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Anyone up for some online play of ssb64 (via the project64k emulator on your pc) or ssbm (via dolphin)? Ideally, you should have some kind of usb controller, but some people get by with keyboards.

Re: HSC 2014 4U Marathon - Advanced Level Differentiability doesn't imply continuous differentiability (which is why I brought up the point). (Consider f(x)=(x^2)sin(1/x) at 0 as a counterexample). So something is going wrong in your proof of this first assertion. (For starters, I don't...

Re: HSC 2014 4U Marathon - Advanced Level I don't really buy this solution... Is the first sentence saying that f' must attain a maximum or minimum on the interval [a,b]? Why is this true if we don't know whether or not f' is continuous? The work that follows also seems to depend on signs a...

Let me start out by saying I don't have the philosophical wherewithal to properly debate you on god's existence. (For the record, my position is agnostic atheism.) I do notice though that your posts here claim to establish the existence of a creator. Out of interest, do these (and other)...

Because you are not starting with 100 and units aren't specified in the first question. The first question is just asking the proportion...which is (0.93)^15. The idea is exactly the same though, of multiplying by a fixed factor for each unit of time.

For the same reason as in the previous question, you are multiplying by a factor of 1-2/7 = 5/7 each year, so the answer is: 100\cdot(5/7)^{10} \textrm{ m}. Chuck it into a calculator to get an answer however accurate you like.

You should try this yourself and post your attempt up, it is exactly the same question with different numbers.

One approach is to write the expression as a polynomial q(t) and check by substitution that: q(0)=0 q'(0)=0. This implies that 0 is a double root and hence t^2 divides the original expression. Alternatively, you can directly calculate (using binomial expansion) that the two lowest order terms...

Why did you think that? I haven't really done that much financial maths but this stuff is pretty easy. I love mathematics to do with games, whether it is probability, random walks or game theory.

Haha yep, the martingale is a classic example of the fallacies some gamblers believe.

A surprising number of people I have met seem to believe in the existence of profitable "betting systems" for casino games like Roulette. Casinos are very happy about this misconception. Here is a thread for high school students to practice their combinatorics skills by suggesting and/or...

There is a little more to it. 1. When you talk about a function, you must also specify a domain X and a co-domain Y (we write f:X->Y. this means that we can apply f to all elements x of the set X and each one gives us an element f(x) of Y). So the function f(x)=x^2 defined on the positive reals...

Not much if the 6 scalars are still just some particular constants. Eg this equation is trivially true with all constants 0, no matter what the u_j's are.

Huh? Can you please elaborate here? Are you changing the question or your answer?

Yeah so the answer is just no then. A really silly/trivial counterexample is as follows: The standard basis (e_1,e_2,e_3) of R^3 is linearly independent, and 1e_1+0e_2+0e_3 can be written as 1e_1+0e_1+0e_1. (But e_1,e_1,e_1 is obviously not linearly dependent.)

What are a,b,c,x,y,z? just some fixed constants? If this is the case the statement certainly isn't true. Or are you saying something more like "If every linear combination of the v_i's can be written as a linear combination of the u_i's, and the v_i's are linearly independent then so are the...

Re: HSC 2014 4U Marathon - Advanced Level Yep, this is pretty much correct. The only thing you have to be wary of is a potential division by zero when dividing by sum of the first k w's. But this is not a big deal. The article I mentioned earlier is attached anyway. one error correction...

Re: HSC 2014 4U Marathon - Advanced Level Induction is enough Sy, I posted a proof of this in the jensen's article I wrote a little while ago. Will post the proof again here when I get home...it is quite short. Sent from my GT-I9000 using Tapatalk 2

Re: HSC 2014 4U Marathon - Advanced Level Assuming a,b,c are positive, then b^2(a^2+c^2), just by expanding and comparing terms.

Fucking around in Paradox games, so good. Not really spending much time on games atm in general though.