Search results

Re: HSC 2018 MX2 Integration Marathon I don't think u^2 = 1+\frac{1}{x^2} is the right substitution for that.

$\noindent Solve the following Diophantine Equation in $ \mathbb{Z} \\\\ a^3 + b^3 + c^3 = a^2 + b^2 + c^2

Fourier Expansion :P

Re: HSC 2018 MX2 Marathon Letting the value of the solution to x = cos(x) be r, the following area expressions are obtained through integration: A₁ = sin(r) - r²/2 A₂ = 1 - sin(r) + r²/2 A₂ - A₁ = 1 - 2sin(r) + r² r > sin(r) (proof is trivial and left as an exercise) - 2sin(r) > - 2r 1 -...

this feels like a meme

\int \sqrt{\tanh{x}}\,\text{d}x

Re: HSC 2018 MX2 Marathon Prove the ellipses: \frac{(x + k y)^2}{a^2} + \frac{y^2}{b^2} = 1, \frac{x^2}{a^2} + \frac{(kx + y)^2}{b^2} = 1 where k is an arbitrary real number have the same area as the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

yeah, idk why they keep trying to push back, since it's really not helping their "member count" if that's something of importance to them

more accurate (even if the distribution of supporters is non-random, which it basically is, from the results, it can be deduced that at least half of the supporters are christian with a high level of confidence)

An answer that isn't an answer.... (As in you technically didn't do the computation, not that you're being cryptic)

$\noindent Assuming $ ax^2 + 2bxy + cy^2 = z $ (where $z$ is positive) \\ describes a general ellipse in the Cartesian Plane, evaluate:$ $\huge \noindent$ \iint_{\mathbb{R}^2} e^{-(ax^2 + 2bxy + cy^2)} \text{d}x \text{d}y Prove the integral diverges if the argument of the exponential does not...

because I like a nice balance of low tech and efficient solutions to integrals

I was looking for a polylog-free solution, but I guess this puts the nail on the coffin :(

Re: HSC 2018 MX2 Integration Marathon same

but we haven't ;) they need to step up their game, or hire us to write questions.

wow so easy this year

Oh come on, it wasn't THAT hard.... :P

when one person is out of commission for a few hours and everyone stays up late getting solutions together :') #sleep4days

I'm looking into this possibility, but the decision ultimately lies with Carrotsticks and Trebla.

"it works" well so does a burning bus.