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Whether or not I do drugs is completely irrelevant to my post. I didn't say anything positive about drug use because that was not my point, I don't want to go there on this forum, and I do not care what you think about any habit you think I have.

Telling anyone not to do something with the air that you know better than them about the risks and/or rewards involved is massively condescending. Along with many other people in this thread, my main issue is with people who don't actually know what they are talking about getting affected by a...

Out of interest do you hold alcohol in the same regard?

The LD50 lethal dose estimate for LSD is gigantic, 0.2-1mg per kg of body mass. Good luck finding a drug dealer generous enough to provide you with that much without you being very aware of it.

I would be more interested in hearing your main reasons for why you think people SHOULDN'T do LSD, beyond its legal status...as that was clearly not the issue with this particular substance.

Re: HSC 2013 4U Marathon Nice. As an alternate solution to a) note that the problem is invariant under the {friendship}<--->{non-friendship} symmetry, so if x is the avg number of friends of Bob we must have x = (n - 1) - x.

Re: HSC 2013 4U Marathon Yep. Just like flipping a number of coins 10 times and asking what the average number of heads would be: the problem is imprecision in the English language. When formal probability/statistics definitions (such as expectation) are used these ambiguities disappear but...

Re: HSC 2013 4U Marathon The situation described is a probabilistic one, not a definite one. Friendship is not a certain relationship. So average = average number of friends over all equally likely friendship arrangements. (there are 2^{nC2} of these)

Re: HSC 2013 4U Marathon There are n people who live in a small town and the probability of any given pair of them being friends is 0.5 (friendship is of course mutual). One of these people is Bob. a) What is the average number of friends Bob will have? b) What is the average number of...

all smash games. and recently installed aoe2 + forgotten empires, played a couple of epic games with two of my housemates today.

Re: HSC 2013 4U Marathon The end expression isn't that pretty but it is certainly an MX2 integral.

Re: HSC 2013 4U Marathon Because "average" means average with respect to time. This is a continuous analogue of rolling a dice 5 times, adding the totals and dividing by 5. Each "roll" is given an equal weighting in our average for rolling dice, and similarly, each infinitesimal period of...

Re: HSC 2013 4U Marathon Close, but with the "average" part of the question you don't want to be integrating with respect to the angle alpha, you want to integrate w.r.t something that changes at a constant rate with respect to time. (And you will have to divide by how much this thing...

Re: HSC 2013 4U Marathon $Let $f$ be a continuous function on $\mathbb{R}$ and define the sequence of functions $(F_n)_{n=1}^\infty$ recursively by the conditions:\\ \\ $F_0(x)=f(x)\\ F_{n+1}'(x)=F_n(x)\\ F_n(0)=0$\\ \\ for all non-negative integers $n$. \\ \\ Prove that we cannot choose $f$...

Re: HSC 2013 4U Marathon An infinitesimally small billiard ball is at the edge of a circular table of unit radius and is hit in a direction that makes an acute angle of theta with the radius joining the starting position to the centre of the circle. Find the minimum, maximum, and average...

Re: HSC 2013 4U Marathon $Let $f$ be a continuous function from the interval $[0,1]$ to itself. Prove that there is some $\alpha\in[0,1]$ with $f(\alpha)=\alpha$. \\ \\By way of example, show that the claim in this question is no longer true if we drop the assumption of continuity. $

Yeah this Socratic style of teaching is effective and can lead to real understanding rather than superficial mimicry of a teachers calculations. Unfortunately I think the time constraints in a teaching year handcuff you somewhat in how much you can employ this.

A proof is just a formal sequence of manipulations of strings of symbols by some predetermined rules to obtain various logical expressions. The strings we are allowed to start with are our axioms (written in a formal language, see http://en.wikipedia.org/wiki/Formal_system). Who decides which...

Re: HSC 2013 4U Marathon Think about which cos^2(theta) you are pairing up with sin^2(90). You are essentially just double-counting something.

Re: HSC 2013 3U Marathon Thread Yeah, you can use floor functions to find an expression for the DEFINITE integral between 0 and a for an arbitrary a. Let this expression be F(a), extend it to the whole real line by asserting that it must be odd, and add an arbitrary constant. This will be a...