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Re: 2015 permutation X2 marathon What is his chance if he fires at nothing - a deliberate miss?

Re: MX2 2015 Integration Marathon Perhaps he is suggesting a title for your textbook.

Re: 2015 permutation X2 marathon You haven't considered a third option! (And no - it has nothing to do with shooting himself)

This is somewhat ambiguous. Does the monster sense a curved path and run to intercept where this curve meets the shoreline. Or does it only sense the current direction of motion? And do we assume that X times the man's swimming speed is only the maximum speed for the monster, and that it is...

Re: 2015 permutation X2 marathon Arthur, Bernard and Charles fight a three way pistol duel. Arthur hits his target 3 times out of 10, Bernard never misses his target, and Charles hits his target 50% of the time. (All combatants know all of these statistics.) They take turns to fire cyclically...

What are you saying there?

I don't get any of the answers either. \frac{2\pi}n=8 n=\frac{\pi}{4} 1^2=\left(\frac{\pi}{4}\right)^2\left(a^2-5^2\right) \frac{16}{\pi^2}=a^2-25 a^2=\frac{16+25\pi^2}{\pi^2} $Ignoring negative:$ \ddot x_{max}=n^2 a =\frac{\pi^2}{16}\cdot \frac{\sqrt{16+25\pi^2}}{\pi} =3.18...

Re: 2015 permutation X2 marathon Perfect!

Re: 2015 permutation X2 marathon On the right track. But the probability that they meet in round one is actually: \frac{2}{3^{k+1}-1} This mistake simplifies the algebra drastically.

Ummmm ........... no But don't worry - your mark will only go up.

That's somewhat different. At a reasonably high ranking school, roughly the same number of people each year would be expected to get an E4. It would be much easier for someone to give you an estimate if you gave your school and your rank in that exam. (Provided there are a reasonable number...

Re: MX2 2015 Integration Marathon So it's related to an existing question. I couldn't tell.

Re: MX2 2015 Integration Marathon What is the significance of this form?

Re: 2015 permutation X2 marathon I'm afraid the inductive step needs a lot more work than that. There is more than just adding 'another win'. You have to consider the chance of them meeting in the first round, or meeting in subsequent rounds. We are considering the probability two teams meet -...

Nice one ... but there's a limit to how much of that I can take.

Are you asking for all parts of the questions? Because parts (a) and (b) of the first two questions are pretty self-explanatory. Just do what they ask.

$Use the formulae:$ $Period $=\frac{2\pi}{n} v^2=n^2\left(a^2-x^2\right) \ddot x=-n^2 x $Along with the fact that the maximumum acceleration occurs at $x=\pm a.

Re: 2015 permutation X2 marathon $A game of 'Speed Blue Ball' is played between three teams, with only one winner. $A knockout tournament is played between $3^n$ teams, in a balanced draw of $n$ rounds. $Assume all teams are equally likely to win a match against all opponents$ $Prove...

Re: 2015 permutation X2 marathon At Wimbledon, 128 players compete in a knockout tournament. In this imaginary Wimbledon, the players are seeded 1 to 128, but the seeds are not used to determine the draw - the draw is done randomly. Assume that every game is won by the higher seed. (a)...

wouldn't HAVE