On his left or to his left
"To your left" versus "on your left"
What counter balances gravity here? Lets consider a stone tied to one end of a massless and unstretchable string... Now if i'll start rotating, it will form a conical pendulum &amp; then the equilibrium is achived when the pendulum attains horizontal circular motion.... Now to maintain that state we give a constant force to string.... Here, which force counterbalances gravity? Is it the torque due to applied force cancels out the torque due to gravity?  The angle θ changes from 0 to 90° How to show that $f$ is differentiable at $x=0.$ How to fix pagination for custom loops? If there is one noble left in line and you play "fled to England" to discard it (thus, ending the day) do you collect a noble from the new day? Single word to denote date and time I want one word that means Date and Time. For example in "the date and time of the event will be announced later" I want to use single word instead of "date and time" How many Marvel Earths (Universes) are there? My host is x64 bits Windows 8.1.  I downloaded the latest Virtual Box (4.3) and I'm trying to create a VM with a 64 bits Ubuntu OS (ubuntu-12.04.3-desktop-amd64).  When I go to New VM wizard, it doesn't give me option to select "Ubuntu (x64)" as I have seen in other people's screenshots, only just "Ubuntu". As a result, the ISO can't boot. I tried in another PC and Virtual Box gives the x64 variants to most listed OS...  Control Panel shows x64 OS, x64 processor. My host laptop is a Sony Vaio VPCZ22UGX/N, Intel® Core™ i7-2640M processor. CPUz shows Vx-t is available on my processor, of course.  Here is what I tried so far:   I enabled IO APIC as required in the docs. I have virtualization enabled in the BIOS. It works fine in VMware. Check that Hyper-V is not running or even installed on my Windows. Same for VMware. I also tried running the command:  VBoxManage modifyvm [vmname] --longmode on    for that VM, but no change.. I think the issue is really that I can't select x64 variant of the Ubuntu OS for that VM. Other people seem to indicate that's a requirement, but I don't get that option for some reason.  I spent a lot of time and can't find what's wrong... Anyone knows what could be missing here?  Thank you very much!!  Eduardo Where is it preferred to place the answer to duplicate questions? We all know you can't do the following because of ConcurrentModificationException:  for (Object i : l) {     if (condition(i)) {         l.remove(i);     } }   But this apparently works sometimes, but not always. Here's some specific code:  public static void main(String[] args) {     Collection&lt;Integer&gt; l = new ArrayList&lt;&gt;();      for (int i = 0; i &lt; 10; ++i) {         l.add(4);         l.add(5);         l.add(6);     }      for (int i : l) {         if (i == 5) {             l.remove(i);         }     }      System.out.println(l); }   This, of course, results in:  Exception in thread "main" java.util.ConcurrentModificationException   Even though multiple threads aren't doing it. Anyway.  What's the best solution to this problem? How can I remove an item from the collection in a loop without throwing this exception?  I'm also using an arbitrary Collection here, not necessarily an ArrayList, so you can't rely on get. I'm using 17.04 ( Clean Install ), and as far as I remember, every try to install any sofware- it fails with that error code.  I tried sudo apt-get update &amp;&amp; apt-get upgrade and problem persists.  any idea why?   edit: Using software Updater gave this result :   edit : output of update  guy@LG-LAPTOP:~$ sudo apt-get update &amp;&amp; apt-get upgrade [sudo] password for guy:  Ign:1 http://il.archive.ubuntu.com/ubuntu zesty InRelease Ign:2 http://il.archive.ubuntu.com/ubuntu zesty-updates InRelease               Ign:3 http://il.archive.ubuntu.com/ubuntu zesty-backports InRelease             Err:4 http://il.archive.ubuntu.com/ubuntu zesty Release                           503  Service Unavailable Get:5 http://security.ubuntu.com/ubuntu zesty-security InRelease [89.2 kB]      Err:6 http://il.archive.ubuntu.com/ubuntu zesty-updates Release                   503  Service Unavailable Get:7 http://archive.canonical.com/ubuntu zesty InRelease [10.2 kB]             Err:8 http://il.archive.ubuntu.com/ubuntu zesty-backports Release                 503  Service Unavailable Get:9 http://archive.canonical.com/ubuntu zesty/partner Sources [1,416 B]       Get:10 http://archive.canonical.com/ubuntu zesty/partner amd64 Packages [1,616 B] Get:11 http://archive.canonical.com/ubuntu zesty/partner i386 Packages [1,612 B] Get:12 http://archive.canonical.com/ubuntu zesty/partner Translation-en [708 B] Get:13 http://security.ubuntu.com/ubuntu zesty-security/main amd64 DEP-11 Metadata [11.7 kB] Get:14 http://security.ubuntu.com/ubuntu zesty-security/main DEP-11 64x64 Icons [9,219 B] Get:15 http://security.ubuntu.com/ubuntu zesty-security/universe amd64 DEP-11 Metadata [14.4 kB] Get:16 http://security.ubuntu.com/ubuntu zesty-security/universe DEP-11 64x64 Icons [31.0 kB] Reading package lists... Done                                          E: The repository 'http://il.archive.ubuntu.com/ubuntu zesty Release' does no longer have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'http://il.archive.ubuntu.com/ubuntu zesty-updates Release' does no longer have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'http://il.archive.ubuntu.com/ubuntu zesty-backports Release' does no longer have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. guy@LG-LAPTOP:~$    output of apt get  guy@LG-LAPTOP:~$ sudo apt-get install putty Reading package lists... Done Building dependency tree        Reading state information... Done The following additional packages will be installed:   putty-tools Suggested packages:   putty-doc The following NEW packages will be installed:   putty putty-tools 0 upgraded, 2 newly installed, 0 to remove and 0 not upgraded. Need to get 661 kB of archives. After this operation, 2,713 kB of additional disk space will be used. Do you want to continue? [Y/n]  Err:1 http://il.archive.ubuntu.com/ubuntu zesty/universe amd64 putty-tools amd64 0.67-3   503  Service Unavailable Err:2 http://il.archive.ubuntu.com/ubuntu zesty/universe amd64 putty amd64 0.67-3   503  Service Unavailable E: Failed to fetch http://il.archive.ubuntu.com/ubuntu/pool/universe/p/putty/putty-tools_0.67-3_amd64.deb  503  Service Unavailable E: Failed to fetch http://il.archive.ubuntu.com/ubuntu/pool/universe/p/putty/putty_0.67-3_amd64.deb  503  Service Unavailable E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing? guy@LG-LAPTOP:~$ My site has 30,000 visits with 86,000 page views. If the bounce rate of 54%, then does it means only 15,000 users generated the 86,000 page views or 30,000 visits generated the 86,000 page views.  My website is www.cricandcric.com  Even though I have got 86,000 page views, my site's Alexa ranking is still getting worse day by day. How do I control that? Is the claim that functions of independent random variables are themselves independent, true?   I have seen that result often used implicitly in some proofs, for example in the proof of independence between the sample mean and the sample variance of a normal distribution, but I have not been able to find justification for it. It seems that some authors take it as given but I am not certain that this is always the case. Accuracy Vs. Precision  What I would like to know is whether I should use System.currentTimeMillis() or System.nanoTime() when updating my object's positions in my game?  Their change in movement is directly proportional to the elapsed time since the last call and I want to be as precise as possible.  I've read that there are some serious time-resolution issues between different operating systems (namely that Mac / Linux have an almost 1 ms resolution while Windows has a  50ms resolution??).  I'm primarly running my apps on windows and 50ms resolution seems pretty inaccurate.  Are there better options than the two I listed?  Any suggestions / comments? Simulating a Brownian Excursion using a Brownian Bridge? How to prevent system applications (like the Software Center) from asking for password? Using `\input` to insert a section of a document into another Let $q \in \mathbb C$, $\|q\|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n: n \in \mathbb N\}$ is dense in $S^1$ Let $q \in \mathbb C$, $|q|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n:  n \in \mathbb N\}$ is dense in $S^1$.  My attempt: As $(q^n)$ is limited, there is subsequence $(q^{n_j})$ convergent. So given $\epsilon &gt; 0, \exists j_0 \in \mathbb N, \quad |q^{n_j} - q^{n_k}| &lt; \epsilon, \quad \forall j,k \geq j_0$. Supose that $n_j &gt; n_k$, then  $|q^{n_j} - q^{n_k}| = |q^{n_k}||q^{n_j - n_k} - 1| = |q^{n_j - n_k} - 1| &lt; \epsilon, \quad \forall j, k \geq j_0$. So, there is a subsequence of $(q^n)$ that converges to $1$.  Using this fact, how can I ensure that for all $w \in S^1$ there is a subsequence of $(q^n)$ that converges to  $w$? Exactly half of the elements of $\mathcal{P}(A)$ are odd-sized Let $A$ be a non-empty set and $n$ be the number of elements in $A$, i.e. $n:=|A|$.  I know that the number of elements of the power set of $A$ is $2^n$, i.e.  $|\mathcal{P}(A)|=2^n$.  I came across the fact that exactly half of the elements of $\mathcal{P}(A)$ contain an odd number of elements, and half of them an even number of elements.  Can someone prove this? Or hint at a proof? I often need to view on the canvas the (selected or not) features from the current active vector layer.  In this situation, I only need to view something on the canvas, without doing anything on the canvas itself (so, the active window is always the Attribute Table).  This is what I usually do:   Open the Attribute Table for the current active layer; Select the first feature; Press Ctrl+P button (i.e. the "Pan map to the selected row" button); Minimize the Attribute Table; View something on the canvas for the current feature; Go to the first step until needed.   Is there a way (a method, a shortcut) for directly browsing every feature on the canvas without the needing of going backwards and forwards with the Attribute Table? I mean, something like a "next" button?  (I may use the workaround of splitting the windows of the Attribute Table and of the canvas within the monitor, or also docking the Atrribute Table, but I would like to work on the full QGIS window).    EDIT I saw that my question was casted as a duplicate of  question. The two questions are very similiar, but I think it should be left as open for two reasons:   the related duplicated question doesn't have an accepted answer; my question is slightly different because I'm looking for the possibility of displaying only the selected features (and the @Joseph's , that I marked as accepted, answers well to my request). Prove if $ p$ is a prime of the form $3n+1$, then $p$ is also of the form $6m+1$ Prove that if $p$ is a prime of the form $3n+1$, $p$ is also of the form $6m+1$.  I guess one could use the division algorithm for this; but, what's the best method?