Could anyone tell which statement is correct : 1. India is playing 2. India are playing
I'd say Microsoft have a way of bending the rules and I know that McLaren have won the championship. While this sounds strange, I believe it is correct English (sorry, I'm not native).   But when it's a small company, would you still use it this way? Is a company always plural, or are small companies singular? I.e., would you say Bakery Johnson makes fine bread or Bakery Johnson make fine bread? Is it My book seller, Woody's, have moved or is it has moved?
The following problem was on a math competition that I participated in at my school about a month ago:      Prove that the equation $\cos(\sin x)=\sin(\cos x)$ has no real solutions.   I will outline my proof below.  I think it has some holes.  My approach to the problem was to say that the following equations must have real solution(s) if the above equation has solution(s):  $$ \cos^2(\sin x)=\sin^2(\cos x)\\ 1-\cos^2(\sin x)=1-\sin^2(\cos x)\\ \sin^2(\sin x)=\cos^2(\cos x)\\ \sin(\sin x)=\pm\cos(\cos x)\\ $$  I then proceeded to split into cases and use the identity $\cos t = \sin(\frac{\pi}{2} \pm t\pm y2\pi)$ to get   $$ \sin x=\frac{\pi}{2} \pm \cos x\pm y2\pi\\ $$  and the identity $-\cos t = \sin(-\frac{\pi}{2}\pm t\pm y2\pi) $ to get   $$ \sin x=- \frac{\pi}{2}\pm \cos x \pm y2\pi.\\ $$  where $y$ is any integer.  I argued that $y=0$ was the only value of $y$ that made any sense (since the values of sine and cosine remain between $-1$ and $1$).  Therefore, the above equations become   $$ \sin x=\frac{\pi}{2} \pm \cos x\implies \sin x \pm \cos x=\frac{\pi}{2}\\ $$  and   $$ \sin x=- \frac{\pi}{2}\pm \cos x\implies \cos x\pm\sin x= \frac{\pi}{2}.\\ $$  Then, by a short optimization argument, I showed that these last two equations have no real solutions.  First, does this proof make sense?  Second, if my proof makes sense, then I feel that it was not very elegant nor simple.  Is my approach the best, or is there a better (i.e., more elegant, shorter, simpler) proof? How many ways can $r$ nonconsecutive integers be chosen from the first $n$ integers? Is it: My apples and orange are/is wrong? Simple question:     My apples and orange are wrong   or     My apples and orange is wrong   I am not a native English speaker, and I am having some trouble choosing between plural are or singular is for that kind of example. Why doesn't Spotlight show invisible files that I know exist? I am running Mac OS X 10.8 (Mountain Lion) and had to edit an invisible file as part of an Android project. While I eventually found it, Spotlight was of no help, since it could not find an invisible file when searching for the exact name (.classpath) and with the 'File Visibility' option set to 'Visible or Invisible'.  Why didn't Spotlight work in this instance? How can I determine that I am looking at the block I need? I want to execute a command if I am looking at a specific block. A command should only be executed if it is targeted. I would like to declare functions in tikz for multiple uses of the same function within the code.  Sadly, it seems that the tikz "declare function" is not compatible with the french option in babel. Indeed, the following code (that I simplifed on purpose) runs fine :  \documentclass[english]{article} \usepackage{babel}                       \usepackage{tikz}  \begin{document} \begin{tikzpicture}     \tikzset{declare function={Carre(\t)=\t*\t;}}     \draw plot [domain=-1:1] (\x,{Carre(\x)}); \end{tikzpicture} \end{document}   But when I replace   \documentclass[english]{article}   with   \documentclass[english,french]{article}   compilation generates an error. This is what the log file says :     Missing character: There is no = in font nullfont!   Missing character: There is no @ in font nullfont!   Missing character: There is no @ in font nullfont!      Runaway argument?   -1:1] (\x ,{Carre(\x )}); \end {tikzpicture} \end {document}    ! Paragraph ended before \pgfmath@local@@functions was complete.                          \par    l.18       I suspect you've forgotten a `}', causing me to apply this   control sequence to too much text. How can we recover?   My plan is to forget the whole thing and hope for the best.   Before posting this, I updated all packages without success.  Any help welcome! Indian Trains Wait List - will I get a seat? After the  of registering an account to book train tickets online using my British VISA card, I finally got into a position of being able to book a ticket, but what it appears to be telling me is that I'm only being added to a wait list, which I assume means my tickets aren't confirmed.  Can someone explain how the wait list works, and what my chances are of getting on the train successfully?    It currently says the wait list is 7 The train is the Mandor Express, from Delhi to Jodhpur on the 18th of Nov   Update: So I got the train! Although it didn't get confirmed until a few hours before it was due to leave. Sorting seach results in Android app The issue is how can user sort questions for a particular search query?   For example, I would want to search questions for  and want to see newest questions first.  Right now If we write any query in Search Questions... input box then users are not able to select sorting options as search questions input box takes whole width of the screen and sorting options box gets hidden.  I have also tried to select sorting options first and then search for  but still its showing questions without considering sorting option I have selected. Are all multiplicative functions additive? Suppose $cf(x)=f(cx)$ and $f:\mathbb{R}\to\mathbb{R}$. I believe it follows that $f(x+y)=f(x)+f(y)$.   Proof: There is some $c$ such that $y=cx$. Then  $$f(x+y)=f\left((1+c)x\right)=(1+c)f(x)=f(x)+cf(x)=f(x)+f(cx)=f(x)+f(y)$$  QED.  I wonder if the same thing holds for when $f:\mathbb{R}^n\to\mathbb{R}^n$? I can't use the same trick, because all vectors are not scalar multiples.  I tried thinking of it in terms of basis units, but didn't get anywhere. Server 2012 Core (no GUI): Remote Server manager not working I am trying cmd --> MMC --> Server Manager and then connecting to my Server 2012 no GUI  but i keep getting the following error The WinRM client cannot process the request  I am unable to upload images right now  This is not related to other post "How to Remote Manage Windows Server 2012 in Server Manager?" because title and description of that post is quite different from what i am asking What is currently the best way to get a favicon to display in all browsers that currently support it?  Please include:   Which image formats are supported by which browsers. Which lines are needed in what places for the various browsers. C# Structs: Unassigned local variable? Peppers evolved chemicals like capsaicin to discourage animals from eating them, and that chemical itself can cause internal damage if consumed in large quantities, though this is usually only a concern for the hottest of peppers (which people do eat).   Still, why is it that humans seem to be the only animal that often "like" spicy food? I have had the last Ubuntu distro (10.something) installed for a year and love it.  But I have run in to an issue when I tried to upgrade it to the latest one it did not work and there has come some serious issues now with almost everything and I want to remove Ubuntu completely and install the new one.  How can I remove the operating system (I don’t mind formatting the whole thing if that’s what’s needed). I am quite new to Javascript. I have made a html script that includes services I published to ArcGIS for server. It all does exactly what I want and I made it by copying working scripts together and getting help from more experienced scripters. I want to finetune my service by adding a legend. Unfortunately I am not able to create a working script. I have added the parts of my script I assume that are necessary to create my legend. Does anybody see what I am doing wrong?        &lt;script&gt;         var map;         var wmsLayer;         var URL;         var legend;         require(["dojo/query", "esri/map", "esri/layers/WMSLayer", "esri/dijit/Legend", "esri/config", "dojo/domReady!"],         function (query, Map, WMSLayer, Legend, esriConfig) {          esriConfig.defaults.io.proxyUrl = "/proxy/proxy_gcx.php";            map = new Map("map", {               basemap: "topo",               center: [5.5, 52.485],               minZoom: 8,               maxZoom: 13,               zoom: 8,               slider: true           });            wmsLayer = new WMSLayer("URL", {               format: "png",               visibleLayers: ["31", "30", "29", "28"]           });            map.on("layer-add", function (results) {               //add the legend               legend = new Legend({                   map: map,                   layerInfos: [{                       layer: results,                       title: "test"                   }]               }, "legendDiv");               legend.startup();           });             map.addLayer(wmsLayer);       });     &lt;/script&gt; &lt;/head&gt;  &lt;body&gt;     &lt;div id="map"&gt;     &lt;/div&gt;     &lt;div id="legendDiv"&gt;     &lt;/div&gt; &lt;/body&gt;   EDIT: I have edited the code. I am still not done. It does give me a legend on my browser but it says there is no content in there. On my arcgis server manager there is a legend. Let us go   is a correct construction in the English language and definitely not:     Let we go   However, the question is: since us is an object-case pronoun, what is the subject of this sentence? How to insert page number in Beamer navigation symbols? How can I remove whitespace when declaring an XSL variable? Group of positive rationals under multiplication not isomorphic to group of rationals Prove $3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$ if $x,y,z$ are positive real numbers,Prove:$$3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$$ Additional info:$\sum_{cyc}$ denotes sums over cyclic permutations of the symbols $x,y,z$. I'm looking for solutions and hint that using Cauchy-Schwarz and AM-GM because I have background in them.  Things I have done: Writing Left hand side in expanded form:$$LHS=3(\sum_{cyc}x^3y^3+\sum_{cyc}xy^4z+3x^2y^2z^2)$$ Right now I don't have good idea were to start(Is expanding and looking for AM-GM is good?).So any hint is appreciated. Source : This inequality can be found as Problem 42, page 13, in the book &quot;Old and New inequalities&quot; by Titu Andreescu, where it is attributed to Manlio Marangelli.