Plot two graphs in the same plot
Plotting two variables as lines using ggplot2 on the same graph
Chromium on Ubuntu 12.04. Youtube says:     This video is currently unavailable   I don't know why but this is the case for some videos, but not all. Well, most videos. And I don't know what's wrong.  Anyone help? I just notice it now as I am new to Illustrator.  When I am in RGB mode, blending transparency seems to be easier as mode such as Screen, Multiply or Overlay looks good naturally.  If I switch the document mode to CMYK then the image is getting messed up.  I'd like to know, if CMYK is not ideal for blending options? If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$. Exercise 11, page 45 from Hungerford's book Algebra.     If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every   subgroup of $H$ is normal in $G$.   I am trying to show that $a^{-1}Ka\subset K$, but I got stuck. What I am supposed to do now?  Thanks for your kindly help. How to download an MP3 track from a YouTube video How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$? I have to compute this integral $$\int_{0}^{\infty} \frac{dt}{1+t^4}$$ to solve a problem in a homework. I have tried in many ways, but I'm stuck. A search in the web reveals me that it can be do it by methods of complex analysis. But I have not taken this course yet. Thanks for any help. Im using a program called Daisy Disk to see what is taking up space in my Mac and I find that the /cores directory is taking up 77gb.   Is that a problem? Can I get rid of it to regain the space? What is a plain English explanation of "Big O" notation? I'd prefer as little formal definition as possible and simple mathematics. Including the interaction but not the main effects in a model Is it ever valid to include a two-way interaction in a model without including the main effects?  What if your hypothesis is only about the interaction, do you still need to include the main effects? Custom Cursor Image CSS I have a number of heroshot images, that have a modal popup when clicked.  I'm trying to get my cursor to turn into  magnifying glass whenever it is moved over the image. The following CSS does not appear to work even though my magnify.cur is present in the right location.  a.heroshot img {   cursor:url(/img/magnify.cur), pointer; }   Has anyone ever done anything similar? I don't mind a JavaScript solution if one exists.  EDIT: It works in Safari, but not in Firefox. I want to have my super key start dmenu. I have set it as a keyboard shortcut in my rc.xml as follows:  &lt;keybind key="0xffeb"&gt;       &lt;action name="Execute"&gt;         &lt;command&gt;dmenu_run&lt;/command&gt;       &lt;/action&gt; &lt;/keybind&gt;   I tried specifying it in the key attribute as W, W-, and 0xffeb, but none of these worked. W responds to pressing the letter w, and the others appear to do nothing.  I want the shortcut to trigger when the super key is pressed and released on it's own. Is this possible?    This is  from super user as per the . I've read this question: , but I didn't see any useful information in it. I need a little hint in a proof on convergence of a sequence. The problem I have is: Suppose $(x_n)$ is a monotone decreasing sequence of real numbers such that $\sum x_n$ converges, prove that:  $$\lim_{n \to \infty} nx_n=0$$  My idea is: proving this fact aims to prove that given $\epsilon &gt;0$ there's some natural $n_0 \in \mathbb{N}$ such that if $n &gt;n_0$ we have $|nx_n|&lt;\epsilon$.  Now, I know that $\sum x_n$ converges, so that given $\epsilon'&gt;0$ there's some $k_0 \in \mathbb{N}$ such that if $k &gt; k_0$ we have:  $$\left|\sum_{i=1}^{k}x_i - S\right|&lt;\epsilon'$$  Where $S = \sum x_n$. Now, since $(x_n)$ is monotone decreasing we know that we must have $x_1 &gt; \cdots &gt; x_k$ so that the sum of all $x_i$ should be less or equal to $k x_k$. So I know that I have:  $$\left|\sum_{i=1}^{k}x_i - S\right|\leq\left|\sum_{i=1}^{k}x_i\right|+|S|\leq|kx_k|+|S|$$  I feel that the proof will come from this, however I'm stuck at this point. Can someone give just a little hint on how to proceed from here?  Thanks very much in advance for your help. How does the subject-verb agreement work when a singular noun describes a plural one? Of the following, which sentence is righter?  The computers is a good choice. The computers are a good choice.  Is there a rule about these types of formations? Please explain. Distance between two hyperplanes I have two parallel hyper planes $$a^Tx=b_1,a^Tx=b_2$$ where $a \in \mathbb{R}^n, x \in \mathbb{R}^n ,b \in \mathbb{R}$ and I want to find the distance between the two. I have read that the distance between the two hyperplanes is also the distance between the two points $x_1$ and $x_2$ where the hyperplane intersects the line through the origin and parallel to the normal vector $\vec a$. These points are given by $$x_1=\frac{b_1}{\|a\|^2_2}a$$ and $$x_2=\frac{b_2}{\|a\|^2_2}a$$ Then the distance is $|x_1-x_2|$ but I don't really understand how we got $x_1$ and $x_2$. When having a number of files opened in Texmaker, at the top of editor pane, there is a drop down panel with the names of open documents in it. I prefer to have tabs of open documents at the top of editor pane, similar to Texstudio and Winedt. Is there a way that I can change this setting? I've just upgraded to Ubuntu 17.10 and am missing the Ubuntu Dock settings, i.e. in gnome-control-center the dock settings are blank:    I think I might be missing the "ubuntu-dock" package, but can't find this anywhere in the software centre.  Also the gnome-control-center was completely missing after the update, and I had to install this separately - not sure if this is related.  I think this is different from  because changing the type of GNOME session doesn't fix the problem. If I go for GNOME* I get no Dock settings section at all, and if I got for Ubuntu* I get the blank Dock settings section described above.  Output of apt-cache policy gnome-shell-extension-ubuntu-dock:  rob@rob-pc:~$ apt-cache policy gnome-shell-extension-ubuntu-dock gnome-shell-extension-ubuntu-dock:   Installed: (none)   Candidate: 0.7   Version table:      0.7 500         500 http://gb.archive.ubuntu.com/ubuntu artful/main amd64 Packages         500 http://gb.archive.ubuntu.com/ubuntu artful/main i386 Packages In the film and book series, Year 4 (Goblet of Fire), how is it Mad-Eye Moody/Barty Crouch could see Harry through his Magical Eye even when he was under the Invisibility Cloak?  As the cloak is a True Invisibility cloak, immune to charms and spells, and according to legend invisible to even Death, how did Mad-Eye detect Harry Potter under the cloak? How Nagini and Mrs. Norris were able to sense Harry were through other senses, such as smell and warmth, but not visually.  I'm referring to the scene/chapter where Snape follows Harry at night. Harry hides under the Invisibility Cloak but his foot is stuck at the broken staircase. Eventually Mad-Eye arrives, sees Harry through his Magical Eye, and talks Snape away. When working with radios, I've seen the term "dBm". What does this mean?  The  gives a table showing the equivalent power in Watts. Is the dBm output just the power level of a transmitter?  How does this differ from signal strength measured in dB? How do I set focus follows mouse? Is there a way to set up "focus follows mouse" behavior in Unity? Query for list of attribute instead of tuples in SQLAlchemy DNS, multiple nameservers and geolocation? Currently, when a DNS client makes a request for a DNS record (say, www.example.com., it needs to traverse the DNS tree. It asks the root servers for the location of com., which it then asks for the location of example.com., which it then asks for the location of www.example.com.. Thankfully, much of this is cached.  If example.com. has multiple, geographically diverse NS records listed, my understanding is that these are listed in random order to avoid all queries going to the first (or last) NS record listed.  This would appear to imply that a DNS resolver in Australia could choose a NS record for a nameserver that's located far away, perhaps in Europe, when there may be another authoritative nameserver that is much closer.  So, my question is: Is there any provision within the DNS spec to allow DNS resolvers to select an authoritative nameserver that's local to them? The only way I can see to achieve this is to have the NS records behind an anycast address and do local resolution that way. Would this work? Is there any other option?