Yeah that's the next problem in my book heh. What I'm seeing is this: I find the total number of possible permutations with the multinomial coefficient, then subtract the multinomial coefficient with one less game played (with n-1 instead of n), and continue the process until I reach (n-1)/2...
So you're saying I should take the possible number of ways the 5 games could be played, which is 10 ways, and subtract the number of games where they win before all 5 games are played?
Hmm any pointers besides that? The only things I can think of are permutations and combinations. If they don't always play 5 games though, how can I use these methods here?
Homework Statement
Suppose two teams are playing a set of 5 matches until one team wins three games (or best of five).
Considering the possible orderings for the winning team, in how many ways could this series end?
Homework Equations
The Attempt at a Solution
So I think I have...
So if I choose \epsilon = \frac{L-1}{2}, I want to find an x that will give me \left|f(x)-L\right|=\left|1+\frac{1}{x}-L\right|=\epsilon=\frac{L-1}{2}.
This is kind of where I'm stuck. I'm not sure what the best way to manipulate the absolute value sign. I know I can do it with either the...
Homework Statement
Show that if L \neq 1 , the statement \lim \limits_{x \to \infty} (1+\frac{1}{x}) = L is false.
Homework Equations
The Definition of a Limit
The Attempt at a Solution
So I've been trying to prove this by negating the logical statement of the definition of a...
The whole point of the row reduction is to find which columns are pivot columns. Once you identify those, you have to go back to the original matrix for the actual vectors that will form the basis. The row reduction will tell you which column, but the actual matrix tells you the vector...
So if you want to find the column space, you have to find the column vectors. To do this, you need to identify which columns are pivot columns by row reducing your matrix B. once this is done, the column space will simply be the span of these vectors. you can check the linear independence of...
it seems that your original guess at the particular solution is a bit lacking. your choice for y(t) is missing something... can you guess what it is missing?
looks good to me. Although if I were to give advice, I would say don't try to memorize those kinds of formulas. Instead, try to remember a method for setting these types of problems up. Usually this involves some form of considering a small "slice" of water of width \Delta x and finding the...
For the second one, try integration by parts. Not sure myself if it will work, but by looking at it I see two functions multiplied together. Anything like that you should think substitution or interation by parts.
I think you're missing what the work in this case means. The work is the energy the pump puts into move the water out of the pool, not the energy required to get the water to the pump.
That's right. If the pump sits at the top of the water as it pumps, some water has to go barely any distance, since its already closer to the top of the water as its pumped out. If the pump is at the bottom however, all the water will have to go the whole depth of the pool to get pumped out...