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I hope you don't think those two particular examples are equivalent.

Re: HSC 2015 3U Marathon It is correct. But you don't need a first principles proof for the n=1 case - it is the gradient of a straight line.

Re: HSC 2015 3U Marathon The royal flush IS a straight flush. It is an ace-high straight flush. Only pub gambling machines treat it as being distinct from a straight flush.

Re: HSC 2015 3U Marathon So are you asking for first principles, or induction?

You say you're located near the Villawood Detention Centre. You you do cell visits? I don't think I can get a pass out.

Re: HSC 2015 4U Marathon Not really relevant since we're doing a volume question. You don't double for volume. Edit: Oops - I thought we were rotating about the y-axis.

Re: HSC 2015 2U Marathon The fact that it should be a general polynomial means it is not 2U. But my alternative question is 2U.

Re: HSC 2015 2U Marathon You mean every odd polynomial. (Although it is always true if you consider Taylor series) Perhaps a better more general question is "Prove that if an odd function is defined for x=0, then it must pass through the origin".

Re: HSC 2015 3U Marathon Including in Pascal's triangle.

Re: HSC 2015 4U Marathon Prove that in any triangle ABC: \cos \frac {A-B} 2 > \sin \frac C 2 and \sin \frac {A-B} 2 < \cos \frac C 2

Re: HSC 2015 3U Marathon Yep ... that's what happens when I try to do it in my head.

Re: HSC 2015 4U Marathon It's not. I was just giving the only answer I could give. (I replied to the wrong person)

Re: HSC 2015 3U Marathon AND .... show that this curve is a parabola, and find its focal length and the coordinates of its vertex.

Re: HSC 2015 4U Marathon k = 0.536 516 425 697 171 ...

Re: HSC 2015 4U Marathon I think this belongs in the advanced marathon. I'm not sure of the difficulty because I haven't tried it, but the wording and notation are going to confuse people, and it is not the sort of question you will see in an HSC exam.

Restating that: If you are in an ellipsoid (not just an elliptical prism), if no radiated heat is lost to convection or other forms of dissipation, if the fire is located at a focus, and you are located at the other focus, then every ray of infrared light from the fire would hit you. The only...

It depends. Firstly, I'm not sure how much heat from a fire is transmitted by radiation and how much is transmitted by convection. My suspicion is that at any reasonable distance from the fire, most heat comes from convection. Only radiated heat reflects (it is infrared radiation) - convected...

"Categorical" seems to have different meanings depending on who you read. Sometimes it seems to be synonymous with "qualitative" (rather than "quantitative"). Other times it seems to be a more general "discrete" (rather than continuous). Using the first definition, it would mean "nominal"...

Re: HSC 2015 2U Marathon The person you are referring to IS a 2015er.

Re: MX2 2015 Integration Marathon That would depend on how you define an asymptote. I believe some sources actually define it as the limiting tangent.