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I'm sorry for seeing this post so late, the thread got bumped down! Added

Added

Re: MX2 2015 Integration Marathon \int \frac{dx}{\sqrt{x} + \sqrt[3]{x}}

Re: HSC 2015 4U Marathon Without the rational root theorem: \\ $If there is a rational root of the polynomial, then the root is in the form$ \ \frac{p}{q} \ $where$ \ p,q \ $are coprime integers$ \\ $So,$ \ \frac{p^3}{q^3} + \frac{p}{q} + 1 = 0 \Rightarrow \ p^3+q^3 = -pq^2 \\ \Rightarrow...

http://community.boredofstudies.org/215/games/336199/sy123s-bos-minecraft-server.html#post6938964 make sure to get whitelisted, PM me or post your minecraft username

This is the official thread for the current BOS Minecraft server. To join the server you need to have bought Minecraft and have it installed for the latest version (1.8). The IP of the server is: 119.252.191.106:26757 The server is whitelisted, if you want to be whitelisted, then either...

If there is enough interest I will have a go at setting a 24-7 one up

Re: MX2 2015 Integration Marathon Since you will want x > 0, then sqrt(1+x) > 1, meaning it is the hypotenuse, and so sin theta =/= sqrt(x) (assuming theta is an angle in the triangle which is right angled)

Re: HSC 2015 4U Marathon - Advanced Level You missed one solution (2,2) \\ $Manipulating the equation results in$ \ \frac{y}{x} =y + 2y^2 - 1 -x^2y \\ \\ $Since the RHS is an integer, then so is the LHS, and so$ \ y = kx \ $for some integer$ \ k \\ $Putting this back into the original...

Re: MX2 2015 Integration Marathon \\ = \int \frac{2x-3}{\sqrt{2 - (x^2-3x)^2}} \ dx \\ \\ $So, use$ \ u = x^2 -3x

Re: MX2 2015 Integration Marathon Nice solution, I was thinking of doing something like: \int \frac{\sin x \cos x}{\sin^4x + \cos^4x} \ dx = \frac{1}{2}\int \frac{\sin (2x)}{1 - \frac{1}{2}\sin^2(2x)} \ dx = \dots But it's a little bit longer I think

Re: MX2 2015 Integration Marathon \int \frac{\sin x \cos x}{\sin^4x + \cos^4x} \ dx

Re: HSC 2015 4U Marathon - Advanced Level \\ $Find all pairs of non-negative integers$ \ (x,y) \ $that satisfy$ \\ x^3y + x + y = xy + 2xy^2

Re: HSC 2015 4U Marathon \\ $Let$ \ P(x) \ $and$ \ Q(x) \ $be polynomials of degree$ \ n \ $and are such that$ \\ P(x) = Q(x) \ $for some$ \ n + 1 \ $distinct values of$ \ x \\\\ $Show that$ \ P(x) = Q(x) \ $for all$ \ x

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There is a reason I quote specific parts of your post at a time You said: "No, it [logicality of omnipotence] is DEFINITELY affected and that is the *entire* point of that argument" You need to show that I'm not asking you to phrase your position, I'm asking you to prove your...

That is because logic is a necessary truth, mathematics is a necessary truth, "everything that begins to exist has a cause" is a necessary truth and etc. "Gravity" is not a necessary truth, and etc. You need to actually read about modality before dealing with my terminology

You keep saying that I'm missing the point when you're the one who is unable to actually provide any systematic reply to anything I've said, and instead have resorted to quoting my whole post so you could safely ignore certain parts of my post Then how about you show it instead of asserting...

You haven't replied to anything else I said here so I assume you concede it, because now you are bringing up a topic that is entirely irrelevant. One can think morality is "arbitrary" or "independent" or even (since the dilemma is not exhaustive) "grounded in the nature of God", and the...

I know what the omnipotence paradox is, and it is clear that God cannot do something illogical, I already clarified this in my very first post. You then ignored all my explanations for why it makes sense to keep talking about omnipotence as the "power to do all things", and omnipotence also is...