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Number of possible combinations of x numbers that sum to y I want to find out the number of possible combinations of $x$ numbers that sum to $y$. For example, I want to calculate all combination of 5 numbers, which their sum equals to 10.  An asymptotic approixmation is also useful. This question seems to be very close to number partitioning, with the difference that a number can be 0. See:    All possible partitions for sum 10 and 3 positions that can be zero, are 63 possiblities: (numbers shown as 3 digits)  019 028 037 046 055 064 073 082 091 109 118 127 136 145 154 163 172 181 190 208 217 226 235 244 253 262 271 280 307 316 325 334 343 352 361 370 406 415 424 433 442 451 460 505 514 523 532 541 550 604 613 622 631 640 703 712 721 730 802 811 820 901 910 Installing two glibc alongside in debian/ubuntu Is it possible to install and use two different glibc versions on the same machine. Where one version is only used to run legacy software, which relies on old glibc binaries?  Is it possible to do that with the aid of the package manager (something like "install this package, and its dependencies, to /opt/old-glibc), instead of managing it dire is the group of rational numbers the fundamental group of some space? It would be similar to trying to be extremely careful or precise.   In French it would be "application", For example: "Qui est fait avec application".   Example usage:      John worked with ________. or ...it was done with _______. Reducing voltage with resistors I have been looking around for an easy way to convert 12V to 5V. I have seen some people saying that a simple resistor is all that is needed.  $$ Volts = Ohms \cdot Amps $$ $$ Amps  = \frac{Volts}{Ohms} $$ $$Ohms  = \frac{Volts}{Amps}$$  So applying a resistor will diminish the voltage of the circuit. That should mean that an appropriately sized resistor could simply be placed in the path of a 12V circuit, converting it to 5v.   If this is the case how would one reduce amps? Would series vs parallel make a difference in this area?   I have seen designs that include a regulator IC and some capacitors, but if a simple resistor/fuse/diode setup will do the trick, I would really prefer that. I'm very new to GIS concepts. Is there a way or procedure of finding out whether the co-ordinate system is in UTM, latitude/longitude or in stateplane using .prj file?   My .prj file contains the following text:      GEOGCS["WGS 84",DATUM["WGS_1984",SPHEROID["WGS   84",6378137,298.257223563,AUTHORITY["EPSG","7030"]],AUTHORITY["EPSG","6326"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.01745329251994328,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4326"]] Double integral of an function odd with respect to $y$ over a domain symmetric with respect to $x$ axis Let $D$ be a region given as the set of $(x, y)$ with $$a \leq x \leq b\quad\text{and}\quad-\Phi(x) \leq y \leq \Phi(x)$$ where $Φ$ is a nonnegative continuous function on the interval $[a, b]$.  Let $f(x, y)$ be a function on $D$ such that $$f(x, y) = - f(x, - y)$$ for all $(x , y) \in D$.  Argue that $$\displaystyle \iint_D f(x, y) dA = 0.$$ Assume that the matrices $A,\: B\in \mathbb{R}^{n\times n}$ satisfy  $$ A^k=0,\,\, \text{for some $\,k\in \mathbb{Z^+}$}\quad\text{and}\quad AB=BA. $$  Prove that $$\det(A+B)=\det B.$$ Does one work in or on an aeroplane? How to self study Linear Algebra I have no idea if this question is appropriate for this forum, but I hope you guys can overlook the fact that I asked it on a wrong forum (if I did) and still help me answer it (of course, if this is indeed the wrong forum for the type of question I'm about to ask, do please say so).  I am a 16 year old guy who is passionate about physics and as a result wants to increase his knowledge in mathematics, the language of physics. I've read and heard a lot about Linear Algebra and how crucial it is to physics and I am deeply motivated to self study this intriguing part of mathematics. However, I have limited knowledge of maths. I (for example) know basic algebra, trig, diff/int calc and some analytical geometry, but I wouldn't say I master these subjects past the high school curriculum. Now my question is: Would you kind people say I am able to self study Linear algebra or is it too tough and/or does it require too much of a math background? And are there any good books out there for BEGINNERS in LA? I found this (free) e-book called: Elementary Linear Algebra by Kenneth Kuttler and another one called 'Linear Algebra: Theory and its applications' also by Kuttler? Are these any good? Or would you recommend other books? If you guys have any tips regarding books for LA but also tips in general, please, I'd appreciate them! Allow all reviewers to see deleted posts they reviewed So moderators just got . Often, these bans are due to specific very bad reviews, like approving spam or non-answers. It will be common for us to give links to these bad reviews in the ban message that the reviewers will be presented with.  However, many of these reviewers lack the necessary reputation to see deleted posts. If we're banning someone from review for approving spam or non-answers, almost all of the time those posts will be deleted. If we give them links to the reviews they performed, they won't see the now-deleted posts that they approved, and won't have a chance to learn what they did wrong.  As examples of this, I had to actually take a screenshot to show the reviewers  and  the posts that triggered their ban, because they could no longer see them.  I propose that reviewers of any reputation level be able to see posts that they reviewed, even ones that were later deleted, if they are presented with a link to their review. They already saw the post once, so there's no harm in showing it to them again, and reviewers are going to need to see why they made a bad call on a particular review. Should 'Hi', 'thanks', taglines, and salutations be removed from posts? I edit a lot of posts every day. I often run across posts with 'Hi' and 'Thanks' on the top and the bottom of the post respectively. I also run across things like:     --User   Should these items be removed during the editing of the post by an editor? How to set a default query timeout with JPA and Hibernate? I am currently using Ubuntu 12.04 because the latest upgrade 14.04 is not working in my system. I need to install the latest Adobe Flash Player 17 plugin, but it only allows me to install up to version 11.02, so media files cannot be opened. It says that Adobe Flash Player 17 is not compatible with my system. Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $ Evaluate $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)}$.   $\bf{My\; Try::}$ Although we can solve it by converting into definite Integration.  But I want to solve it without Using Integration.  So $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} = \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{(n-1)(n-2).......(n-k+1)}{k!\cdot n^{k}\cdot (k+3)}$  Now How can i solve after that, Help required, Thanks How do I permanently allow a website to access my location? In iOS, I only need to be asked once whether I want to allow a website to share my location data. Is it possible to permanently do this in OS X version of Safari as well? Is there a way to force a C# class to implement certain static functions? Comparing $\pi^e$ and $e^\pi$ without calculating them I've just returned from several unusual countries in Asia, and annoyingly despite being told I'd have no problem, I'm unable to find anyone in London to change back to pounds.  I've tried Travelex in Heathrow, a currency exchange place, and the post office.  The currencies include cash from: Mongolia, Kyrgyzstan, Kazakhstan and Uzbekistan.  Most of the responses when shown the money is to the tone of "What the hell currency is this?" which doesn't fill me with confidence.  Any suggestions welcomed for places that may change this. Otherwise I may need to go back next year ;) How do you pull first 100 characters of a string in PHP