This appeared in the Area Level of the 19th Philippine Mathematical Olympiad. Electronic calculators were not allowed during the competition of course. The closest I got to was to express it as:  $$ \dfrac{1}{\sqrt[6]{2}(\sqrt[6]{7813}-\sqrt[3]{6}\sqrt[6]{217})}. $$  The answer using an electronic calculator is 9375. Can anyone show how this can be approximated without the use of electronic calculators?
Find the integer which is closest to the value of   $\frac{1}{\sqrt[6]{5^6+1}- \sqrt[6]{5^6-1}}$  I have tried putting them between n and n+1 and tried manipulating  n but I cant seem to find a strategy.
I have a DB Server running CentOS 6.4 and MySQL 5.5 from RPMs (not source).  I have dozens of databases but one of them is being hit quite hard with large selects which locks out other updates which in turn locks out other selects (at least I think this is what's happening!)  To alleviate this I would like to replicate one of the databases onto the same server so that the writes can write to the "master" and reads can be done on the "slave". I don't have the luxury of additional hardware.  I have found a lot of guides on the internet describing how to replicate to a different server, and one () describing how to replicate to the same server but it doesn't seem to be geared towards retrofitting this functionality to an existing database with 10s of GB of data in it already. It also talks about compiling MySQL from source.  Does anyone know how I can retrospectively convert my MySQL 5.5 config to replicate one of my databases on the same server?  My existing DB runs on port 3306 so I feel it should be as easy as firing up another instance of MySQL on port 3307 and making some changes to my.cnf but not sure what changes.  Thanks in anticipation. My recollection is very sketchy but this is what I remember....   Film was possibly black and white I saw it as a child in the late '80s early '90s but it's older It was subtitled and in Russian or similar language It involved some astronauts  travelling in space with possibly time travel The astronauts (mostly men) encounter a planet/civilization of only women The women no longer need men to breed and are so become superior and possibly want to eliminate all men    That's all I have to go on, sorry. How do I remove the Me-User-Indicator from the Panel? How do I remove the Me-User-Indicator from the Panel?  The indicator contains two items: the written user name and the icon of a human. Is an empty set equal to another empty set? I have a definition that claims that two sets are equal A = B, if and only if:  $\forall x ( x \in A \leftrightarrow x \in B)$  An empty set contains no elements. If I define the sets:  A = $\emptyset$  B = $\emptyset$  then can I conclude that A $\neq$ B? Since they contain no elements? Or would I have to show that an elements exists in one but not the other? To me it seems that these are not equal, but I'm struggling to wrap my head around this.  Thanks, Paul Figure subfigure layout with different numbers would this be considered a 'methodology' or a 'method'? Say I developed something called "Methodology for Establishing Remaining Life of Components". Basically, at work, we have components (or equipment). I wanted to develop a way to identify how much longer the components / equipment can last before they ware out and cannot be used.  It takes into account "the degree of damage currently in the component, the rate of future damage accumulation based on realistic operating scenarios, and the degree of damage required to cause failure." Taking these three into account, the remaining life of a component can be assessed. This is what I call "Methodology for Establishing Remaining Life of Components".   My question is, would this be considered a 'methodology for establishing remaining life of components' or just a 'method for establishing remaining life of components'? Or do you need more information to figure out if it is a method or methodology?   I cannot provide all the information for business purposes, but if additional  information is required to figure out if it is a method or methodology, I will provide it. I wish to display a map in QGIS (world country shapefiles) showing all countries but centered on the Pacific area.   I am not familiar with Proj4, so is there any way this can be done in QGIS? Inverting Polygons using QGIS? I have a Shapefile with Polygon features  representing the world's land areas (continents, islands).   Is it possible to invert these, and get a geometry that represents the world's oceans and seas?   So the original land Polygons need to become rings in a single global Polygon that covers the planet.  Basically, I'm looking for something like Select > Inverse in Photoshop.   I am using QGIS. When can a (finite) group be written as the quotient of some other group by its center? So if I'm given $H$, when I can conclude there is a group $G$ such that $H\cong G/Z(G)$? It's easy to show that non-trivial cyclic groups are not of this form. More generally, any group with the property that all finitely generated subgroups are cyclic (e.g. $\mathbb{Q},\mathbb{Q}/\mathbb{Z}$) cannot be of this form. Are there are any others? From official :     Due to a head injury, Cyclops is unable to shut off his optic blasts   at will and must therefore wear ruby quartz lenses to block the beams.   From the same page:     Cyclops possesses the mutant ability to project a beam of heatless   ruby-colored concussive force from his eyes, which act as   inter-dimensional apertures between this universe and another.   When his eyes are always blocked by ruby-colored beam of concussive force, how does he see? If a stock doesn't pay dividends, then why is the stock worth anything? I read somewhere that companies are not required to pay dividends to shareholders (this is correct, yes?).   If so, then if company A never pays dividends to its shareholders, then what is the point of owning company A's stock? Surely the right to one vote for company A's Board can't be that valuable.   What is it that I'm missing? What countries allow me to pass their borders visa-free?  Am I allowed to visit and work in EU and Schengen countries? dpkg error: "trying to overwrite file, which is also in..." For example:  $ sudo apt-get install curl Reading package lists... Done Building dependency tree Reading state information... Done You might want to run 'apt-get -f install' to correct these: The following packages have unmet dependencies: bsh : Depends: libjline-java but it is not going to be installed groovy : Depends: libjline-java but it is not going to be installed rhino : Depends: libjline-java but it is not going to be installed E: Unmet dependencies.   Try 'apt-get -f install' with no packages (or specify a solution).   I get the same or similar errors when I attempt to install clojure1.3, leiningen, and several other packages.   When I try the suggestion made in the error message, this is what happens:  $ sudo apt-get -f install  Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following packages were automatically installed and are no longer required:   diffstat linux-headers-3.2.0-26-generic linux-headers-3.2.0-26 dh-apparmor dkms html2text libmail-sendmail-perl libsys-hostname-long-perl Use 'apt-get autoremove' to remove them. The following extra packages will be installed:   libjline-java Suggested packages:   libjline-java-doc The following NEW packages will be installed:   libjline-java 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. 23 not fully installed or removed. Need to get 0 B/72.0 kB of archives. After this operation, 129 kB of additional disk space will be used. Do you want to continue [Y/n]? Y (Reading database ... 226243 files and directories currently installed.) Unpacking libjline-java (from .../libjline-java_1.0-1_all.deb) ... dpkg: error processing /var/cache/apt/archives/libjline-java_1.0-1_all.deb (--unpack):  trying to overwrite '/usr/share/java/jline.jar', which is also in package scala 2.9.2-400 Errors were encountered while processing:  /var/cache/apt/archives/libjline-java_1.0-1_all.deb E: Sub-process /usr/bin/dpkg returned an error code (1)  $ sudo apt-get upgrade Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run 'apt-get -f install' to correct these. The following packages have unmet dependencies:  bsh : Depends: libjline-java but it is not installed  groovy : Depends: libjline-java but it is not installed  rhino : Depends: libjline-java but it is not installed E: Unmet dependencies. Try using -f. Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module I want to draw a TikZ matrix with its border and I would like to define the distance between most external matrix nodes and matrix border. Something like a matrix inner sep. If I change inner sep in matrix options declaration, all nodes inside the matrix also change its inner separation.      I know how to do it with fit library. I just want to know if its possible without it. Has the wall been repaired? access controller variable in javascript Is there any way to access controller variable set in a Method in Javascript. In the example above the value is set in constructor. But when I set it in a method it is showing as NULL in Javascript  In controller:  public class abc {     public string varA { get;set; }     public void fn(){         varA='hello';     } }   In VFPage:  function hello(){     var bool = '{!varA}';     alert(bool); }   The alert statement in the VF Page(i.e bool) is displayed as null. Can you please help how to access a variable set from a method instead of constructor? I know that to better balance paragon and epic level players against similar level monsters, WotC changed the math used for monsters for MM3, and I believe that they changed some of the types of powers they gave monsters.   If I want to update monsters from MM1 or MM2 to be in line with MM3 era monsters, what changes should I make? Does Blender support any form of collaborative editing? how to concatenate string variables into a third?