prove that the following equation has exactly 2 solutions
Prove that equation has exactly 2 solutions
Priority and timing between enchantments and instants If I have priority and cast an  on a just summoned 2/3 creature, then, passing priority, my opponent casts a  on that creature, does my creature survive? The first spell that resolves is obviously the bolt, that deals 3 point of damage to the creature; but immediately after, will the  Unholy Strength resolve (giving +2/+1), allowing the creature to survive? How do I show the current node title in page.html.twig OR in node.html.twig? If I want to show the current node title in page.html.twig (by default it seems to only be available in node.html.twig) I have to create a preprocess function like so:  function theme_preprocess_page(&amp;$variables, $hook) {   // Set our page title so we can access it in page.html.twig   if ($node = \Drupal::routeMatch()-&gt;getParameter('node')) {     $variables['my_node_title'] = $node-&gt;title-&gt;value;   } }   And then I have to overwrite page-title.html.twig by copying it into my current theme folder and commenting out everything.  This doesn't seem "right".  Is there a better way? Present tense in Flashback story for something that is still true now? I'm wondering whether I should use the present tense for a descriptive statement but in a past context. For example:     (1) I went to the zoo and saw a giraffe last week.       (2) A giraffe is a mammal with long neck.       (3) It is the first time I see that animal with my own eyes.   Statement (2) is a description of a giraffe in general, not the specific one in the zoo, so is it correct to use is?  Statement (3) is an event that is still true now, so should I use is and see?  I'm not native speaker so forgive me if the question is very obvious to others. How do you performance test JavaScript code? CPU Cycles, Memory Usage, Execution Time, etc.?  Added: Is there a quantitative way of testing performance in JavaScript besides just perception of how fast the code runs? I am a Physics undergrad, and just started studying Topology. How do you define neighborhood and open set in Topology.Wikipedia gives a circular definition.   An  is defined as follows.      In topology, a set  is called an open set if it is a neighborhood of every point    While a  is defined as follows:     If $X$ is a topological space and $p$ is a point in $X$, a neighbourhood of $p$ is a subset $V$ of $X$, which includes an open set $U$ containing $p$   which itself contains the term open set.  How do you define it exactly? How can I show that if some group $G$ has only one subgroup $K$ of order $n$, then $K$ is a normal subgroup? Would that mean that it only has one subgroup total? If so then I guess that makes sense. If $F:M\to N$ is a smooth embedding, then so is $dF:TM\to TN$. I have installed Ubuntu 13.04 on my desktop (runs like a charm). Then I used Crouton to install Ubuntu 12. 04 on my chromebook samsung (ARM). It also works quite well.  Here comes my question. Can we have a true Ubuntu (preferably 13.04) on my ARM chromebook?  It seems that the Crouton/Ubuntu is not 100% the real thing.  The best option would be to have the full Ubuntu 13.04 and remove the Chrome OS. If granted omniscience and we know that $\beta_1$ in a multiple linear regression model is truly 0, what does that mean in words (and math notation)?  The model is: $Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon$  Does $\beta_1 = 0$ mean:   Empirically: "If we make infinite, perfect measurements of our data, $\hat\beta_1$ approaches 0 at the limit?" [Math: ??] Formally: "In the true, finite population of our data, $X_1$ has 0 association with $Y$ and their vectors of values are perfectly linearly independent, uncorrelated, and orthogonal?" [Math: ??]   What does $\beta_1 = 0$ mean, precisely? Why does Windows only show about 3.5 GB of my 4 GB of RAM? Show that there is no solution to the congruence $x^2\equiv3\bmod5$.   I'm not sure if the fact that the only numbers divisible by $5$ are those ending in $0$ or $5$ will help&hellip; What Hogwarts classes are taught to two houses at once? I remember from my mumble about nine mumble rereads of the Harry Potter series that the following classes Harry took were taught to more than one house in the same lesson:   Potions with the Slytherins  Herbology with the Hufflepuffs  Care of Magical Creatures with the Slytherins  broomstick riding with at least the Slytherins (maybe other houses, too?)    I don't remember any student from a house that isn't Gryffindor being mentioned in the sections on Transfiguration, Charms, Defense Against Dark Arts, History of Magic, or Divination. That would mean McGonagall had to teach twice as many classes as Snape, if both subjects got the same number of lessons (which I think I recall).   Were any subjects other than Potions, Herbology, and Care of Magical Creatures taught to more than one house in the same lesson? And do we know why some subjects are taught to more students at the same time than others? Convert 12-hour date/time to 24-hour date/time I have a tab delimited file where each record has a timestamp field in 12-hour format:     mm/dd/yyyy hh:mm:ss [AM|PM].   I need to quickly convert these fields to 24-hour time:     mm/dd/yyyy HH:mm:ss.   What would be the best way to do this? I'm running on a Windows platform, but I have access to sed, awk, perl, python, and tcl in addition to the usual Windows tools. Extension “RANDR” missing on xvfb My system:  $lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 14.04.3 LTS Release:        14.04 Codename:       trusty   Xvfb:  $ dpkg -s xvfb Package: xvfb Status: install ok installed Priority: optional Section: x11 Installed-Size: 2140 Maintainer: Ubuntu X-SWAT &lt;ubuntu-x@lists.ubuntu.com&gt; Architecture: amd64 Multi-Arch: foreign Source: xorg-server Version: 2:1.15.1-0ubuntu2.7 Provides: xserver   Current problem:  Xvfb do not support RANDR extension, even if I add the flag:  +extension RANDR   If I run xdpyinfo, RANDR is not on the list. It's a missing feature or a bug. I found a reference here with a patch:   And looks like that in other distros like debian, there is already a testing build of Xvfb with support:   I am trying to run a program throught Xvfb, and it returns the following error:  Xlib:  extension "RANDR" missing on display ":99".   The program works if I run it via ssh/command line. The problem appears to be the the lack of support for "RANDR" in xvfb.  My question is: what is the easiest way to get xvfb with "RANDR" support in my system? How can I prevent Google mistakenly offering to translate a page? Several of my site's pages are appearing in search results with [Translate this page] next to it. When I click that it takes me to Google Translate and translates my page "from Catalan to English".  The pages are in English but have a couple of foreign words (actually Japanese romanisations, not Catalan) that appear to be tripping Google up.  A few weeks ago I set the html tag to &lt;html lang="en"&gt; which from research appears to be the best method to specify the language of a document. Google has cached the pages with this attribute but it is still offering to translate.  More research led me to a "notranslate" attribute which prevents translation entirely: &lt;html lang="en" class="notranslate"&gt;. The problem now is users cannot translate from English to their desired language!  Are there any other solutions that force Google to parse my site as English only? Solving $f(x+y) = f(x)f(y)f(xy)$ This is my circuit. I need to find the power dissipated by Vlamp. So the lamp turns on if the Vlamp is more than 2V. When the lamp is on it has an internal resistance of 10 Ohms, and when it is off it acts like an open circuit.  How would I find the power dissipated? I know how to do it for Voltage sources and Resistors, but not elements like these.  One more thing, I already figured out that: Battery has open circuit voltage of 4V R1 = 5 Ohms R2 = 5 Ohms k = 0.2A/V When lamp on and Vlamp = 2V, Rbat = 10 Ohms   . Getting the class name of an instance? How do I find out a name of class that created an instance of an object in Python if the function I am doing this from is the base class of which the class of the instance has been derived?  Was thinking maybe  might have helped me out here, but it doesn't seem to give me what I want. And short of parsing the __class__ member, I'm not sure how to get at this information. When is it correct to use "yourself" and "myself" (versus "you" and "me")? How to shrink Windows 7 boot partition with unmovable files