How to count the number of words in a string in Bash
How to count number of words from String using shell
I am just starting into calculus and I have a question about the following statement I encountered while learning about definite integrals:  $$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$  I really have no idea why this statement is true. Can someone please explain why this is true and if possible show how to arrive at one given the other? Custom ordering of duplicate targets is not necessarily honored on mobile apps I have an iPhone and run Ubuntu on all of my personal computers. Since I did not want to keep a separate partition with Windows on it for the sole purpose of running iTunes, I attempted to install It using Wine.   I installed Wine 1.4 from the Software Center and installed iTunes 10.6.3. When I tried to run it I got a slew of error messages. I hopped over to google where it was suggested that I install it through PlayOnLinux. I did so with the same result. Further googling revealed that iTunes 10.6.x is confirmed to work with Wine 1.5.1 and up.   I installed Wine 1.5.1 following the instructions I found and was unable to get it to open. I did the same with 1.5.9 with the same results. I opened the Package Manager and installed the Wine 1.5.9 packages through it, and it appears to have installed properly.   When trying to install iTunes I got he error "This iTunes installer requires Windows Vista 64 bit or later". Realizing that Wine uses XP as a default I ran winecfg and changed it to Windows 7. This changed nothing and I tried changing it through winetricks to no avail. I even changed it to Vista with the same results.   Does anyone know what is going wrong here and how to fix it? Thanks Maybe the underlying question is what the Voltage-Current curve looks like. Can I drive it from a voltage source (like you drive a heater) or from a current source (like you drive an LED)? Or even different than those two options?  ADDITIONAL1: Say (hypothetically) I have two commercially available identical Peltier's, they are spec'd 6V/3A. Can I connect these in series to a 12Vdc power supply without any worries?  CONCLUSION1: Current/Voltage load curve is reasonably linear, both driving from current or voltage source will do fine as long as the device is operated within its spec. (Olin Lathrop, Russell McMahon)  CONCLUSION2: Don't drive a Peltier from PWM, power loss due to current increase, grows more rapidly than cooling power. (Olin Lathrop)  CONCLUSION3: Beware the mechanical wear of the device with continues cycling. Eg. don't use a thermostat on/off controller. (Russell McMahon) Short description of the scoping rules? What exactly are the Python scoping rules?  If I have some code:  code1 class Foo:    code2    def spam.....       code3       for code4..:        code5        x()   Where is x found?  Some possible choices include the list below:   In the enclosing source file In the class namespace In the function definition In the for loop index variable Inside the for loop   Also there is the context during execution, when the function spam is passed somewhere else. And maybe  pass a bit differently?  There must be a simple reference or algorithm somewhere.  It's a confusing world for intermediate Python programmers. prove that : $\cos x \cdot \cos(x-60^{\circ}) \cdot \cos(x+60^{\circ})= \frac14 \cos3x$ I should prove this trigonometric identity. I think I should get to this point : $\cos(3x) = 4\cos^3 x - 3\cos x $ But I don't have any idea how to do it (I tried solving $\cos(x+60^{\circ})\cos(x-60^{\circ})$ but I got nothing) states that the relationship between current ( I ) voltage ( V ) and resistance ( R ) is  $$I = \frac{V}{R}$$  However  cause the resistance of a material to go to zero, and as I understand it, as $R \to 0$, $I \to \infty$. Does this present a problem for Ohm's law? In GKP's Concrete Mathematics, there is a useful and interesting feature I would like to see in more books. The bibliography entries include:   a - the page numbers where the book or article is cited in the document. b - a few lines of review of the cited work.   It is a kind of mix between bibliography, index and review.  Are there stable LaTeX packages/BibTeX styles to do (a) and (b) ?  EDIT: I wrote (b) initially as "comments about the work cited". It could be understood as "gathering comments made in the book about the work and reproducing them in the bibliography".  This is not what I meant but this could be something useful for others. Center of mass in a straight rod I got an assignment to prove that in a straight homogeneous rod, you can always choose a coordinate system in such a way that  $$\int_S x_1 \, dx_1 \, dx_2=0 $$  $$\int_S x_2 \, dx_1 \, dx_2=0 $$  $$\int_S x_1x_2 \, dx_1 \, dx_2=0$$  where $S$ is the cross section of the rod  Now, intuitively, I can understand that the first two expressions basically state that if you find the mass center of the rod, then all you have to do is to put the origin of the coordinate system in the mass center, and the integrals turn out to be zero. What I'm curious about is whether or not this is a good enough of an explanation, and also, a hint on how to obtain the third equality. Automatic pyqgis categorized renderer classification I have some layers in my project and I would like to alter their styles, since ranges of values for underlying columns have changed.  Normally it would require to enter each layer style settings separately and trigger "Remove All", and "Classify" button, however I would like to execute it from the code.   I found such method for graduated symbol:  renderer.updateClasses(layer,0,bins)   ,however I'm having trouble to find corresponding method for categorized symbol class  Is there any way to do this from pyqgis without the need to specify the layer style from the scratch (create category, label etc.) ? Some equivalent of "Classify" button from below screenshot: dropping ticklabel on pgfplot axis I'm trying to figure out a good workflow for developing scripts and add-ons in Blender. Here's what I'm currently doing as I try my luck with a PyNode add-on:   Open blender Create a text editor panel Open my script (external text file) Edit my script in a nice external editor Reload the script Save the .blend file Run the script   Now that I can see what my code does, this Blender instance has been modified, so I can't (make changes to my script and) run my script again. So I do this:   Close blender Open blender with the .blend from step 6 and repeat steps 4-7, over and over and over..   Is there a better workflow for this sort of thing? This girl that I'm friends with and have actually seen in person before, keeps posting [on social media] that she "loves when the transfer goes through" and gets $2000-$6000 for free quite often. She said you can make up to $6500 a day. She is not very smart and barely spells correctly. She keeps saying that all she is doing is "transfers" and that's it. So many of my friends are feeding into this crap. So I asked her what it is. She basically said "it's legit" and asked me for my bank username and password so she could see how much money to deposit into my account. I said no way and left it at that. She also said she is not stealing or doing anything illegal. She is getting her friends free money and I think they're naive. What is she actually doing? Is it illegal? I am sure she is incapable of doing crazy money wiring to different countries.   Thank you everyone for answering my question. I am not stupid, I did not give her my information. I knew she was up to something illegal, so thank you for giving me some input on what exactly she is doing. I submitted an anonymous tip to my local sheriff's department. I'm hoping they see it and pursue it, or forward it to the right authorities I.e the FBI or something. Using differentiation for computing $\int_{0}^{1}\frac{\arctan(ax)}{x\sqrt{1-x^2}}\,dx$ How can I prove that I can differentiate the integral:  $$ \int_{0}^{1} \frac{\arctan(ax)}{x\sqrt{1-x^2}}\,dx $$  First I have to prove this integral converges. Next I have to prove the integral $$ \int_{0}^{1} f_{a}'(x, a)\,dx $$ converges uniformly.  Then I can differentiate integral with Leibniz's rule.  I tried Weierstrass and Dirichlet's tests. Nothing succeeded.   Thank you for help in advance. I'd like to declare some new operators using \DeclareMathOperator and some of the names are already taken by other commands (that I do not want to use). Is there an equivalent to the \renewcommand command for \DeclareMathOperator or a different way to overwrite the commands using \DeclareMathOperator? Is it possible to load some package from a .sty file only if some option is selected?  (Naive approach \DeclareOption{something}{\RequirePackage{something}} doesn't work.) Write $\frac 11 + \frac12 + ...\frac1{(p-1)} =$ $\frac ab$.Such that $(a,b)=1$. Show that $p^2 \mid a$ $\text{if}$ $p\geq 5$.  I was trying to apply something with prime modulus, but I am unsure how exactly to go about it. How do I get my C# program to sleep for 50 milliseconds?  This might seem an easy question, but I'm having a temporary brain failure moment! Xpath expression with multiple predicates Does infinity exist in physical systems? Sometimes people fail at asking a question by being too broad, unclear like . So I'll take a stab at what I believe to be the same question, but more concise and clearly stated:     Does infinity exist in either terms of structure, parameters, or   measurement in any physical systems?   Can infinity have any real connection with reality?  Or is infinity purely a mathematical concept just used by physicists as a convenient way to describe the very large, an approximation?  I have heard that if you model a physical system (), and you run into infinity as a solution, then you have either made an error in your calculations or your model is wrong.