let $a,b,c\ge 0$,and such $a+b+c=1$,show that $$\sqrt{1-ab}+\sqrt{1-bc}+\sqrt{1-ac}\ge2\sqrt{2}$$  maybe can use C-S to solve it.  My attempt is  $$\sum_\mathrm{cyc}\sqrt{a^2+b^2+c^2+ab+2bc+2ac}\ge 2\sqrt{2}$$ then I want to square, but it's ugly.
Let $x,y,z\ge 0$,and $x+y+z=2$, show that $$\sqrt{1-xy}+\sqrt{1-yz}+\sqrt{1-xz}\ge 2$$  Mt try: $$\Longleftrightarrow 3-(xy+yz+zx)+2\sum_\text{cyc}\sqrt{(1-xy)(1-yz)}\ge 4$$ or $$\sum_\text{cyc}\sqrt{(1-xy)(1-yz)}\ge\dfrac{1}{2}(1+xy+yz+zx)$$
A bunch of CSS files were pulled in and now I'm trying to clean things up a bit. How can I efficiently identify unused CSS definitions in a whole project? LaTeX Classes or Styles for Schedules and/or Calendars? Maybe TeX isn't the best for this particular problem, but any teachers out there use a particular class or package to plan lessons?  Right now I'm just using a spreadsheet, but I always find myself wishing there was a 'lessonplan.sty' or 'classschedule.sty' file out there somewhere so I could still use the LaTeX for equations, tables, lists etc.    A bit of searching yielded a few results, but there doesn't seem to be a consensus.  Anyone used any of these:        Any recommendations from anyone on best way to make calendar-based class schedules and/or lesson plans? is keyword in Python Restore a SQL Server 2012 backup file in SQL Server 2016/2014 I have SQL Server 2012 backup files and want to restore these to SQL Server 2016/2014. Will it work?  I need to find this out before I uninstall SQL Server 2012. how to pass objects between intents When I learned English at school, I was taught that I should not end a sentence with a preposition.  Is it correct to end a sentence with a preposition?     To avoid starting a sentence with a conjunction, I don't write sentences similar to "I miss you. And your kisses." Is there a similar way to avoid ending a sentence with a preposition? I'm trying to have a surface with soft body hold obects that are falling on it with rigid body physics, but for some reason, no what matter what mass I give it, the objects just fall trough the softbody enabled surface.  Is there a toggle or a value I need to change to make them stay there? How do lexical closures work? Sometimes it is convenient to use an absolute path to include a preamble. To do so, I use the following "hack":  \documentclass[a4paper, 12pt]{article} \newcommand{\folder}{/path/to/folder} \input{\folder/preamble}  \begin{document} \end{document}   Now my question is, whether there is a more elegant way to do this, especially a way which is compatible with one of the flatten scripts from  ? Creating a DateTime in a specific Time Zone in c# I'm trying to create a unit test to test the case for when the timezone changes on a machine because it has been incorrectly set and then corrected.  In the test I need to be able to create DateTime objects in a none local time zone to ensure that people running the test can do so successfully irrespective of where they are located.  From what I can see from the DateTime constructor I can set the TimeZone to be either the local timezone, the UTC timezone or not specified.  How do I create a DateTime with a specific timezone like PST? The Equation $11^x + 13^x + 17^x =19^x  $  Has    No Real Roots Only One Real Roots Exactly Two Real Roots  More than Two Real Roots    What I have done is   The function $f(x)=11^x + 13^x + 17^x -19^x  $ is strictly increasing and being always positive it have no roots How do I split a string, breaking at a particular character? We are planning a trip with a bike rack attached to our trailer hitch. What is the best way to lock the bikes while the vehicle is unattended? I see some racks have locks on the knobs but they don't seem very strong.   What do you suggest? I am new to Game Development, All I have developed is some 2d Games, using Game Maker by . There game development is much more easy, just as simple as Drag and Drop. But, Now I wish to evolve in Game Development, and wanna try some hands with the common programming languages like, Java, C++ or C. In order to achieve this, I came around the first topic, Game Engine. So, What is Game Engine.? That is a broad question, with various answers. I came out with some conclusion after reading various links,  Wikipedia: A game engine is a system designed for the creation and development of video games. The core functionality typically provided by a game engine includes a rendering engine for 2D or 3D graphics, a physics engine or collision detection (and collision response), sound, scripting, animation, artificial intelligence, networking, streaming, memory management, threading, localization support, and a scene graph.  It exists to abstract the (sometime platform-dependent) details of doing common game-related tasks, like rendering, physics, and input, so that developers (artists, designers, scripters and, yes, even other programmers) can focus on the details that make their games unique. Engines offer reusable components that can be manipulated to bring a game to life. Loading, displaying, and animating models, collision detection between objects, physics, input, graphical user interfaces, and even portions of a game's artificial intelligence can all be components that make up the engine.  Now what I understand is, Game Engine takes care of all the common work, like physics, loading etc... As far my question is concerned, what is a Game Engine (Programmatically)? Is it a Library? With pre-defined functions and classes, which can be inherited? Or what so ever, what is it? How does the twitter bot work? I heard that there was a twitter bot which automatically posted questions and asked for answers for specific questions on every site. How do they work? Is there an algorithm for doing this or is it purely random? I know that it doesn't tweet closed questions, but that's it. Proof of $\sin nx=2^{n-1}\prod_{k=0}^{n-1} \sin\left( x + \frac{k\pi}{n} \right)$ I have seen this identity on Wolfram mathworld and in a comment to another similar trigonometric proof:    I can't seem to find a proof to this identity online anywhere. What method is used to prove this? story on forest timescale I'm looking for the title of a short story by Ursula Le Guin about a scientist (?) who is given a drug that slows the timescale of his perception enormously, so that he can perceive that an alien (?) forest is actually behaving as a sentient being, reacting to current events, but at an enormously slow (from a normal human point of view) timescale. It might be in , but I don't remember the title (and it doesn't jump out at me from the list of titles) and don't have access to that collection right now. It is not &quot;The Word for World is Forest&quot;, nor &quot;Direction of the Road&quot; (from ), nor &quot;Vaster than Empires and More Slow&quot;, the latter two of which look at similar plant perception/time-scale issues. Update: it turns out that the description was right, but I had most of the details wrong: not Le Guin, not alien, not a scientist ... What exactly happens when you browse a website in your browser? Why can I modify a read-only file? Short Question:  Why can we manipulate a read-only file in Vim using : + w + q + ! even without being an administrator?  Long Question:  I have a text file (myFile.txt) which is read-only for everyone:  navid@navid-ThinkPad-T530:~/ubuntuTest$ ls -l myFile.txt  -r--r--r-- 1 navid navid 26 Aug 22 21:21 myFile.txt   I can open it with Vim without having admin privileges:  navid@navid-ThinkPad-T530:~/ubuntuTest$ vi myFile.txt    I modify it and press: Esc + : + w + q + Enter and I see this error message:  E45: 'readonly' option is set (add ! to override)   So far, everything makes sense.  But when I press: Esc + : + w + q + ! + Enter, Vim saves the changes.  I'm using Ubuntu 16.04 and VIM 7.4. I've googled and also searched the answers here but couldn't find my problem so here goes:  I know how to bevel a curve using another object and when I try it with a normal circle it's fine. But I'm trying to use this flat oval shape to bevel a larger curve of the same shape and it's not following the curve at the correct rotation. I've tried everything, rotating the bevel object, clicking random options in the object data menu.. I can't seem to budge it from looking how it is in the screenshot. In the screenshot you can see the curve I've failed to bevel correctly and also the bevel object in the bottom right.  Basically, I want the flat part of the oval to be above and below the curve, not on the sides as it is. I hope that makes sense. Anyone know what I need to do?