Why does $a+b+c=3\;$ imply $\;a\sqrt{a+3} + b\sqrt{b+3} + c\sqrt{c+3} \ge 6$ Let $a,b,c$ be positive real numbers such that $a+b+c=3$. Prove that      $$a\sqrt{a+3} + b\sqrt{b+3} + c\sqrt{c+3} \geqslant 6$$
$a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$ $a, b,c $ are positive real numbers such that $a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$  Any ideas ?
Network simplex method, leaving and entering variables One of my coworkers has provided me with a Bash syntax that I am unfamiliar with.  My Google foo has failed me on figuring out what it does and why/when I should use it.    The command that he sent me was of this form:  someVariable=something command   Initially, I thought that this was equivalent to the following:   someVariable=something ; command   Or  someVariable=something  command   But this doesn't appear to the be case.  Examples:   [Jan-03 11:26][~]$ # Look at the environment variable BAZ. It is currently empty [Jan-03 11:26][~]$ echo $BAZ  [Jan-03 11:27][~]$ # Try running a command of the same format     [Jan-03 11:27][~]$ BAZ=jake echo $BAZ  [Jan-03 11:27][~]$     [Jan-03 11:27][~]$ # Now, echo BAZ again. It is still empty:     [Jan-03 11:27][~]$ echo $BAZ  [Jan-03 11:27][~]$     [Jan-03 11:28][~]$     [Jan-03 11:28][~]$ # If we add a semi-colon to the command, we get dramatically different results: [Jan-03 11:28][~]$ BAZ=jake ; echo $BAZ jake [Jan-03 11:28][~]$ [Jan-03 11:28][~]$ # And we can see that the variable is actually set: [Jan-03 11:29][~]$ echo $BAZ jake [Jan-03 11:29][~]$   What does this syntax do?  What happens to the variable that has been set?  Why does this work? Why is FIFA against adding instant replay to the game? Is there any evidence or reason why FIFA is so against adding instant replay to soccer? I find myself seeing many unlucky or just plain wrong decisions made by refs that could be corrected with instant replay. What MySQL query will do a text search and replace in one particular field in a table?  I.e. search for foo and replace with bar so a record with a field with the value hello foo becomes hello bar. Solving SDE: $dX(t) = udt + \sigma X(t)dB(t)$ Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$ Moving status bar in iOS 7 Is PCA still done via the eigendecomposition of the covariance matrix when dimensionality is larger than the number of observations? I have a $20\times100$ matrix $X$, containing my $N=20$ samples in the $D=100$-dimensional space. I now wish to code up my own principal component analysis (PCA) in Matlab. I demean $X$ to $X_0$ first.  I read from someone's code that in such scenarios where we have more dimensions than observations, we no longer eigen-decompose the $X_0$'s covariance matrix. Instead, we eigen-decompose $\frac{1}{N-1}X_0X_0^T$. Why is it correct?  The normal covariance matrix is of size $D\times D$, each element of which tells us the covariance between two dimensions. To me, $\frac{1}{N-1}X_0X_0^T$ is not even of the correct dimensions! It is $N\times N$ matrix, so what would it tell us? Covariance between two observations?! On our minecraft server, I've built a Nether portal in my basement. Which connected two-way (tested) to a location in the Nether.    This nether portal took me to an area in the nether which was a small cave. I dug upwards and surfaced close to a Nether Fortress. After clearing the fortress of Blaze spawners, I decided to 'move in'. So I went back to the portal, dismantled it, and reactivated in in a location in the Fortress.    The fortress would be within the same 128m radius I would assume as it's really close to the original place. Literally some steps to the surface, then a ladder up the nearest Nether Fortress bridge support.  Now, taking this portal back to my original doesn't work, I spawn deep underground in an Abandoned Mine Shaft.  I read somewhere that my Nether portal has found a 'better match' and this could be remedied by disabling the 'wrong' portal in the mine shaft.  However, upon multiple attempts, a new nether portal is dynamically created in the same area. See screenie for example. You'll see two 'stacked' portals on the left (from my different attempts at disabling) and then the current active one on the right.    My question is, how can I make sure these portals go to the correct place. Is it a matter of returning the portal to it's original location or am I stuck for returning to the basement? How to make terminal autocomplete when there are several files/directory? If I have several directories, like:  afoo abar   sometimes my terminal will refuse autocomplete when I press tab (e.g. "cd a" then tab), and print the list of directories instead. Sometimes it even throws a noisy, annoying sound. Any idea how to make it autocomplete in cases like this? E.g it can show abar first, and then afoo if I press tab again. I saw this is the case in windows, or some applciation in Ubuntu Why is my Canon 300D not switching on despite changing both batteries and the CF card? How to avoid having my father's down payment assistance get taxed as a gift i want to compile several pgfplots pictures with lualatex, since it dynamically allocates memory for compiling (in contrast to pdflatex).  In some plots, like my MWE.tex given below, i want to use a contour plot. This is typically done with gnuplot. To compile a document like this i need to use --shell-escape, such that gnuplot command can be executed while compiling the document.  \documentclass[a4paper]{article}  \usepackage[utf8]{luainputenc} \usepackage{pgfplots} \pgfplotsset{compat=newest} \begin{document} \begin{tikzpicture}   \begin{axis}     \addplot3[contour gnuplot]      {x+y};       \end{axis}   \end{tikzpicture} \end{document}   If i use  pdflatex --shell-escape MWE.tex   everything works fine, and the log says something along the lines  This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016) (preloaded format=pdflatex 2016.6.12)  13 JUN 2016 10:46 entering extended mode  \write18 enabled. .... Package pgfplots notification 'compat/show suggested version=true': document has been generated with the most recent feature set    (\pgfplotsset{compat=1.13}).  \openout3 = `MWE_contourtmp0.dat'.  \openout3 = `MWE_contourtmp0.script'. runsystem(gnuplot "MWE_contourtmp0.script")...executed.   If i use     lualatex --shell-escape MWE.tex i get the following error:  This is LuaTeX, Version 0.95.0 (TeX Live 2016)  (format=lualatex 2016.6.12)  13 JUN 2016 10:52  system commands enabled. ... Package pgfplots notification 'compat/show suggested version=true': document has  been generated with the most recent feature set (\pgfplotsset{compat=1.13}).  Package pgfplots info on input line 10: Using 'lua backend=false' for plot 0 (type 'contour external'): plot handler does not support LUA.  \openout3 = MWE_contourtmp0.dat  \openout3 = MWE_contourtmp0.script gnuplot "MWE_contourtmp0.script"  ! Package pgfplots Error: sorry, plot file{MWE_contourtmp0.table} could not be opened.   The .table file exists and looks identical to the one created by pdflatex, but it says that it cannot be executed.  (I just installed texlive 2016 yesterday, so everything should be up to date.) Solve congruence system $\ x\equiv m_i-1 \pmod{m_i}\,$ for $\,i = 1,\ldots, k$ I'm trying to set up file transfer via FileZilla and it doesn't seem to matter what details I put in, I always get the following error:     Status: Connection attempt failed with "ECONNREFUSED - Connection   refused by server". Error: Could not connect to server   My Dad has tried on his computer (with FileZilla on Windows) and it connects and everything is fine.. When I try on mine with all the same details that he put in, it comes up with that error.  I read that a firewall might be blocking it so I double checked and my firewall through system preferences and it is off.  Anybody know why this might be???  Additional info:  Macbook Pro running OS X El Capitan version 10.11.6  FileZilla version 3.23.0.2 input to pic with 12V and resistors I have 12V, Use these 12V to power a device (that has a 12V output signal) and to power a 7805. After the 7805 there is a pic microcontroller where I would have to connect the output from my device. I was thinking of having 2 resistors in a 3/1 ratio in order to have about 4V at the pin of the pic. Can this be done, given that the ground is common, or will it give some sort of problem with the lm7805? Virtualbox has no 64-bit options ASP.NET MVC Default Project Structure and the Scripts Folder I took an English assessment test online and this was my answer:     Someone suggested to go for a walk.   My answer was wrong and this was the correct sentence:     Someone suggested going for a walk.   Can someone please explain why my answer was wrong? Most efficient way to convert an HTMLCollection to an Array Is there a more efficient way to convert an HTMLCollection to an Array, other than iterating through the contents of said collection and manually pushing each item into an array?