Maximize the volume given triangle's perimeter
maximize volume of triangle in given perimeter
What is an idiom/slang for "someone who pretends to be good when they're not"? This is not from real life, but from a movie on my local TV. A character in the movie is really bad, but when she talks with others, she pretends to be an innocent/ good woman. I want to know how to describe this kind of person. How to prove that eigenvectors from different eigenvalues are linearly independent How can I prove that if I have $n$ eigenvectors from different eigenvalues, they are all linearly independent? Evaluate the following limit of finite sum Evaluate the limit $$\lim_{n\to \infty}\frac{1}{n}\sum_{k=0}^{[n/2]}\cos \left(\frac{k\pi}{n}\right)$$  I tried through considering two cases : (i) When $n$ is even (ii) when $n$ is odd.  When $n$ is even then the limiting value is $\frac{1}{\pi}$. But when $n$ is odd then ??  Case 1 : $n$ is even..  Then , take $n=2p$ where $p$ is positive integer. Then $$\lim_{n\to \infty}\frac{1}{n}\sum_{k=0}^{[n/2]}\cos \left(\frac{k\pi}{n}\right)$$  $$=\lim_{p\to \infty}\frac{1}{2p}\sum_{k=0}^{p}\cos\left(\frac{k\pi}{2p}\right)$$  $$=\frac{1}{2}\int_0^1\cos(\pi x/2)\,dx$$  $$=\frac{1}{\pi}.$$  Case 2 : When $n$ is odd.  Take, $n=2p+1$ , where $p$ is a positive integer. Then ,   $$\lim_{n\to \infty}\frac{1}{n}\sum_{k=0}^{[n/2]}\cos \left(\frac{k\pi}{n}\right)$$  $$=\lim_{p\to \infty}\frac{1}{2p+1}\sum_{k=0}^p\cos\left(\frac{k\pi}{2p+1}\right)$$  From here how I proceed ? I have an org with hundreds of apex classes, all of which have api versions ranging between 30-37. Is there an easy way to bring them all to the latest api version at once without resorting to manual updates? Eclipse is giving me a warning of the following form:     Type safety: Unchecked cast from Object to HashMap   This is from a call to an API that I have no control over which returns Object:  HashMap&lt;String, String&gt; getItems(javax.servlet.http.HttpSession session) {   HashMap&lt;String, String&gt; theHash = (HashMap&lt;String, String&gt;)session.getAttribute("attributeKey");   return theHash; }   I'd like to avoid Eclipse warnings, if possible, since theoretically they indicate at least a potential code problem.  I haven't found a good way to eliminate this one yet, though.  I can extract the single line involved out to a method by itself and add @SuppressWarnings("unchecked") to that method, thus limiting the impact of having a block of code where I ignore warnings.  Any better options?  I don't want to turn these warnings off in Eclipse.  Before I came to the code, it was simpler, but still provoked warnings:  HashMap getItems(javax.servlet.http.HttpSession session) {   HashMap theHash = (HashMap)session.getAttribute("attributeKey");   return theHash; }   Problem was elsewhere when you tried to use the hash you'd get warnings:  HashMap items = getItems(session); items.put("this", "that");  Type safety: The method put(Object, Object) belongs to the raw type HashMap.  References to generic type HashMap&lt;K,V&gt; should be parameterized. Flying EU to UK to EU. Can I get duty free alcohol? On the 20 of March this year I will be flying from Ireland to the UK and then on the another EU country.  Can I buy duty free alcohol (as in alcohol with no tax) leaving the UK ? Word/phrase for the activity of hiding mistakes What word/phrase can I use to describe the activity of hiding a stupid mistake/incident, such as quickly cleaning up tea spilled by accident before anyone could notice? How can I install more recent versions of software than what Debian provides? Suppose I want a more recent version of software than is available for my current version of an operating system, what can I do?  Cases to consider:   There are semiofficial/official sources of additional packages available for that version of the OS. E.g. backports.org for Debian or PPAs for Ubuntu. There are no more recent versions of the package available for that version of the OS, but there are more recent versions available for more recent versions of the OS. This is the standard case for backporting. There are no packaged versions of more recent versions of the software available. Options available are to package the more recent version.     Per  this is intended as a place to put canonical answers for the following. Answers should probably be made community wiki. Volume generated by revolving the region in the first quadrant bounded by the parabolas $y^2=x$, $y^2=8x$, $x^2=y$, $x^2=8y$ about the $x$-axis. I came across this question from Schaum's Outlines of Advanced Calculus:     Show that the volume generated by revolving the region in the first quadrant bounded by the parabolas $y^2=x$, $y^2=8x$, $x^2=y$, $x^2=8y$ about the $x$-axis is $\dfrac{279\pi}{2}$.   My solution was to divide the region into three parts:    $$\pi\int_{1}^{2}(x^2)^2 - (\sqrt{x})^2\;dx = 4.7\pi$$  $$\pi\int_{4}^{8}(\sqrt{8x})^2 - (\sqrt{x})^2\;dx = 42\pi$$  $$\pi\int_{2}^{4} (x^2)^2 - \left(\frac{1}{8}x^2 \right)^2\;dx = 44.9\pi.$$  Hence the total volume will be  $$\pi(4.7 + 42 + 44.9) = 91.6\pi$$  which is wrong.  Can someone point out my mistake? Serializing and Deserializing Expression Trees in C# Is there a way to Deserialize Expressions in C#, I would like to store Expressions in a Database and load them at run time. biblatex: Full Citations in Footnotes on Every Page How can I create this sort of bibliography using biblatex, ie, bibliography at the footer of every page? How do I convert between big-endian and little-endian values in C++? For clarity, I have to translate binary data (double-precision floating point values and 32-bit and 64-bit integers) from one CPU architecture to another.  This doesn't involve networking, so ntoh() and similar functions won't work here.  Note: The answer I accepted applies directly to compilers I'm targeting (which is why I chose it).  However, there are other very good, more portable answers here. Easy to bypass "Are You paying Attention" test by viewing question in detail I think many of us already aware, still I wanted to let you know that First Post and Late Answers review posts are generated on specific time interval. When time comes for post generation I follow some tricks   Click and till a Post appears for review Then right-click and select Open in new tab 5-8 time. Then in every page follow the below steps   Open the Question of post appeared in review in New tab If Page/Question not exists then simply downvote since post was deleted because of -ve response. Else if page exists then   Check the review post's Net Reputation If reputation is -ve then simply downvote the post came in review Else one may select No Action needed.    This way if in any case a post comes for "Are you paying attention" can be handled easily.  I think if a post comes in review should not allow to view post. Execute PowerShell Script from C# with Commandline Arguments I need to execute a PowerShell script from within C#. The script needs commandline arguments.  This is what I have done so far:  RunspaceConfiguration runspaceConfiguration = RunspaceConfiguration.Create();  Runspace runspace = RunspaceFactory.CreateRunspace(runspaceConfiguration); runspace.Open();  RunspaceInvoke scriptInvoker = new RunspaceInvoke(runspace);  Pipeline pipeline = runspace.CreatePipeline(); pipeline.Commands.Add(scriptFile);  // Execute PowerShell script results = pipeline.Invoke();   scriptFile contains something like "C:\Program Files\MyProgram\Whatever.ps1".   The script uses a commandline argument such as "-key Value" whereas Value can be something like a path that also might contain spaces.  I don't get this to work. Does anyone know how to pass commandline arguments to a PowerShell script from within C# and make sure that spaces are no problem? Create a floating div on top of divs Best way to put commas into large numbers I've started a new job and it involves looking at a bunch of big numbers. Is there an easy way to add commas to an int or decimal field to make it readable?  For example, SQL Server outputs the column on the left, but for my own sanity, I need it to look like the one on the right:  2036150 -&gt; 2,036,150     ...or would I have to write some heinous   left(right(vandalized_data),6),3) + ',' + right(left(vandalized_data),6),3)   function?  The perfect thing would be commas in the display grid, then plain integers in the output. Better Information On Defense Damage Clash of Clans The way that Clash of Clans chooses to convey information about how much damage defense buildings output is bad. The current method of telling the user that a mortar does X dmg a second is pretty worthless since they fire much slower than once a second.  Where can I find a break down / what is the damage break down for how much damage these buildings do per shot rather than per second?  Sure, information on each level of the buildings would be nice but if that is too much I think simply providing the data for level one of each building would also work. I am trying to do a new environment or command (i tried both) where i can put in the name, description and code of a Method in c++ and it gives me a new section with the MethodName, the code listed and the description below. But i am not able to use the listings environment in a new command or new environment.. Consider my MWE   \documentclass[a4paper,11pt]{article} \usepackage{listings}  \newcommand{\method}[3] { \section{#1}\label{#1} \begin{lstlisting} #2 \end{lstlisting} #3 }   \begin{document}  \method{MethodName}{Method Void MethodName()}{Description of the Method blablabla}  \end{document}   How can I fix this?   I would prefer to do it using a macro since I don't need an ending. Beamer - Color of header foreground with AnnArbor theme I use beamer with the theme AnnArbor and colortheme whale.  I tried to use:  \setbeamercolor{section in head/foot}{fg=white, bg=blue}   or  \setbeamercolor{palette tertiary}{fg=white, bg=blue}   But for an unknown reason, the bg works but not the fg... The sections names stay black in the header.    EDIT : the problem comes from the hyperref package.  This code works well :  \documentclass{beamer} \usetheme{AnnArbor} \usecolortheme{whale} \setbeamercolor{frametitle}{fg=white,bg=blue}  \begin{document}     \section{Test 1}     \subsection{Test 1.1}     \begin{frame}         \frametitle{Test}     \end{frame} \end{document}   Whereas this one doesn't works :  \documentclass{beamer} \usetheme{AnnArbor} \usecolortheme{whale} \setbeamercolor{frametitle}{fg=white,bg=blue} \usepackage{hyperref} \hypersetup{     colorlinks=true,     linkcolor=black,     urlcolor=blue,     citecolor=gray,     frenchlinks=false,     pdfborder={0 0 0} }  \begin{document}     \section{Test 1}     \subsection{Test 1.1}     \begin{frame}         \frametitle{Test}     \end{frame} \end{document}   And that's pretty normal because of this line :  linkcolor=black, ARMA/GARCH estimation in sequence