Quark's bar takes payment in Latinum; and perhaps, as discussed in  - in Federation "credits" (backed by something - not clear what). Now, in another discussion e.g. in , the mechanism of distributing Latinum or credit is supposedly not interesting.  Except - it's very interesting. Let's By what mechanism does a Federation subject, or military personnel ("Starfleet"), get either credits or Latinum? Is there a wage? An allowance? Savings?  Or - maybe they don't get them at all? i.e. maybe Quark logs orders then bills the Starfleet directly? I don't remember DS9 scenes with Starfleet personnel paying or settling their tab.
In the begining of "" episode (Star Trek Next Generation 6x16) an Yridian tells Worf, that he has a certain information,      that Worf's father is still alive (apparently not killed in ) and is held in a prison camp on Carraya IV.   Yridian is an information broker and agrees to reveal details (i.e. location) only for a price.      Worf agrees.   How or with what Worf would pay for this? There is no economic factor inside the Federation (no money is being used) and I don't recall anything, Worf would have on board Enterprise, that would have enough value for an information this kind.
Prove that $\lim_{N\rightarrow\infty}(1/N)\sum_{n=1}^N f(nx)=\int_{0}^1f(t)dt$ Suppose $f$ is continuous and periodic on the reals with period 1. Prove that if $x\in[0,1]$ is an irrational number, then  $$\lim_{N\rightarrow\infty}\frac{1}{N}\sum_{n=1}^N f(nx)=\int_{0}^1f(t)dt$$   Suggestion: First consider $f(t) = e^{2\pi(ikt)}$ where k is an integer.   I can see that this is a limit of a weighted average, but the suggestion throws me off. I've seen the suggestion in fourier transforms but it's not clicking at the moment. Any help would be welcome. Put a where clause around a stored procedure I cannot edit Prove that the expression cannot be a power of 2 How do I set a user environment variable? (permanently, not session) I'm trying to wrap my head around this very Hello World-y problem in game development. I've created a TicTacToe game in XNA so I guess the next step would be a  clone.  Keep in mind that I have no knowledge on game programming or even what maths I should apply to where. That's why I'm asking this question.    To the question: How can I determine where the ball should bounce when it hits the paddle at the bottom of the screen?  I'd imagine it would be something like:   Capture speed and angle from incoming ball. Detect where it touched the bar (far left, far right, center) and according to that give it a higher speed if it touched the outer areas. This is where I'm stuck. Hehe.   Any insights? I realize this is not a straightforward answer type question, but I'm sure it's one everyone faces at some point.  I'm reading the book Linear Algebra that was recommended on this website, but I still have no idea if I should apply it here. Display the full URL of the home page? Is it possible to display the full, absolute URL of the home page in Drupal 7, like  www.example.com/The-best-example-possible ?  I'd like to display the full URL of the home page, not just the hostname. My (very simple) question to a friend was how do I prove the following using basic trig principles:  $\tan75^\circ = 2 + \sqrt{3}$  He gave this proof (via a text message!)  $1. \tan75^\circ$   $2. = \tan(60^\circ + (30/2)^\circ)$  $3. = (\tan60^\circ + \tan(30/2)^\circ) / (1 - \tan60^\circ \tan(30/2)^\circ) $  $4. \tan (30/2)^\circ = \dfrac{(1 - \cos30^\circ)}{ \sin30^\circ}$    Can this be explained more succinctly as I'm new to trigonometry and a little lost after (2.) ?    EDIT  Using the answers given I'm almost there:   $\tan75^\circ$    $\tan(45^\circ + 30^\circ)$   $\sin(45^\circ + 30^\circ) / \cos(45^\circ + 30^\circ)$   $(\sin30^\circ.\cos45^\circ + \sin45^\circ.\cos30^\circ) / (\cos30^\circ.\cos45^\circ - \sin45^\circ.\sin30^\circ)$    $\dfrac{(1/2\sqrt{2}) + (3/2\sqrt{2})}{(3/2\sqrt{2}) - (1/2\sqrt{2})}$   $\dfrac{(1 + \sqrt{3})}{(\sqrt{3}) - 1}$   multiply throughout by $(\sqrt{3}) + 1)$   Another alternative approach:   $\tan75^\circ$    $\tan(45^\circ + 30^\circ)$   $\dfrac{\tan45^\circ + \tan30^\circ}{1-\tan45^\circ.\tan30^\circ}$   $\dfrac{1 + 1/\sqrt{3}}{1-1/\sqrt{3}}$   at point 6 in above alternative It is possible to make ls -l output the size field with digits grouped by thousands? If so, how?  For instance:  $ ls -l -rw-rw---- 1 dahl dahl 43,210,052 2012-01-01 21:52 test.py   (Note the commas in the size).  Maybe by modifying the LC_NUMERIC setting inside the locale I'm using (en_US.utf8)?  I'm on Kubuntu 12.04 LTS. (This is not homework; a friend shared with me this puzzler and neither of us can figure it out.) Suppose you are in a plane traveling at velocity $v_1$ relative to the ground. The flight attendent pushes a cart of mass, say, $m$, accelerating it from rest to $v_2$, relative to the plane (so relative to the ground, its velocity goes from $v_1$ to $v_1+v_2$). From your perspective, the work done is then $$W = \Delta E = \dfrac{1}{2}mv_2^2$$ but from the perspective of the ground, the work done is $$W = \Delta E = \dfrac{1}{2}m(v_1+v_2)^2 - \dfrac{1}{2}mv_1^2 = \dfrac{1}{2}mv_2^2 + mv_1v_2.$$ Why are these quantities unequal?  I've seen some similar problems, like a body colliding with a wall in different reference frames, but I don't have the physics experience to tell if that question is analogous to this one. So, my apologies if this is a duplicate. :) How to show the inequality for $\int_{0}^{\pi/4}\tan^n(x) dx$ I can't seem to figure out the inequality option, I substituted n=2 for the answer bit is there any elegant way of getting it? Why do a lot of questions from around 2008 seem to have really high upvotes? One of my friends argues that princessship is the only word which has 3 identical letter comes together (s) ,but I think there is no word such as princessship.  Can anyone tell me whether this is a real word, and if there are any more English words which have 3 letters consecutively? Normalizing the final weights vector in the upper bound on the Perceptron's convergence The convergence of the "simple"  says that:  $$k\leqslant \left ( \frac{R\left \| \bar{\theta} \right \|}{\gamma } \right )^{2}$$  where $k$ is the number of iterations (in which the weights are updated), $R$ is the maximum distance of a sample from the origin, $\bar{\theta}$ is the final weights vector, and  $\gamma$ is the smallest distance from $\bar{\theta}$ to a sample (= the margin of hyperplane).  Many books implicitly say that  $\left \| \bar{\theta} \right \|$ is equal to 1. But why do they normalize it ? I've been writing in English for many years, but there are certain recurring issues that come up in my writing, which I can't seem to resolve permanently. Primarily I have a problem with punctuation. In my native language, commas are very commonly used. One would place a comma to separate any portion of the sentence that serves a specific grammatical role. At least, this is the case according to the rules I was taught in school. I can see when I write in English that there are extraneous commas, but I can't always figure out which ones, and why. When dependent clauses require commas, when do they allow them, and when are they definitely incorrect? What's the difference between Kage Bunshin no Jutsu and Tajuu Kage Bunshin no Jutsu? While the Kage Bunshin no Jutsu seems to be taught, the Tajuu Kage Bunshin no Jutsu is sealed, so nobody can learn the jutsu. Does that mean that there's a difference between these jutsus, aside from the number of Kage Bunshin created?   Or, why was the Tajuu Kage Bunshin no Jutsu sealed away? If there's no other difference, everybody could use this without reading the sealed scroll. A cardinal $\kappa$ such that $2^{\lambda}<\kappa$ for all $\lambda<\kappa$ is regular? A cardinal $\kappa$ such that $2^{\lambda}&lt;\kappa$ for all $\lambda&lt;\kappa$ is regular?  I would appreciate very much an answer MySQL Replication : 1 Slave / Multiple Masters For a distribution function $F(x)$ and constant $a$, integral of $F(x + a) - F(x)$ is $a$. For any distribution function and any $a \geq 0$, $\int_{-\infty}^{\infty} (F(x+a)-F(x))dx = a$.   In this case, "distribution function" means a right continuous function F with $F(-\infty) = 0$, $F(\infty)= 1$.   This problem comes after a section in the book on mathematical expectation, so I suspect I should use some property of expectation to prove it. Expectation appears to be something that applies to random variables, so I think I should be somehow transforming the problem into something in terms of expectations of random variables, but I'm not sure how. I know that given a distribution function, I can get a probability measure, but I'm not sure how to go from there to a random variable and actually get a relation between the expectation of the random variable and this integral. I'm sure whether this is the right way to go about this problem, but if it is, I'm missing a connection somewhere. I get weird > symbols in my output — what does it mean? I have a manuscript that is under review in a major journal which is a main result out of a few recent years of my research. When applying for faculty positions, I would like to send the draft as a part of my writing sample. But since the material is not yet published, I am not sure if it is a good idea.  What are the foreseeable disadvantages of sending an article in review to the faculty search committee?  My area is neuroscience / biomedical engineering.  Update: The paper got into a high-profile journal, and I got a job at a different place which did not require a writing sample.