I have searched but could not find the exact question.  Two circles with radii 5 intersect such that the center of one circle lies on the circumference of another. What is the area of the overlapping region in terms of pi?
Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres of the circles?
Hump, Rump, Lump, Bump I’m referring to the similar definitions of these four nouns – something raised and rounded.  Why do these four rhyming words have similar meanings?  I have not found very specific sources for these words on the  and . Hump is “probably from Dutch homp.” Rump is “from a Scandinavian source,” “from Old Norse rumpr” ultimately from Proto-Germanic “rumpo.” Lump is “perhaps from a Scandinavian source” and finally, Bump is “perhaps from Scandinavian,” “probably of North Germanic origin.”   Could these words come from the same root? Other than the fact that they all might come from northern Europe, the only hint I have in this direction is the following from , tracing the origin of Hump through Dutch, Middle Low German, Old Saxon and Proto-Germanic, to Proto-Indo-European *kumb-, *kumbʰ- (“curved”). Could this PIE root, which is not given in these online sources for any of the other three words, be a common root to all four words? I find myself looking at other –ump words and “seeing” a curved or rounded line: jump (a curved trajectory), grump (a downturned mouth), pump (the action of the pump handle), clump (a rounded clod of earth, not sharp), etc. Am I just seeing this because the words sound similar, or is there something more to my tendency? For example, the  suggests the origin of jump is "perhaps onomatopoeic (cf. bump)" although this view is not echoed on Wiktionary. Is it possible that these words do all share a common root and are simply onomatopoeic variations of each other? Are there other pairs or groups of words like these in English? (Wham! Bam! Ka-blam!) Does     this phenomenon have a name? Global setting of hyphenation for words containing dashes I estimated the sample covariance matrix $C$ of a sample and get a symmetric matrix. With $C$, I would like to create $n$-variate normal distributed r.n. but therefore I need the Cholesky decomposition of $C$. What should I do if $C$ is not positive definite? When app is moved to SD card, where is the app data stored on SD card? When should I use \input vs. \include? Asking the position of a person in a sequence How to ask the position(?) of a president (like 10th) of a country, correctly? Export objects to separate files in Illustrator Why is the $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group realized as the vector space of Hermitian $2\times 2$ matrices? Was The Empire in Star Wars inspired by Nazi Germany? I switch back and forth between two computers constantly:   OSX Snow Leopard  Ubuntu 10.10    I'd like to be able to make Ubuntu use the same keyboard shortcuts as OSX System Wide, for the following keyboard sequences only (ie I don't want to make Ctrl act like Super)   Super+C -> Copy Super+V -> Paste Super+T -> Open a new tab in whatever browser I'm in.  Super+W -> Close a tab in whatever browser I'm in.    So in short, is there anyway for me to map just these keyboard sequences to the following, system wide ?   Super+C -> Ctrl+C Super+V -> Ctrl+V Super+T -> Ctrl+T  Super+W -> Ctrl+W   I know there are ways for me to do this for vim, and Firefox, and I'm sure specifically for most applications... but I would prefer to have to do this just once and have it work that way system wide!  I'm using a standard PC keyboard, that is "Generic 105 key (intl) PC" on Ubuntu. I'm also using the same keyboard on my Mac mini. PUA.Phishing.Bank Found If you are talking on behalf of you and someone else what is the correct usage?  On behalf of my wife and me On behalf of my wife and I On behalf of me and my wife On behalf of myself and my wife On behalf of my wife and myself ...  My understanding is that after that phrase you would carry on talking in first person. Execute bash commands over SSH while staying in interactive mode afterwards Probably it is a weird thing I would like to achieve but: I would like to SSH to a remote host and then execute some bash commands like "alias" automatically to use them afterwards in an interactive mode. The remote host does not allow the personal environment.    Is this possible? Would "expect" do it? Or is there any other way to achieve this? Basically I would like to have my bashrc without modifying any files on the remote host. Are locks unnecessary in multi-threaded Python code because of the GIL? If you are relying on an implementation of Python that has a Global Interpreter Lock (i.e. CPython) and writing multithreaded code, do you really need locks at all?  If the GIL doesn't allow multiple instructions to be executed in parallel, wouldn't shared data be unnecessary to protect?  sorry if this is a dumb question, but it is something I have always wondered about Python on multi-processor/core machines.    same thing would apply to any other language implementation that has a GIL. How do I download torrents? Lightsabers are not made of light, nor have they anything to do with lasers (even if there are people who mistakenly refer to them as "laser swords").   Blaster bolts are also not lasers. They travel significantly slower than light, they travel even slower than ordinary bullets fired by gunpowder. (called slug throwers on the Star Wars universe)  Was there any use of lasers ever presented in the Star Wars universe, either as we use them today, or as weapons?  By laser I mean something which behaves like laser does, even if it's not called by that name in a movie or book. If something is called a laser (in the script or by fans) but clearly doesn't work like a laser (for example, it travels slowly, and in visible blocks) it doesn't count. Ubuntu 20.04 still supporting Python2 Change font size of the verbatim environment I want to apply small fonts inside the Verbatim environment e.g.  {\small  \begin{Verbatim}  1   double x, y; 2   double z, w; 3   main(); 4   return 0;  \end{Verbatim}}   Before the command \small and after the closing braket } text has normal size, which is obvious but the font size should be small inside the brakets.     Why is this command not applied to the environment's contents? This is what I have come up with so far, but I am rather lost at lines 3-4...  $$\begin{align} (a,b)\in A\times (B\setminus C)\iff&amp; a\in A \land b\in (B\setminus C)\\ \iff&amp; a\in A \land (b\in B \land \lnot(b\in C))\\ \iff&amp; (a\in A \land b\in B) \land (a\in A \land b\notin C)\\ \iff&amp; (a\in A \land b\in B)\setminus (a\in A \land b\in C)\\ \iff&amp; (a,b)\in (A\times B)\setminus ((a,b)\in A\times C)\\ \iff&amp; (a,b)\in (A\times B)\setminus (A\times C) \end{align}$$ Which databases use real multidimensional indices? Is oracle ever using several indices to get data from tables, or will it always take the one that seems to have the highest selectivity? How about other dbms?