The roots of $x^2-2x+3=0$ are $\alpha$ and $\beta$. Find the equation whose roots are: $\alpha+2$, $\beta+2$. Not sure of answer in book.
If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$
Will Google punish me if I import a story from my own blog to content sharing sites such as Medium.com? I've heard that Google punishes sites with duplicate content.   If I write an article on my blog then import it on Medium (basically a copy/paste) will Google regard it as a duplicate?   Medium.com is a blog platform (sort of). Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$ I tried to manipulate a cube with the Boolean modifier. I tried to cut out an edge of the cube with a cylinder. Also, the shading result looks awful in FLAT SHADING mode, so I turned on SMOOTH SHADING.   Has anyone an idea how to achieve a better result. (I also cut out a Sphere first, this made the result less awful).   I used Blender Internal and rendered with smooth shading for smoothness.  Using flat shading looks okay, except the "round" cutouts :/  Face normals are okay.  First image is smooth shading.    EDIT: User Pisurquatre suggested the EdgeSplit modifier, works perfect to me (Maybe a little tweaking here and there): I don't understand, because if 'don't' is 'do not' then wouldn't the sentence without conjunctions be 'do not you dare' which I'm pretty sure isn't grammatically correct. Like, when we say the term it means something else, certainly not 'do not you dare' anyway. Any ideas on why? I am so glad English is my first language. How can I model flips until N successes? You and I decide to play a game where we take turns flipping a coin. The first player to flip 10 heads in total wins the game. Naturally, there is an argument about who should go first.  Simulations of this game show that the player to flips first wins 6% more than the player who flips second (the first player wins approx 53% of the time).  I'm interested in modelling this analytically.  This isn't a binomial random variable, as there are no fixed number of trials (flip until someone gets 10 heads). How can I model this?  Is it the negative binomial distribution?    So as to be able to recreate my results, here is my python code:  import numpy as np from numba import jit   @jit def sim(N):      P1_wins = 0     P2_wins = 0      for i in range(N):          P1_heads = 0         P2_heads = 0         while True:              P1_heads += np.random.randint(0,2)              if P1_heads == 10:                 P1_wins+=1                 break              P2_heads+= np.random.randint(0,2)             if P2_heads==10:                 P2_wins+=1                 break     return P1_wins/N, P2_wins/N   a,b = sim(1000000) SSH in shell script with password The internal storage on my phone is almost full. The storage screen tells me    2.77GB / 2.91 GB taken Apps 0.89GB Other 1.89 GB Available 138MB   What is this "other" and how can I clean it up? I already followed the steps of "make more space", it barely makes a difference.   Phone Storage then tells me 43.00MB / 1.09GB is taken.  And on the SD card I have 1.86GB / 14.72GB taken.  I have plenty of storage in various places yet when I try to install apps I'm unable to do so cause of "insufficient storage". How can I fix this? Feedback Request: New Timeline Question View There is an experimental timeline view for questions now available on meta ONLY! (Now working on SO, SF, and SU as well)  This is partially motivated by comments about how difficult it is to follow very active questions which have a lot of activity, and also the feedback on the API which was heavily dominated by "we need to know what happened in this time range" type responses.  It can only be accessed through URL hackery at the moment. To get to it, enter question URLs like so:  https://meta.stackexchange.com/posts/{id}/timeline  This is a chronological timeline of everything that happened on a question, including   initial question ask answers  revisions comments closure, deletion, reopen, undelete, etc votes   all based on when they happened in chronological order.  We are thinking about making this a fourth tab on the question, like so:  Timeline | Oldest | Newest | Votes  Please try it out and provide feedback. It is still a little rough, so we are not looking for highly detailed bug reports, just more general feedback.  Timeline view for this question: What are the mechanics of time dilation and length contraction? Going beyond the mathematical equations involving light and the "speed limit of the universe", what is observed is merely a phenomenon and not a true explanation of why time dilates or length contracts.  It has been proven to work out, but do we know why?  Is it something that happens at a subatomic level? What are the differences between 32-bit and 64-bit, and which should I choose? What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit? Relationship between Binomial and Beta distributions I'm more of a programmer than a statistician, so I hope this question isn't too naive.  It happens in sampling program executions at random times. If I take N=10 random-time samples of the program's state, I could see function Foo being executed on, for example, I=3 of those samples. I'm interested in what that tells me about the actual fraction of time F that Foo is in execution.  I understand that I is binomially distributed with mean F*N. I also know that, given I and N, F follows a beta distribution. In fact I've verified by program the relationship between those two distributions, which is  cdfBeta(I, N-I+1, F) + cdfBinomial(N, F, I-1) = 1   The problem is I don't have an intuitive feel for the relationship. I can't "picture" why it works.  EDIT: All the answers were challenging, especially @whuber's, which I still need to grok, but bringing in order statistics was very helpful. Nevertheless I've realized I should have asked a more basic question: Given I and N, what is the distribution for F? Everyone has pointed out that it's Beta, which I knew. I finally figured out from Wikipedia () that it appears to be Beta(I+1, N-I+1). After exploring it with a program, it appears to be the right answer. So, I would like to know if I'm wrong. And, I'm still confused about the relationship between the two cdfs shown above, why they sum to 1, and if they even have anything to do with what I really wanted to know. I'm looking for an answer considering both technical limitations and user experience.   Does it need a reload from a technical standpoint? QM and Renormalization (layman) I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the particle's field as you approach the particle.  First, did I get that part right?  Second, how does (in very simple terms) renormalization try to fix this in Quantum Mechanics? If you can include some type of word picture that would be great. Accepted answer will go to the clearest explanation.  Update  I got a little further in the book (lol) and Kaku talks about using symmetry to remove the divergences in the math. I'd appreciate an answer that incorporates this also. Thanks guys! Minimize absolute values of errors instead of squares I have this code:  DECLARE @MyTable AS TABLE (    [Month] INT,    Salary INT );  INSERT INTO @MyTable VALUES (1,2000), (1,3100);  SELECT [Month], Salary FROM @MyTable;   Output:    I want to concat the Salary (grouping by month) so that it will be NVARCHAR like this: '2000,3100'  How would I do this efficiently? I accidentally closed the window for the verfication code I wanted to create an account for Ubuntu One, but I got impatient when the email with the verification code didn't arrive... I thought I might have typed the wrong address, closed the window and tried again. it told me the address already existed and I just got the code. But since I closed the window I missed it. Is there any way to recover the code? I've upgraded from 12.04 to 14.04 via command-line when my system froze, had to do REISUB and dpkg --configure -a to recover from crash after rebooting.  Now everything seems to work except automatically mounting external thumb drives and external hard disk drives. After plugging in said drives, they fail to show up on the left pane and remains unmounted. I can see the device if I run lsusb and fdisk though, so it's possibly to manually mount it but I'd rather resolve why it's not automatically mounting. Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$ Successfully connected to a bluetooth speaker, but how do i direct sound there? The FAQ says that Community Wiki works:     by transferring ownership of the post   from the original author to the   community. They make the post easier   to edit and maintain by a wider group   of users, but they do not contribute   to any user's reputation.   But using the new edit suggestion system, everyone can edit. It's no longer true that community wiki makes a post easier to edit.  Does community wiki still serve a function?    What are good examples of community wiki mode doing what it's supposed to do?