This is for my combinatorics class so I took the  approach that we've been taught in class, though we haven't been showed how to do it for a pair of equations. So the second question can be solved by $${7 + 2\choose 2}$$, given that I can substitute back into my first question so $$(x_1 + x_2 + x_3 ) + x_4 + x_5 + x_6 = 20 $$ Treating the second equation as one we can solve the first equation through $${13 + 2\choose 2} $$ Since both equations are indep. of each other, we need to multiply them. Is this right or have I completely butchered it? Thank you in advance for your time
How many nonnegative integer solutions are there to the pair of equations  \begin{align}x_1+x_2+\dots +x_6&amp;=20  \\ x_1+x_2+x_3&amp;=7\end{align}  How do you find  non-negative integer solutions?
Will higher temperatures damage a computer over time, even when not reaching max? How to mount a NTFS partition in /etc/fstab? I have two partitions that I want to mount on startup: /dev/sda3   /mnt/devel  ext4    defaults    0   2 /dev/sda2   /mnt/excess ntfs    defaults    0   2  The ext4 partition mounts fine (owned by me, writable only by me), but the NTFS mounts owned by root with R\W permission for all. How to fix this? drwxr-xr-x  7 amanda amanda 4096 2012-03-14 19:07 devel drwxrwxrwx  1 root   root   4096 2012-03-14 22:38 excess Typesetting a function defined by case analysis Can any one suggess me the code to write this equation in LaTeX. What steps must an educational institution wanting to recruit good faculty take? There is a cycle in the academia:    Good doctorates from top universities invariably join other top universities as faculty members.  Good students aspire to study in top universities under excellent faculty members.   Suppose a new educational institution or department springs up and desires to set up a top-quality group, how does it break into this cycle? I suppose this could take some years, but is money-power the only thing that could be wielded by the institute to achieve its end? Changing Login Logo After modifying the code in my functions.php file to display a different logo on my login page, I'm getting a blank square instead.  I've added a custom .png image (326x67) to my (child) theme's image folder, and the code I've added to functions.php is as follows:  function custom_loginlogo() {     echo '&lt;style type="text/css"&gt;     h1 a {background-image: url('.get_bloginfo('template_directory').'/images/login_logo.png) !important; }     &lt;/style&gt;'; } add_action('login_head', 'custom_loginlogo');   Could it be a permissions problem (like an .htaccess file blocking the image)? How can I unlock my phone? I locked it using Android Device Manager, but it claims I entered a wrong password I have an Samsung Galaxy S3 Neo.  Bus 002 Device 042: ID 04e8:6860 Samsung Electronics Co., Ltd GT-I9100 Phone [Galaxy S II], GT-I9300 Phone [Galaxy S III], GT-P7500 [Galaxy Tab 10.1]   The keyboard &amp; language setting is português.  I today installed Android Device Manager and to test it's functionality I locked the phone with the password: "abcd" (4 letters were required).  After entering the password and confirming with the "OK" button of my keyboard, the phone showed me that the password is wrong. "Senha incorreta".  I reset the password after some tries to "123456" and the phone reloaded the lock screen. Again the password showed up to be wrong. I also tried the alphabetic password: "abcdefg" - same error.  I changed the language of my Google account from German to Portuguese and reset the password to "123456" again and I tried to really reboot my phone and unlock the SIM card again. But anyways I can not get through my lock of the Android Device Manager.  I tried to enter the password 35 times wrong with hope to get a chance to authenticate with my Google Account login.  I also tried to connect the phone with adb but it does not show up in this state with:  adb devices   So what can I do to get access to my phone again? We are developing a new Lightning Community to replace our Partner Community. However, when we use our visualforce pages with LightningStylesheets=true on the Lightning Community, the Lightning styling is not applied.  I understand that this is the case because Lightning Communities are not Lightning Experience.  Is there a way to force LightningStylesheets anyway? I am trying to stay away from having to rebuild/restyle all our legacy visualforce pages. When my phone starts up there are several application/services running in the background that I would rather not.  And when I press the Home button while using an app, that app usually goes into the background without exiting.  How can I stop these apps from running? What's the best way to extend the User model (bundled with Django's authentication app) with custom fields? I would also possibly like to use the email as the username (for authentication purposes).  I've already seen a   to do it, but can't decide on which one is the best. File and directory comparison tool? I'm looking for something that will compare directories and files like Beyond Compare does for windows.  Its mainly for use of source control, but I need to use it for deployment as well. I can easily find files with given string in name:  me@comp:/usr/local/hydra/hydra-7.4.2$ find -D stat -name "*hack*" ./hack881663129.txt ./hack881663129_7.txt ./hack881663129_5.txt ./hack881663129_4.txt ./hack881663129_4_7.txt ./hack881663129_6.txt ./hack881663129_1_6.txt ./hack881663129_8.txt   How can I also print file details, like size, date of creation etc.? How to write a survey paper? Full List of inventory items After beating the game, I still have several empty inventory spots.  I most likely missed several items in my addicted frenzy to finish the game.  What are all the items that can be found in the game? And where can they found? Background  My Lenovo X250 is arriving in two weeks, which according to  will work well only with "a special image of Ubuntu pre-installed by the manufacturer."   points out that the X250 has "Excellent" compatibility to the Linux OSes they install. On the other hand, a quick search on  or  shows that a standard image of Ubuntu on the X250 is rife with hardware problems.  Ubuntu Certified Hardware acknowledges this for the X250: "Standard images of Ubuntu may not work at all on the system or may not work well." This  clearly shows the difference between an Ubuntu standard image installation and the one that comes pre-installed by the manufacturer. Hardware seems to work fully on the OEM version.  Question  Any idea where we may access or download these "special images of Ubuntu"?  (Hopefully not only for the X250, but also for the other systems out there.) How does one write on the outside of a circle?  I am looking for sample files/packages which imitate a magazine lay-out. Specifically a page with two columns having a circular picture between the two columns.    Example of the desired layout, created using Word: Value of having done applied math research when applying to PhD programs in pure math I will be a second year math under-grad in September, and currently doing an internship at applied math research institute. Most probably, I will come up with a research paper at the end of the internship.  However, my interest after my bachelors is to do PhD in pure math from a top math school.My question is this:     Would the admission committee consider my current research since it is in applied math?    In addition, if anyone can suggest me some ideas on how can I bridge the gap between my paper in applied math and my interest in analysis, I would be extremely grateful.  P.S.:  is a related but different question also of mine. Let $f(z)$ be entire function. Show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function using Maximum Modulus theorem Let $f(z)$ be entire function. Consider the functions $e^{if(z)}$ and $e^{−if(z)}$ and applying the Maximum Modulus Theorem, show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function.  (We take $f(z)=u(z)+iv(z)$)  I am confused as so far I have $|g(z)|=|e^{if(z)}|=|e^{-v(z)}|$ and then since $f(z)$ is real, $f(z)=u(z)$ and $v(z)=0$ so I assumed it would follow that $|g(z)|=|e^{v(z)}|=1$.  Similarly, $|g(z)|=|e^{-if(z)}|=|e^{v(z)}|=1$.  Using Liouville I assumed one could say that both $g(z)$ and $h(z)$ are bounded entire functions, they are constant and so it follows that $v(z)$ is constant, meaning that both its partial derivatives are equal to 0 and, due to Cauchy Riemann, both of the partial derivatives of $u(z)$ are equal to zero.  It would then follow that $f(z)$ is constant.  I don't know how to go about the question using the Maximum Modulus Theorem, also I feel I am overlooking the importance of $|z|=1$ perhaps?  Any help would be much appreciated!! creating a tar archive without including parent directory I am trying to create a graphical program for my script.  Inside the script I use tar to create a tar archive.  From the graphical program I get the full name of file that I want to create a tar archive.  tar -cvf temp.tar /home/username/dir1/dir2/selecteddir    My tar archive includes home, username, dir1, dir2 and selecteddir while i want tar to create archive only including selecteddir. "Inspirational" quote at start of chapter I have a desktop (Ubuntu 13.04 &amp; Win 7 Home Premium) and a Laptop (Ubuntu 12.04), both having WiFi adapters. I also have a WiFi router connected to internet which both my computers can access.  I want to share files between my desktop and my laptop using WiFi (similar to Homegroup on Windows 7 but without using Ethernet cables).  How do I set-up that?  I want to share files using both OSs, if anyone have have information about sharing files with any of the OS please answer!