fav

Re: MX2 2016 Integration Marathon \\ $Evaluate $ \int_{0}^{\frac{\pi}{2}}{\log{\sin{x}}}\textrm{d}x

Re: MX2 2016 Integration Marathon \\ $Find a reduction formula for the integral ${ I }_{ n }=\int {x^{p-2}(1-x^p)^n}\textrm{d}x

Re: HSC 2015 4U Marathon - Advanced Level yep, integer

Re: HSC 2015 4U Marathon - Advanced Level Hi seanieg89. I can get some sort of induction argument going, but was wondering if there is a proof by contradiction. It seems just right for one!?

Re: HSC 2015 4U Marathon - Advanced Level $A function $f(x) = ax^2 +bx+c$ has real coefficients and satisfies $|f(x)|\leq 1$ for all $x\in[0,1]$. \\ Find the maximal value of $|a|+|b|+|c|$ $

Re: HSC 2014 4U Marathon - Advanced Level $Case I: \textbf{X and his wife and Y and his wife are all in the same boat}. \\\\This means that the remaining eight men can be distributed amongst the other boats in $ \frac{8!}{4!(2!)^4} $ ways. Here I am assuming the boats themselves are...

Re: HSC 2014 4U Marathon - Advanced Level I think what's going on here is that you are assuming that different boats means different arrangement. I think the question is asking how many different ways can they be separated. Sort of life "how many ways can 10 people be divided into two teams"...

Re: HSC 2014 4U Marathon - Advanced Level yep both cases. i.e. Case 1. X and Wife and Y and Wife all in the same boat. Case 2: X and Wife in one boat. Y and wife in another boat

Re: HSC 2014 4U Marathon - Advanced Level can you explain how you got your answer? I got 4498200, which i'll explain later

Re: HSC 2014 4U Marathon - Advanced Level A group of 10 married couples is getting ready for an excursion in small boats; in particular, they have to split into five groups of four persons each. In how many of these cases will there be two men X and Y each on the same boat with his wife...

Re: HSC 2014 4U Marathon - Advanced Level Nice. I just left the t business till the end and Found the necessary distance between the two hands first i.e. \sqrt(7) Otherwise, pretty much exactly the same as yours.

Re: HSC 2014 4U Marathon - Advanced Level Here's a follow up question. A clock has an hour-hand of 3 units and a minute-hand of 4 units. If the hands are currently positioned at three-o'-clock, determine the first time when the tips of the hands are moving away from each other the fastest

Re: HSC 2014 4U Marathon - Advanced Level Good job on pt i) and ii): for pt ii) I did if \textrm {Let } T^* \textrm{ be first time for planets to be aligned, one on either endpoint. Then } 2T^* \textrm{ will be the first time planets are aligned with planets on same side.} \therefore 2T^* =...