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lol, there's something else wrong with my attempt.

Well, at the time that I wrote the solution I rushed and thought that too. On second thought, how could f '(x+f(x))=[1+f '(x)]*f '(x+f(x) and f '(x+f(x))=f '(x)?

Yeah, that's why I wasn't sure about it. Pretty sure it's wrong now.

Think it works dude, nice. I'm not so sure about my method though:

f(x)=f(x+f(x))
f '(x)=[1+f '(x)]*f '(x+f(x))=[1+f '(x)]*f '(x) => f '(x)=0 for all x. Since f(x) is continuous and...

Hey guys, here's a question from last year's UNSW maths competition. Let f(x) denote a strictly positive continuous function defined on all real numbers with the property that f(2012)=2012 and...

Did it. ^ That happened.

\int x^3

1) [(1/a)-(1/b)]^2 + [(1/a)-(1/c)]^2 + [(1/b)-(1/c)]^2 >=0 (equality occurs iff a=b=c)
2/a^2 + 2/b^2 + 2/c^2 -2[(1/ab)+(1/bc)+(1/ac)] >=0
=> (1/a)^2 + (1/b)^2 + (1/c)^2 >= 1/bc + 1/ac + 1/ab for...

It's fine lol.

How so?

Was that in an exam bro? I think you mean (-1/4) not (-1/8).

lol this thread

2U Maths - 97% (1st, don't care about this)
3U Maths - 99% (1st)
4U Maths - 99% (1st)
Physics - 83% (2nd, highest was 87%)
Chemistry - 97% (1st)
English - Haven't gotten my final mark yet

When the motor of an electric drill is experiencing a load, its rotational speed lowers which in turn lowers the back EMF of the motor. Net EMF = Supply EMF - Back EMF. If the back EMF is decreased,...

Thanks for that man, appreciate it. Just one final thing, what's wrong with this? There must be something wrong with the direction of the induced magnetic field but it's not clear to me.

28045

By symmetry, it's just pi*r^2*H/4

I get what you're saying man but do you mind explaining how you could deduce it using the right hand grip rule? I tried using that and got a result that violated the law of conservation of energy lol.

Here's what I was thinking. Since when t=0, V=0, the plane would initially be perpendicular to the direction of the magnetic field. If you turned it clockwise or anti-clockwise, the induced current...

So that means current flows in the opposite direction if turned anti-clockwise, right?

Yes, I agree but DC in the external circuit. The question says 'Which graph below best represents the EMF induced in the coils after the changes were made?', not the external circuit. The current...

If someone in second place is behind first by about 2% by the time all internal assessments are over and this person performs better externally than the person ranked first, who gets the better final...

Thinking about it again actually, I think it's A (call me crazy). I don't think either changes would cause a change in the V-t graph.

With q11), since it says the EMF induced in the coils, wouldn't the correct answer be B? I'm thinking it would be D if you're talking about the EMF in the external circuit.

The balls have to be in different colours though i.e. one must be white, one must be yellow and one must be purple. So wouldn't it be 3!=6?

Yeah, both are correct expressions for the primitive.