Recent content by Joffan

No... you calculated the specific ##a##, now put that back into ##F=ma## along with the second block's mass Unfortunately the confusion between the abstract "F" and the specific "F" in this problem is perhaps making understanding a little harder than it should be.

What force is necessary to produce your calculated acceleration in the second block?

Back to my 2 questions... 1. The total number of functions in F is relatively simple: what is that number? Obviously you could assign ##m## possible values for ##f(1)##, then ##m-1## possible values for ##f(2)##, etc., to count all functions 2. What functions does the condition "##f(i)<f(j)##...

You need to find out for what values of ##n## the expression ##\frac {n^2+12n-43} {n+6} ## is an integer. It's not an arithmetic progression. Try defining ##m=n+6## and then express ##n^2+12n-43## in terms of ##m##.

No, those are simpler questions: the first about the whole of F, not the restricted set your question asks for, and the second about the nature of the excluded functions in your question. But they can lead to answering the original question.Incidentally... No.

You can also think of this as doing division in an unknown number base (in which case it will help to able to use negative digits within the place notation). 1, 2 r 4 _______________ 1, 1 ) 1, 3, 6 1, 1...

Two more questions: - How many functions are there in F altogether? - What kind of functions fail to satisfy the given property?

Note for Q2 that 0C = 0

You can use a positive exponent with (1/2) as your base or you can use a negative exponent with 2 as the base. And p0 should be in there somewhere.

Maybe you could use Ceva's theorem - it seems a little overpowered. I would proceed by marking X as the intersection of the new line from A with CM and Y as the intersection of the new line from B with CM. Then show that |MX| = |MY| and thus that X == Y

Interesting approach... it feels like you are using more advanced results to try to prove a simpler result, though - and that simpler result was perhaps used to prove the more complex results. "A complete graph is a simple undirected graph in which every pair of distinct vertices is connected...

Oops... think about RUber's question first :-)

Hi Mark, this is the construction as I understand it:

You've generated some similar triangles there which should help, if you work out the scaling. Note that |AM| = |BM|

Haha, I misread the challenge as asking for 3 non-Abelian groups, so - also using searching skills - I came to a different answer.