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Re: HSC 2012 Marathon :) y=|kx| rotated about the y axis

Re: HSC 2012 Marathon :) That was a nice question Carrot - looks hard, but when you actually work out HOW to do it, the working out itself is easy. Next question, do it in 3d (i.e. a sphere being dropped into a cone)

Re: HSC 2012 Marathon :) \frac{1}{2}(k-\tan ^{-1} k) 1/2 shouldn't be there.. hmm... Edit 2: Worked it out, I had simplified it to half of the area to make the working out easier and forgot to multiply by 2 again :p

Re: HSC 2012 Marathon :) For the last part: <a href="http://www.codecogs.com/eqnedit.php?latex=\alpha @plus;\frac{1}{\alpha}=\frac{1}{b}\\ \alpha ^2@plus;1=\frac{\alpha}{b}\\ \alpha ^2-\frac{\alpha}{b}@plus;1=0\\ $For $\alpha$ to be real, $\Delta \geq 0\\ \left (-\frac{1}{b} \right...

Re: HSC 2012 Marathon :) Got it, nice question :) I'll type up my solution after school tomorrow if nobody else has by then.

Re: HSC 2012 Marathon :) Yay! 3rd time lucky :p

Re: HSC 2012 Marathon :) Oh god yes. Me too.

Re: HSC 2012 Marathon :) Redid it and got 7.1... :s Oops. typo - 7.3.

Re: HSC 2012 Marathon :) Was my method correct at least?

Re: HSC 2012 Marathon :) I'll try describe it, but it's kind've tough without a diagram to point at and whatnot :p (h=height of lamp, x=distance to lamp from pos. 1, y=distance to lamp from pos. 2) I used the two pairs of similar triangles to create two expressions for h in terms of x and y...

Re: HSC 2012 Marathon :) I'm pretty sure my method is correct... it's just a matter of whether or not I actually did the calculations correctly.

Re: HSC 2012 Marathon :) 5.9? Wouldn't be surprised if I'm wrong, my working's rushed and messy :p

Re: HSC 2012 Marathon :) I'm curious, what was the fraction you had in mind?

Re: HSC 2012 Marathon :) I didn't use a fraction substitution, nor the given result. I'll tex my working after I finish the second part. On second consideration, I guess I sort of did use a fraction... Pt. 1 <a href="http://www.codecogs.com/eqnedit.php?latex=I= \int...

Been unmotivated ever since half yearlies. It's a bad position to be in. My abundance of other problems isn't exactly helping either. Oh well.

Aim for first.

<a href="http://www.codecogs.com/eqnedit.php?latex=I=\int^{\sqrt{3}}_{-1}\frac{x^2}{\sqrt{4-x^2}}\\ $Let $x=2\sin \theta\\ dx=2\cos \theta d\theta\\ x=-1\Rightarrow \theta = -\frac{\pi}{6}\\ x=3 \Rightarrow \theta = \frac{\pi}{3}\\ ~\\ I=4\int^{\frac{\pi}{3}}_{-\frac{\pi}{6}}...

Titration is pretty rare in prac exams because of the time it takes and the fact that most schools don't have enough equipment to go round. That being said, a modified/simpler version of titration came up in the prac this year at my school, so it still could. I haven't the slightest idea what...

Memorising is the stupidest thing ever for anything other than quotes/names of things. Sure, you might get decent marks, but you're going to do a lot better if you actually LEARN (learning at school? what kind of madness is this!?!) what you're doing, rather than just swallowing the textbook and...

I use a gridbook ruled down the middle for exercises (except for when we did binomial expansion, because each line of working took up a good 1.5-2 lines of an unruled page), simply because it makes doing exercises where you're drawing a graph basically every question a lot quicker and less...