The first time I knew about the hyperbolic function was when I was studying the derivatives. And I know that the derivative of   $\sinh x=  ( e^x - e^{-x} )/ 2$ , but i still confused with what are they really are? and how did we get them and for what we are using them?  Thanks very much, and i hope that wasn't a long question.
I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful.  Is there any good examples of their uses outside academia?
How can we extract specific files from a large tar.gz file? I found  but, when I tried the mentioned command there, I got the error:  $ tar --extract --file={test.tar.gz} {extract11} tar: {test.tar.gz}: Cannot open: No such file or directory tar: Error is not recoverable: exiting now   How do I then extract a file from tar.gz? Product of two cyclic groups is cyclic iff their orders are co-prime Say you have two groups $G = \langle g \rangle$ with order $n$ and $H = \langle h \rangle$ with order $m$. Then the product $G \times H$ is a cyclic group if and only if $\gcd(n,m)=1$.  I can't seem to figure out how to start proving this. I have tried with some examples, where I pick $(g,h)$ as a candidate generator of $G \times H$. I see that what we want is for the cycles of $g$ and $h$, as we take powers of $(g,h)$, to interleave such that we do not get $(1,1)$ until the $(mn)$-th power. However, I am having a hard time formalizing this and relating it to the greatest common divisor.  Any hints are much appreciated! What is the difference between “say” and “tell”? I really get confused when to use say and when to use tell. Which is appropriate in the following:   What did he tell? / What did he say? What are you saying? / What are you telling? If $H$ has maximum vertex degree at most $3$ and is a minor of $G$, then $H$ is a topological minor of $G$. If  $H$ has maximum vertex degree at most $3$ (so $\Delta(H)\leq 3$) and $H$ is a minor of $G$, then $H$ is a topological minor of $G$.   The converse follows by definition. However, most sources state this proposition without a proof. Any help is greatly appreciated. Keep the same field headers after joining a table to a shapefile in QGIS I noticed that after joining a table to a shapefile the headers of each fields in the table used for the join are changed by QGIS and they are attributed to a different name.  For instance, I had a shapefile with vegetation_codes and a table with vegetation_codes and veg_definition (these were the headers). After joining the table to the shapefile and also saving the shapefile and creating a new one, the vegetation_classes header was changed into vegetati_1.  Is there a way to keep the original headers?  I am using QGIS Dufour on Windows 7 and the table that I join to the shapefile is CSV (tried with dbf as well and the problem is the same). How do I find out which program and process ID accesses a given IP address in Windows? Is it possible to catch, which program is accessing a specific IP address?   I found my computer is flooding and wish to check addresses one by one.  May be it is possible to set up some audit for this? My new laptop came preinstalled with Windows 8. Naively, as I am, I just formatted the harddrive and installed fine old Ubuntu. Now I want to install Windows 8 for dual boot again, but I have no DVD and do download the ISO one needs a product key. That key is not on the back of the laptop anymore but somewhere on the mainboard.  Is there any way to recover the product key from the mainboard using Ubuntu? I am looking for a step by step instruction to guide me in the ways of installing, configuring and debugging many of the issues new users have when dealing with Wine in Ubuntu.  What is the recommended way of installing Wine, some of the key issues that it has and how to solve them?  If I have a specific problem with an App in Wine, how do I go about solving it? What are the recommended steps to ensure that I can fix a problem related to an app I wish to use? According to HTML specs, the select tag in HTML doesn't have a readonly attribute, only a disabled attribute. So if you want to keep the user from changing the dropdown, you have to use disabled.  The only problem is that disabled HTML form inputs don't get included in the POST / GET data.  What's the best way to emulate the readonly attribute for a select tag, and still get the POST data? Is "mens" a valid word? I've been living in Ireland for almost a year now and I start noticing they use the word "mens" a lot. I can see it used in:   Shops, to denote the area where you can find men's clothes In sport, when they talk about "mens team".    My guess is just that they are lazy about the use of quotes, so that mens should actually be men's. However, there may be some rule I'm not aware of. So, is "mens" only limited to Irish English? When I'm allowed to use it? Converse to Chinese Remainder Theorem So as seen on this question , we know that if $(n,m) \neq 1$, then $\mathbb{Z} /mn \mathbb{Z} \ncong \mathbb{Z}/n\mathbb{Z} \times \mathbb{Z}/m\mathbb{Z}$, because the right hand side does not have an element of order $nm$.  But take a more general setting. Let $R$ be a commutative ring, and let $A,B$ be ideals in $R$. $A$ and $B$ are said to be comaximal if $A+B=R$. If $A, B$ are comaximal, then we have: $R/AB \cong R/A \times R/B$. In this setup, is the converse true?      If we have $A, B$ ideals in $R$ such that $R/AB \cong R/A \times R/B$, do we always have that $A$ and $B$ are comaximal? Having trouble adding objects to NSMutableArray in Objective C Why particle hole symmetry and chiral symmetry are called symmetries? $PHP^{-1}=-H$ (particle-hole symmetry) and   $\Gamma H \Gamma^{-1}=-H$ (chiral symmetry)   I understand why we get the negative signs but im just a bit confused as to why such equalities mean $H$ is particle hole and chiral symmetric.   When we say $H$ is symmetric under some operation, like time reversal,  don't we usually mean that $H$ is invariant under the said transformation?  $THT^{-1}=H$ if $H$  is time reversal symmetric.  On the contrary, we say $H$ is symmetric under particle hole and chiral operations when $H$ picks up a negative sign. This seems to contradict our usual convention of what we mean by $H$ being symmetric(invariant). EmptyListToVisibilityConverter I'm using ubuntu 13.10 as htpc. To save some power, i have set it to suspend after 30minutes of inactivity. Before entering suspended state, a popup appears to warn me that computer is about to get put to sleep. This is a little annoyance since it appears when i resume the pc later.   How can i disable this notification for good? I am crawling some data using Apache Nutch and storing it on my USB Drive. The OS itself is Ubuntu Live Boot OS. But for every restart or shutdown I am losing my data. I also tried suspending my Ubuntu user still data was not visible when I reinserted my live USB.  Is there any way I can keep the data intact and does not loose and application settings installations when I do restart Ubuntu.  Used USB installer provided by pendrivelinux.com at Accessing AWS S3 via a REST API (Apex callout with a Named Credential) SharePoint Migration 2007 to 2013 In the 3d-view workspace, we can use a random color to give our separated object a distinct look.  What if I don't like the result and I want to randomize the color again?   Swapping the setting doesn't change the random seed in color.    (Blender 2.80.64.) Custom script "invoked too many times" error Credit:   function getDirection(city1, city2, unit) {   var directions = Maps.newDirectionFinder()     .setOrigin(city1).setDestination(city2)     .setMode(Maps.DirectionFinder.Mode.DRIVING)     .getDirections();   var d = directions.routes[0].legs[0].distance.text;    var distance, value = d.split(" ")[0].replace(",", ""), text = d.split(" ")[1];   if(text == unit) {     distance = value;   } else if(text == "km" &amp;&amp; unit == "mi") {     distance = value / 1.6;   } else {     distance = value * 1.6;   }   return Math.round(distance); }   I have used this code snippet in one of my sheets. I am working on a dataset with roughly 6000 entries and I am getting some errors because of the large volume.      Script invoked too many times per second for this Google user account. (line 0).      Service invoked too many times for one day: route. (line 4).   I considered purchasing a Google Apps business account to increase my quota, but that might not even help. Do you maybe have any advice for me in this regard?