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\frac{dL}{dx}=\frac{x}{\sqrt{x^2+25}}+\frac{x-3}{\sqrt{25-6x+x^2}} \\ \\ -\frac{x}{\sqrt{x^2+25}}=\frac{x-3}{25-6x+x^2} \\ \\ \frac{x^2}{x^2+25}=\frac{x^2-6x+9}{25-6x+x^2} From there cross multiply, you will get cubic terms and a quartic terms, however they will cancel out. You are left with...

Carrotsticks cancelled out cos x, so in the given domain, he can because cos x =/= in that domain. (I think) EDIT: I graphed both sides of the equation on Geogebra, and they seem to be the exact same for all values of x, I was guessing that they might of given you that domain, because it was...

Definitely, R&C3 is easily the best Ratchet and Clank game, followed closely by Ratchet and Clank 1. Anyway my list cannot rank, because I cant rank them, but they are my top 5 if I had to choose 5, they arent in any order of superiority. -Ratchet and Clank 3 -Minecraft -Pokemon Pearl...

y=ax^3+bx \\ y'=3ax^2+b \\ x=1 \Rightarrow y'=2 \ \ \ \ ($Since tangent at$ \ x=1 \ $parallel to line gradient of 2$) \\ \therefore 2=3a+b \\ \\ x=1 \Rightarrow y=7 \\ \\ \therefore 7=a+b \\ \\ 2=3a+b \ \ \ [1] \\ 7=a+b \ \ \ [2] \ \ \ \ [1]-[2] \\ \\ \\ a=\frac{-5}{2} \\ \therefore...

So is it wise to look up 4u questions on Harder 3u Circle Geometry, as some practise in 3u circle geometry? Because I wish to do those questions faster, because they usually slow me down while Im doing trial papers.

delelted sorry

Re: HSC 2012 Marathon :) $Prove that for all integers$ \ \ n>0 \\ \\ x^n \neq \ln{x} Its a question entirely possible within 3u boundaries (depending on how you do it you will have to use 3u knowledge) I made the question up after I proved that result. So enjoy :3

Re: HSC 2012 Marathon :) \ddot{x} =-n^2 x \\ \frac{1}{2}v^2=\frac{-n^2 x^2}{2}+C \\ \\ x=a \rightarrow v=0 (\text{Where a is extremety}) \\ \\ \therefore C=\frac{n^2 a^2}{2} \\ v^2=-n^2 x^2+n^2 a^2 (2\sqrt{2})^2=-9n^2+n^2 a^2 \\ \\ 8=-9n^2+n^2 a^2 \\ \\ \Abs{\ddot{x}}=1 \ \ \ when \ \ \...

Ill go through each team member individually Haxorus: The EVs are in the right place somewhat, however replacing Swords Dance withDragon Claw as a secondary Dragon attack to not get locked into, and putting a Choice Scarf on Haxorus will benefit it and willl give you a nice late game sweeper...

Generally within most forums, if you lurk around for a bit, its easy to spot who are the popular ones, helpful etc. For example in the Math section which I lurk alot, there are many users, if I need help with something, I can count on their genius to help me out, and I have gathered such...

If anyone could, a nice hard 3u past paper would be very much appreciated. Thanks.

Re: HSC 2012 Marathon :) Show that \sin{\cos^{-1}{x}}=\sqrt{1-x^2} \ \ \text{For all x} -1\leq x\leq 1 Difficulty: Easy I will have a better one tommorow.

Re: HSC 2012 Marathon :) \begin{align*}\ddot{x}&=-16x \\ \left(\frac{1}{2}v^2\right)\frac{d}{dx}&=-16x \\ \frac{v^2}{2}&=-8x^2+C \\ \\ x=3 \Rightarrow v=16 \\ \frac{16^2}{2}&=-8(3)^2+C \\ C=200 \\ \frac{v^2}{2}&=200-8x^2 \\ v^2&=400-16x^2 \\ v&=+\sqrt{16(25-x^2)} \\ v&=+4\sqrt{25-x^2} \\ \\...

Err, yes, but Im ALSO asking whether alpha needs to be an integer, or can it just be rational, or can it just be any real number of alpha. Also, a b and c should be integers

So I had formed a hypothesis that: \sin {\alpha} =a+b\sqrt{c} Where alpha is any integer degree. Could I write the sine of that angle, be it any angle, in exact form And a, b and c are all integers. Now the above RHS is probably wrong (maybe not) But Im just wondering if it could be done...

As my math teacher always says, they never give anything in the question in vain.

I was able to get it using the sum and products of roots rules. I will use roots a, b, c and d because writing alpha in latex is really annoying especially when you have to write ALOT of them. Well here we go. 8x^4-2x^3-27x^2+6x+9=0 \ \ \ \text{Let a, b, c and d be roots to the equation...

Draw the triangle, do Pythagoras and you find: \tan{\theta}=\frac{-3}{\sqrt{7}} \ \ \ (\text{Since from}) 90 < \theta < 180 \ \ \ \tan{\theta}<0 \\ \\ \tan{2\theta}=\frac{2\tan{\theta}}{1-\tan^2{\theta}} \\ \\ \tan{2\theta}=\frac{2\times \frac{-3}{\sqrt{7}}}{1-\frac{9}{7}} =...

Unfortunately, it makes it less enjoyable. Also, to get into medicine, the minimum requirement is English Standard or above English, so unless you plan on dropping to Fundementals of English, you have nothing to worry about except the UMAT and getting a really really high ATAR. Which is a...

Also what is the average external marks and external internal marks in your school (just an estimate, to judge difficulty of your school's tests)