Question: A floor is paved with rectangular bricks each of length $a$ units and breadth $b$ units. A circular disc of diameter c is thrown on the floor. Show that the probability that it falls entirely on one brick is $\frac{(a-c)(b-c)}{ab},( c&lt;a, c&lt;b)$   I tried to solve but ended up getting $\frac{\pi^2}{4ab}.$ What am I missing?Help!
A floor is paved with rectangular marble blocks,each of length $a$ and breadth $b$.A circular block of diameter $c(c&lt;a,b)$ is thrown on the floor at random.Show that the chance that it falls entirely on one rectangular block is $\frac{(a-c)(b-c)}{ab}$  I thought over this problem,i found total number of cases as area of rectangular marble block,but i cannot find the favorable number of cases.Favorable number of cases cannot be area of rectangular marble block$-$ area of circular block,as the answer suggests.What should be the correct logic,please help.
How can I run a script that starts before my login screen? I was calibrating my touch screen, and saw that the best tool around was xinput_calibrator. So I used it. It have two options (one of which did not work), so I am here for the second. It says I should execute this command "in a script that starts with your X session":  xinput set-int-prop "3M 3M USB Touchscreen - EX II" "Evdev Axis Calibration" 32 14410 2146 14574 2115  So I tried ~/.xinitrc, ~/.xsession and ~/.xsessionrc, all of which did not exist. So I created them and the exact content was this command. The first two files made my logins fail (after I login, I fall back to the login screen).  With the last file, the calibration was functional, but only after logging in...  I need that command to run before the login dialog shows up. I thought of adding this command to the end of /etc/X11/xinit/xinitrc with no result (nothing changed). Also, I tried to add it to the end of /etc/X11/Xsession.d/40x11-common_xsessionrc (after inspecting some of the files), but the result was exactly the same as adding it to ~/.xsessionrc.  How can I make this command run before the login screen shows (is this before the window manager starts, or before the X session starts)?  (I am running Kubuntu with the default window manager, if that matters)  UPDATE As I am using Kubuntu, my display manager is kdm. As the accepted answer suggests, I edited the file /etc/kde4/kdm/Xsetup, and as mentioned  I added the command before the command that is there by default. And it works like a charm :) What kind of "mathematical object" are limits? What does "bad girls go backstage" mean? (sorry for my poor English)  I saw this phrase somewhere but I don't know what this means..     Good girls go to heaven, bad girls go backstage   What means 'bad girls go backstage'?   Maybe.. it's when good girls try to be good, but bad girls become famous?  Am I right? How to find out who called a method? How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$ Show that $2730\mid n^{13}-n,\;\;\forall n\in\mathbb{N}$   I tried, $2730=13\cdot5\cdot7\cdot3\cdot2$  We have $13\mid n^{13}-n$, by Fermat's Little Theorem.  We have $2\mid n^{13}-n$, by if $n$ even then $n^{13}-n$ too is even; if $n$ is odd $n^{13}-n$ is odd.  And the numbers $5$ and $7$, how to proceed? Java - Splitting a CSV file into an Array Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$ Given that $xyz=1$, prove that $$\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le\frac{3}{2}.$$  I proved this with , but: is there a better/more elegant way? Change desktop background to a solid color (e.g. pitch black) in GNOME 3 This is a bit of a more unusual bug to report:    The screenshot above is unedited - the black box is rendered by the Stack Exchange application.  Phone:  running Android 4.0.4 (ICS) I am trying to convince my friend that the integral of $0$ is $C$, where $C$ is an arbitrary constant. He can't seem to grasp this concept. Can you guys help me out here? He keeps saying it is $0$. After I deleted my Ubuntu partition, I rebooted my computer and I only get a prompt:   grub rescue &gt;   The command ls lists   (hd0) (hd0,msdos5) (hd0,msdos3) (hd0,msdos2) (hd0,msdos1) (hd1) (hd1,msdos1)   I check them one by one:  ls (hd0,msdos5)/ ls (hd0,msdos1)/   But I cannot find the right partition. Mac OS X Darwin: how to reset admin password? Today I bought an ibook G4 from a garage sale. The people who sold it to me didn't know the password for the 2 accounts on it. Apparently it was the guys late father's laptop. Any suggestions on how to get into the laptop and set a new admin account and password? How to run .sh script with keybind Why "a user" instead of "an user"? I am getting confused while using an article an. Because an is used while referring to vowels (a,e,i,o,u).  But today I read an article where for user they used a user.  My question is, why was an not used?  Could someone explain this with an example? This has been , but a long time ago, and got closed for a rather confusing reason (converting comments to answers is not an "exact duplicate" of converting answers to comments), so I'm going to bring it up again.  I think it makes sense to have a user (not asker) option to convert a comment they posted on a question to an answer on the question, if it turns out it led to the asker figuring out the answer. We've all seen askers reply to comments with "@foo Hey, that was it! Post that as an answer and I'll accept it"; why not make it simple for the user to do that? It seems trivial to implement, and there's no formatting issues like there is going from answers to questions. I'm not sure how it could be "abused", because you need less rep to answer a question than to comment on it. I don't know if the answer's post time should be the time of the comment or the time it was converted; I think probably the latter. I also don't know if the comment should be deleted, left alone, or replaced with a link to the answer; again I think probably the last How to insert HTML to PHP DOMNode? What is the true origin of the orcs? There are a bunch of theories about the true origin of the orcs. Tolkien tried out a few different origins for his Orcs throughout his life but died before he could fully revise The Silmarillion with his final view on their origins and nature.   There is a list of origins proposed by Tolkien():   Made of stone and slime through the sorcery of Morgoth; East Elves, where The Silmarillion contains a suggestion that Orcs are descended from East Elves captured by Melkor, their minds and bodies distorted and corrupted. Sentient beasts, another of Tolkien's theories proposes that Orcs may have begun as soulless animals of vaguely humanoid shapes, empowered by the will of the Dark Lord (Morgoth) and learning language only as parrots do. Fallen Maiar, there are hints in the History of Middle-earth series of books, (especially in Morgoth's Ring in the section "Myths Transformed"), that some Orc leaders, such as the First Age's Boldog, or the Great Goblin encountered by Bilbo and the Dwarves, may in fact have been fallen Maiar which had taken Orc form. Corrupted Men, while Tolkien at some point saw all Orcs as descended from the original corrupted and tortured Elves, later comments of his indicate, according to Christopher Tolkien in Morgoth's Ring "Myths Transformed" text X, that he began to feel uncomfortable with this theory. At about the same time he removed the references to the Thrall-Ñoldorin, he also began searching for a new origin for the Orcs. It seems Tolkien wanted to change the origin of the Orcs to make them corrupted and twisted Humans.  A mix of corrupted Elves and Men, A late idea of Tolkien seems to be that Orcs (or Orks, showing the late spelling change) had a mixed origin of Elves and Men. Some cross-bred with Men, Tolkien also suggested that Men were cross-bred with Orcs under Morgoth's lieutenant, Sauron (and possibly under Morgoth himself). The process was later repeated during the War of the Ring by Saruman. This possibly refers to the way the Uruk-hai and the Half-Orcs were created, in The Lord of the Rings.   Of all these theories, which is the most accepted, and which did Tolkien agree with the most? I always thought that orcs were made of East Elves, as explained in The Lord of The Rings, but the story goes beyond this, there are the stories in many other books that explain different things.  What can you tell me about this? How quickly does the Ultimate Meter fill up? The information on the :     Ultimate abilities are powerful abilities only available to a hero   once their Ultimate Meter has filled. Progress towards an Ultimate   persists through death. The Ultimate Meter fills by killing/dealing   damage to enemy heroes, though Mercy gradually fills hers through   healing with her Caduceus Staff, and Torbjörn's turret generates   Ultimate progress for him. The amount of Ultimate gained appears to   vary between heroes, and kills seem to grant less Ultimate than   dealing damage.   Nowhere does it explain how quickly the meter is gained, and what % of meter corresponds to damage.  I know that in addition to that, meter is also passively gained for all heroes, albeit very slowly. What is the rate of that passive Ultimate meter? How does damage correspond to ultimate meter %? Understanding Euclid's proof that the number of primes is infinite. In Euclid's proof, if $p_1, p_2, \dots, p_n$ are the only primes then $p_1 \times p_2 \times \dots \times p_n + 1$ is not divisible by any of $p_1, p_2, \dots, p_n$ (because of some algebraic facts), which makes another prime and is a contradiction.   The proof makes sense logically, and I tried some numerical examples to "feel" the proof better but...  $2 \times 3 \times 5\times 7\times 11\times 13+1$ is not a prime! $2 \times 3 \times 5\times 7\times 11\times 13 \times 17+1$ is also not prime! Why is the general case proof is not working for these examples? Collection was modified; enumeration operation may not execute I can't get to the bottom of this error, because when the debugger is attached, it does not seem to occur.  Collection was modified; enumeration operation may not execute  Below is the code. This is a WCF server in a Windows service. The method NotifySubscribers() is called by the service whenever there is a data event (at random intervals, but not very often - about 800 times per day). When a Windows Forms client subscribes, the subscriber ID is added to the subscribers dictionary, and when the client unsubscribes, it is deleted from the dictionary. The error happens when (or after) a client unsubscribes. It appears that the next time the NotifySubscribers() method is called, the foreach() loop fails with the error in the subject line. The method writes the error into the application log as shown in the code below. When a debugger is attached and a client unsubscribes, the code executes fine. Do you see a problem with this code? Do I need to make the dictionary thread-safe? [ServiceBehavior(InstanceContextMode=InstanceContextMode.Single)] public class SubscriptionServer : ISubscriptionServer {     private static IDictionary&lt;Guid, Subscriber&gt; subscribers;      public SubscriptionServer()     {                     subscribers = new Dictionary&lt;Guid, Subscriber&gt;();     }      public void NotifySubscribers(DataRecord sr)     {         foreach(Subscriber s in subscribers.Values)         {             try             {                 s.Callback.SignalData(sr);             }             catch (Exception e)             {                 DCS.WriteToApplicationLog(e.Message,                    System.Diagnostics.EventLogEntryType.Error);                  UnsubscribeEvent(s.ClientId);             }         }     }          public Guid SubscribeEvent(string clientDescription)     {         Subscriber subscriber = new Subscriber();         subscriber.Callback = OperationContext.Current.                 GetCallbackChannel&lt;IDCSCallback&gt;();          subscribers.Add(subscriber.ClientId, subscriber);                  return subscriber.ClientId;     }      public void UnsubscribeEvent(Guid clientId)     {         try         {             subscribers.Remove(clientId);         }         catch(Exception e)         {             System.Diagnostics.Debug.WriteLine(&quot;Unsubscribe Error &quot; +                      e.Message);         }     } }