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I will look over my work again, but I got sqrt(189/20) using my own method which was pretty different too.

Yeah its sqrt(189/20).

Which question?

lrn2maths.

Definitely on the easy side for a Q16/8.

If they got 98/100 you mean? Almost certainly, I can't imagine there being 10 people in the state doing better (especially if his 3U mark is good as well).

Anyone here remember Worms Armageddon (not W2A, the original released around the year 2000)? It holds up incredibly well and I have been playing a ton of multiplayer with housemates and friends from interstate recently. BoS should get some online games going!

A man is in the middle of a circular lake and a monster is at the edge of the shore. The monster runs around the lake at a speed X times the swimming speed of the man (but much slower than the man's running speed), and chooses his running direction at all times optimally in order to catch the...

good luck everyone.

Logically, the fallacy is exactly the same as making the following argument: If the number n is prime, then the number n+1 is prime.

The "changing of range" is not the critical issue here. This entire argument is logically misguided: The premise is that p+q-r is non-negative. This is a statement about p,q and r. The desired conclusion is also a statement about p,q, and r. If you were to "let" p=p+1/p (pretending for the...

Re: HSC 2013 4U Marathon I tried a few different ways of approaching Carrots problem but yeah, the best one can do it seems is find an expression in terms of alpha (where alpha is the positive solution in (0,pi/2) to tan(t)-t=2*pi).

Re: HSC 2013 4U Marathon It's not as simple as that, think of what happens if you stand at an arbitrary point holding the string and then pull it taut, it doesn't wrap around the post in the way you have shown in your diagram. For instance, on one side of the pole a taut string won't make any...

Re: HSC 2013 4U Marathon Meaning could you explain your method? I don't think it can possibly be this as your answer only grows linearly with r. If we just look at the semicircular part of the region, this scales as r^2.

Re: HSC 2013 4U Marathon Working?

Re: HSC 2013 4U Marathon No, the string wraps around the water tank as you walk around, the shape is not circular. From a quick glance it seems the integrals involved may not have nice closed expressions (especially since r is variable).

Re: HSC 2013 4U Marathon With these sorts of things, try to reduce to problem to a two dimensional one. In this case, we want to find the length OP in terms of r and theta. Try this by drawing a 2-d diagram and using things you know about circles and triangles.

Re: HSC 2013 4U Marathon Informed by whom? What if the method completely circumvents the concept they are trying to test? Where do you draw the line? You certainly shouldn't be allowed to use out of syllabus theorems in "Prove" questions, as that would let you write zero-effort proofs...

Re: HSC 2013 4U Marathon Do you mean yes as in it is mathematically valid or yes as in it will be awarded marks according to the marking guidelines set forth by the board? I am extremely skeptical about the latter.

Cool, then his working pretty much does it. we have z/i must be real and hence z must be imaginary or zero. (book should have specified zero as a possibility).