Why does Joule's Law of Heating defined by $H=i^2R$ only?
Why high voltage transmission lines?
I seem to have clicked on something that changed my display preferences. The main site is now very minimalistic, with fewer controls and different fonts.  I want to change it back, but where is it? Showing that $\lnot Q \lor (\lnot Q \land R) = \lnot Q$ without a truth table I've done a truth table after reducing it to this and it seems to be equal to $\neg Q$:  $$\lnot Q \lor (\lnot Q \land R) = \lnot Q$$  But when I try to show it without a truth table (with just transformations), I end up in a loop between that and:  $$\lnot Q \land (\lnot Q \lor R)$$  Is there a way to show this is true without using a truth table? What am I missing?!  Thanks in advance! Show path of a body of where it should go after linear impulse is applied I am making a game with Andengine and Box2D. I have a dynamic body and I apply linear impulse on the body to move it around when the user have touched the screen.  Now I want to show the path where the body will go when the user have touched. If you have played Angry Birds or Basket Ball Shoot or any other which have projectile motion with a path shown you will get my point. I want to show the white dots which are shown in those games. A function that is continuous at the origin but not differentiable there Show that $f(x,y)=\dfrac{xy^2}{x^2+y^2}$ (with $(x,y)\not=(0,0)$ and $f(0,0)=0$) is continuous but not differentiable at $(0,0)$.  I tried to show continuity with an $\epsilon -\delta$ argument but I don't know how to factorize the expression so that I can have something useful.   For differentiability I think I should show that the partials are not continuous at $(0,0)$. But finding the partials is also painful. Choosing GeoCoding service? I'm looking for a web service providing a full address based on coordinates (and reverse).  I'm ready to pay for that service.  I don't want to use Google's API. I am having trouble finding out why the white space between my paragraphs is variable. Sorry, I am not allowed to post images but sometimes there is no white space (like it should be), just an indent to denote that a new paragraph has started. While sometimes the paragraphs start with an indent AND there is (sometimes substantial and thus variable) white space between the last sentence of the previous paragraph and the first sentence of the new paragraph.  In my tex file, there is no difference between what I do in the first and second examples of my text: just two hard returns to denote the start of a new paragraph. I was wondering whether it could be due to placement of figures and footnotes but I have no idea how to change it. I don't mind a little variable white space between paragraphs but the above example is too extreme for my taste. Thanks for your advice! Is it possible that by mutation a human could see infrared or other 'colours'? Incoming light reacts with the several types of cone cells in the eye. In humans, there are three types of cones sensitive to three different spectra, resulting in trichromatic color vision. Each individual cone contains pigments composed of opsin apoprotein, which is covalently linked to either 11-cis-hydroretinal or more rarely 11-cis-dehydroretina.  The opsins (photopigments) present in the L and M cones are encoded on the X chromosome.  A very small percentage of women may have an extra type of color receptor because they have different alleles for the gene for the L opsin on each X chromosome. X chromosome inactivation means that only one opsin is expressed in each cone cell, and some women may therefore show a degree of tetrachromatic color vision. Tetrachromacy is also demonstrated among several species of birds, fish, amphibians, reptiles and insects.  Humans cannot see ultraviolet light directly because the lens of the eye blocks most light in the wavelength range of 300–400 nm.  So, besides above mentioned exceptions, is it possible due to mutations or genetic engineering to see UV or infrared. What kind of mutations should be made or are the changes to be made in the opsines to big to create 'alien' eyes? I need to draw a tree, and constantly using dotty and including the PNGs is starting to be a pain. Is there a way to get LaTeX to draw it's own trees that doesn't involve learning an entirely new language like TikZ? How to secure my laptop so that hacking by physical access is not possible? I messed up my system earlier, I was greeted with a black screen, when booting in to Ubuntu. When I started up my laptop, I selected the recovery option from the grub menu, and chose fallback at root terminal. I saw that I was able to use the add user command, with it, I probably could use to create a privileged user on my machine.   Isn't that a security issue?  One could have stolen my laptop and at startup chose recovery and add another user, I'm fudged then. Including my data.  Come to think of it, even if you somehow remove that entry, one could boot from a live-CD, get a chroot up and running and then add another user, with the right privileges that allows it to see all my data.   If I set the BIOS to boot at my HD only, no USB, CD/DVD, Network startup, and set a BIOS password, it still wouldn't matter, because you'd still have that grub recovery startup entry.  I am fairly certain that someone from China, Russia can't hack my Ubuntu Trusty Tahr, from the network, because it's secure like that. But, if one has physical access to my - your - machine, then, well, that's why I'm asking this question. How can I secure my machine so that hacking through physical access is not possible?    Bug Report: Use template_include with custom post types I want to check for an appropriate template in the theme folder before falling back to the file in my plugin directory. Here’s my code:  add_filter('template_include', 'sermon_template_include'); function sermon_template_include($template) {     if(get_query_var('post_type') == 'wpfc_sermon') {         if ( is_archive() || is_search() ) :            if(file_exists(TEMPLATEDIR . '/archive-wpfc_sermon.php'))               return TEMPLATEDIR . '/archive-wpfc_sermon.php';            return dirname(__FILE__) . '/views/archive-wpfc_sermon.php';         else :            if(file_exists(TEMPLATEDIR . '/single-wpfc_sermon.php'))               return TEMPLATEDIR . '/single-wpfc_sermon.php';            return dirname(__FILE__) . '/views/single-wpfc_sermon.php';         endif;     }     return $template; }   Problem is, it doesn’t work! :-) It always picks the file in my plugin folder. Any idea what to do? I’ve tried alot of variations but I can’t seem to get anything to work! Thanks in advance! Jack  EDIT  I'm expecting the archive-wpfc_sermon.php to be returned from the theme folder if it exists. However, the file from my plugin always gets returned. Thanks for your help! This is from my Sermon Manager plugin available in the repository. What are the obj and bin folders (created by Visual Studio) used for? What graphics packages are there for creating graphics in LaTeX documents? What packages do you use and recommend for creating graphics in your LaTeX documents?     As this is a community wiki post, please add your package to the accepted answer (or add a comment, and someone with >100 rep will add it to the CW answer), and include a brief description of what differentiates it from others and how it can be used (GUI drawing tool which generates code, type in raw text, or generates image for inclusion in document).   We'll eventually sort these answers under headings. How can I add "page # of ##" on my document? I want to add a footer to my document displaying the current number out of total number of pages. How do I do that? Why is variance squared? How to create vertical and horizontal dotted lines in a matrix? How to grep a specific line _and_ the first line of a file? Assuming a simple grep such as:  $ psa aux | grep someApp 1000     11634 51.2  0.1  32824  9112 pts/1    SN+  13:24   7:49 someApp   This provides much information, but as the first line of the ps command is missing there is no context for the info. I would prefer that the first line of ps be shown as well:  $ psa aux | someMagic someApp USER       PID %CPU %MEM    VSZ   RSS TTY      STAT START   TIME COMMAND 1000     11634 51.2  0.1  32824  9112 pts/1    SN+  13:24   7:49 someApp   Of course, I could add a regex to grep specifically for ps:  $ ps aux | grep -E "COMMAND|someApp"   However, I would prefer a more general solution as there are other cases in which I would like to have the first line as well.  Seems like this would be a good use case for . I followed  to create a soccer ball.  Now I want to texture it in a way that every pentagon has an image inside itself and the exagons are white, but I also want everything to be a little glossy. I managed to successfully UV Map the ball and paint the texture in photoshop but now I am having big problems in applying the texture material to the mesh.    I've created a new material in Blender Render mode with Diffuse and the texture applied to it. I also set the Texture mapping to UV. I've gone in edit mode, selected all the mesh and applied the material. Unfortunately in Texture View Mode I see just a white ball and while rendering I see everything's black.      If I try to do this in Cycles Render and use a Mix Shader with the FAC set to the texture image I get what I want in the Texture View Mode but while rendering I just see everything black and white of my colored images.        I hope I've been clear enough and that someone will help me in this easy/difficult task! Thank you in advance Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$ How do I send a file as an email attachment using Linux command line? I've created a script that runs every night on my Linux server that uses mysqldump to back up each of my MySQL databases to .sql files and packages them together as a compressed .tar file.  The next step I want to accomplish is to send that tar file through email to a remote email server for safekeeping.  I've been able to send the raw script in the body an email by piping the backup text file to mailx like so:  $ cat mysqldbbackup.sql | mailx backup@email.com   cat echoes the backup file's text which is piped into the mailx program with the recipient's email address passed as an argument.  While this accomplishes what I need, I think it could be one step better, Is there any way, using shell scripts or otherwise, to send the compressed .tar file to an outgoing email message as an attachment?  This would beat having to deal with very long email messages which contain header data and often have word-wrapping issues etc. Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?