Find angle $ \angle AED $ in the following triangle.
Problem about angle in isosceles triangle
ClassNotFoundException: org.eclipse.jetty.util.component.AbstractLifeCycle running inside jetty regexp in ksh for extensions tgz, tar.tgz I'm trying to get a regexp (in ksh) to identify files with only the following extensions: tgz, tar.gz, TGZ and TAR.GZ. I tried several but can't get them to work. I'm using this regexp to select only files files with those extensions to do some work with them:  if [ -f $myregexp ]; then    .....  fi java.lang.RuntimeException Cannot find FacesContext If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$. If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.  My attempt at answering the question:  \begin{align*} x &amp;\equiv 0 \pmod{a}\\\ &amp;\Longrightarrow x\text{ is divisible by $a$}\\\ &amp;\Longrightarrow x = ma\text{ for some integer $m$}\\\ \ \\\ x &amp;\equiv 0 \pmod{b}\\\ &amp;\Longrightarrow  x\text{ is divisible by $b$}\\\ &amp;\Longrightarrow x = mb\text{ for some integer $m$}\\\ \ \\\ x^2 &amp;= (ma)(mb)\\\ x^2 &amp;= (m^2)(ab)\\\ x &amp;= \sqrt{m^2ab}\\\ x &amp;= m\sqrt{a}\sqrt{b} \end{align*} Let $m$ be $k\sqrt{a}\sqrt{b}$. Then \begin{align*} x &amp;= kab\\\ &amp;\Longrightarrow x \equiv 0 \pmod{ab} \end{align*}  Is this correct, if not can someone point me in the right direction? I need to factory reset my Macbook but cannot recall the password. So I used Cmd+R during startup and go to terminal and typed 'resetpassword' according to this advice    Now 'Reset Password' application appears but there is nothing where I have to select the volume containing the user account. Why does this happen? Why is the Yang-Mills gauge group assumed compact and semi-simple? What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories?  I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even from a computational perspective. really given these assumptions much thought. PDO SQL-state "00000" but still error? Why can't I edit attribute table imported through 'text as layer' I imported the coordinates from an Excel table. They show as single points as intended. Now I want to add columns to the attribute table, but I'm not able to edit it. I wanted to import the following columns from Excel as well, but that doesn't seem to work either.  Sorry for the noob-question, but I couldn't find anything relating the theme through google and such.  Ok, with pictures then: I want to use that to add columns with information to these       You see, the small pensil thingy is greyed out, so I can't edit anything in this layer and I can't add any information to my points.  If I try Ale suggestion I get this error: Is my ESTA valid for a second trip? I visited the USA in May this year, on an ESTA which I applied for in April. It was approved and I was allowed entry into the country.    I'm re-visiting again this November for two weeks. Am I able to use the same ESTA again or do I need to re-apply for a new one? I know it says it's valid for two years, but is that valid for every use within those two years, or I have to use it within two years, and once I have visited on that visa, it's invalid? How to find the frequency and type of my current RAM? How shall I find out the frequency and type of my current RAM? My OS is Ubuntu 12.04. How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$? I am able to evaluate the limit $$\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$$ for a given $n$ using l'Hôspital's (Bernoulli's) rule.  The problem is I don't quite like the solution, as it depends on such a heavy weaponry. A limit this simple, should easily be evaluable using some clever idea. Here is a list of what I tried:   Substitute $y = x - 1$. This leads nowhere, I think. Find the Taylor polynomial. Makes no sense, it is a polynomial. Divide by major term. Dividing by $x$ got me nowhere. Find the value $f(x)$ at $x = 1$ directly. I cannot as the function is not defined at $x = 1$. Simplify the expression. I do not see how I could. Using l'Hôspital's (Bernoulli's) rule. Works, but I do not quite like it.   If somebody sees a simple way, please do let me know.    Added later: The approach proposed by Sami Ben Romdhane is universal as asmeurer pointed out. Examples of another limits that can be easily solved this way:   $\lim_{x \to 0} \frac{\sqrt[m]{1 + ax} - \sqrt[n]{1 + bx}}{x}$ where $m, n \in \mathbb{N}$ and $a, b \in \mathbb{R}$ are given, or $\lim_{x \to 0} \frac{\arctan(1 + x) - \arctan(1 - x)}{x}$.   It sems that all limits in the form $\lim_{x \to a} \frac{f(x)}{x - a}$ where $a \in \mathbb{R}$, $f(a) = 0$ and for which $\exists f'(a)$, can be evaluated this way, which is as fast as finding $f'$ and calculating $f'(a)$.  This adds a very useful tool into my calculus toolbox: Some limits can be evaluated easily using derivatives if one looks for $f(a) = 0$, without the l'Hôspital's rule. I have not seen this in widespread use; I propose we call this Sami's rule :). Saving image from PHP URL What happened to these edits (and the associated reputation)? My reputation rating on SO took this hit an hour ago, and it is due to what appears to be the simultaneous deletion of multiple questions.  I am uncertain why it happened, am concerned, and would appreciate an explanation.  Going to  shows that it was removed due to moderation.  Was a script run deliberately, or were we hit with a question deletion attack; what happened?  -12     today -2  1 hour ago  removed     How to send a 2d Vector over UDP in c++ -2  1 hour ago  removed     How do I use the Eclipse debugger to debug a Java application? -2  1 hour ago  removed     PHP string error; inconsistency with local and server -2  1 hour ago  removed     Unable to start the MySQL service after a server migration -2  1 hour ago  removed     How to use Java to print a text file on a ticket printer? -2  1 hour ago  removed     How can all of the ZBrush Obj files be imported to make a complete model? Suppose that $f : \mathbb{C} \to \mathbb{C}$ is entire. Let $\Omega = \{ z : \frac{1}{2} &lt; |z| &lt; 2\}$. Furthermore, suppose that $ \mathcal{F} = \{f(kz) : k \in \mathbb{C}\}$ is a normal family of analytic functions defined on $\Omega$; the family $\mathcal{F}$ is normal on $\Omega$ iff each sequence from $\mathcal{F}$ has a subsequence converging uniformly on compact subsets of $\Omega$. Prove that $f$ is a polynomial.  I'm studying for my qualifying exam in complex analysis, and this question appears on an old exam. Usually, when I want to show that some entire $f$ is a polynomial, I just try to show that there exists some $N$ so that $f^{(k)}(0) = 0$, all $k \ge N$, but I'm having trouble getting that strategy to work here. I've been looking at the sequence $f(\frac{z}{n})$ trying to make something work, but have not had any success.   I would prefer to receive a hint or two, and then I'll try to post my own solution. Thanks in advance! The limit of a complex integral If $f(z)$ is continuous in the neighborhood of the point $z=a$, then $$\lim_{r\to 0^+} \int_{\vert z-a\vert =r} \frac{f(z) dz}{z-a}=2\pi i\,f(a)\tag{1}$$  In my desperate intents of proving the above exercise, I tried to prove a 'particular' case of it, which is when $z=0$.   So if $z=0$ and as $f$ is continuous on a neighborhood of zero, given $\epsilon&gt;0$, there exists $\delta&gt;0$ such that $|f(re^{i \theta})-f(0)|\le \epsilon$ for $r\in[0,\delta)$ and $\theta\in\mathbb R$. Hence,  $\left\lvert\int_{0}^{2 \pi}(f(re^{i \theta})-f(0))d\theta\right| &lt;2\pi\epsilon \Rightarrow \limsup_{r\to0}\left\lvert\int_{0}^{2 \pi}(f(re^{i \theta})-f(0))d\theta\right| \le2\pi\epsilon.$  If $\epsilon\to0$, then $\limsup_{r\to0}\left\lvert\int_{0}^{2 \pi}(f(re^{i \theta})-f(0))d\theta\right|=0 \Rightarrow \lim_{r\to0}\int_{0}^{2 \pi}(f(re^{i \theta})-f(0))d\theta=0.$  Is this proof correct?  How can I make the proof for $(1)$ following the 'particular proof'? Can someone help me? I installed Android studio some time ago using the following suggested method:     To set up Android Studio on Linux:      Unpack the downloaded Tar file,   android-studio-ide--linux.zip, into an appropriate location   for your applications. To launch Android Studio, navigate to the   android-studio/bin/ directory in a terminal and execute studio.sh. You   may want to add android-studio/bin/ to your PATH environmental   variable so that you can start Android Studio from any directory.   Follow the links to install the SDK outside of the Android Studio   directories.   For whatever reason it has become corrupt and insists I must un-install and re-install. I can't for the life of me find how to un-install it however.  I didn't use apt-get so I can't do apt-get remove.  Does anyone have any suggestions? Find the tangent lines to the graph of $x^2+4y^2 = 36$ that go through the point $P=(12,3)$ I was solving a few problems from a textbook and I came across this one:     Find the tangent lines to the graph of $x^2+4y^2 = 36$ that go through   the point $P=(12,3)$   I could find the tangency points $$ but my solution was completely messy (I had four equations that I had to go back-and-forth with.  Is there an elegant/simple solution to that?  Tangency points:  $$P_1 = (0,3)$$ $$P_2 = \left( \frac{24}{5} , 3-\frac{24}{5} \right)$$ I'm giving training to a large group of people remotely and will be covering a number of application shortcut keys.  I've seen 's on-screen display of keystrokes; is there a similar product for Windows?    The other features of MousePose (fancy mouse pointers, etc.) aren't really useful to me, just the OSD of key presses. So what does Cyanogen Inc shutting down mean for CyanogenMod and similar ROMs? So Cyanogen Inc (cyngn), known for their support for their support for CyanogenMod and their efforts to integrate Cyanogen OS into devices such as the OnePlus One, Alcatel POP Mirage, and . Cyanogen Inc just recently .  What does this mean for CyanogenMod, Cyanogen OS, and the devices which originally shipped with Cyanogen OS? Will they no longer receive OTA updates? When my receiver that I have hooked up to my pc turns on it causes my monitors to turn black is there a way to stop this?