How much voltage will i generate from this DC motor?
DC Motor as a Generator Voltage and Current
To show that $\sum a_nb_n$ is absolutely convergent What are the technical differences between using a DSLR viewfinder and live view? The earlier question  asks for practical advantages of optical viewfinders. But what's the technical difference, and why does a camera behave differently in each mode?  For example, on my Nikon D5100:   Slower auto-focus — I saw this explained in the related issue, but just partially: "The other major drawback of live view is that because it requires the mirror to be locked up, it means that the auto focusing mechanism is unavailable."  option not available. No . The manual says that it's dangerous to shoot direct light, when it's on live-view. There's no range finder available.   Why are all these things different?  Live view also has some advantages, like:   automatic scene selection grid lines on the screen other smaller things, like possibly easier operation on a tripod where the viewfinder might be inconvenient to look through   Some of these things, like the tripod operation, are natural. But are there technical reasons the others can't be done with an optical finder? Are there other advantages enabled by live view for technical reasons? Distribution of range of Uniform $(0,1)$ distribution How to use XMLHttpRequest to download an HTML page in the background and extract a text element from it? An example to show that convergence of Cesaro sum to $0$ does not imply the original sequence converges to $0$. I'd like construct a non-negative sequence $\{a_{k}\}_{k=0}^{\infty}$ with $a_{0}=0$ such that the Cesaro sum $\frac{1}{n}\sum_{k=0}^{n-1}a_{k}\longrightarrow 0$ but $a_{n}$ does not converge to $0$.   I have a really bad attempt:  Define $a_{0}=a_{1}=0$, and $a_{k}:=\log(\log(k))$ for $k\geq 2$, then $a_{k}\longrightarrow\infty$. But $$\dfrac{1}{n}\sum_{k=0}^{n-1}a_{k}=\dfrac{\log\Big(\prod_{k=2}^{n-1}\log(k)\Big)}{n}$$ and Wolframalpha told me that this series converges to $0$ as $n\longrightarrow\infty$.  However, I have no idea about how to show this convergence to $0$. Also, I wish to have a sequence as simple as possible, since at some stage I need too how $f(k):=a_{k}$ is positive semi-definite.   Is there any simpler example?   Thank you! workspace switching via ctrl + alt + arrow not working after upgrade to 13.04, how to fix this? Would Gravitational Time Dilation still apply between two gravitational sources? As explained on , when an object is experiencing strong gravitational forces, time passes slower for it. If, in theory, you had two objects exerting the same amount of gravitational pressure on an object in opposite directions, effectively cancelling each other out, would they cancel out the time dilation, or would they compound, making the time dilation more prevalant? Fold a plane. then fold again Imagine a piece of paper and you fold it in half and then fold it again. that's what I am trying to do and cant. If I use bones the influence of the bones won't allow me to because I need 2 bones to control the same area. If I try shape keys it just deforms the mesh if I try to make it in multiple steps or does the wrong animation because it draws the shortest path instead of rotating from a point like a piece of paper would. My sketch exports seem to be pixelated even when am exporting it to 1x How can I get a debug log for the sites guest user/public profile? [updated for Spring 18] HDMI over cat extender video (Almost) double light speed From Stewart 7e pg 614 # 9  "One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard th eremor and the fraction who have not hear the rumor. a) Write a differential equation that is satisfied by y. b) Solve the differential equation c) A small town has 1000 inhabitants. At 8 am 80 people have heard a rumor. By noon half the town has heard it. At what will 90 percent of the population have heard the rumor? "  The wording of this is very ambiguous to me and I can't really make sense of it.  They mention a product, so I know that something is being multiplied and that y is a fraction which belongs to the population who have seen it so I think that "have not" heard is a constant, and that y is a fraction taht represents who have. I tried to set this up and it is the wrong answer. I am not sure what they want from that, the English usage is too ambiguous to make sense of it. The complete lack of punctuation is what really does it. Evaluating the integral $\int_0^\infty \frac{x \sin rx }{a^2+x^2} dx$ using only real analysis Calculate the integral$$ \int_0^\infty \frac{x \sin rx }{a^2+x^2} dx=\frac{1}{2}\int_{-\infty}^\infty \frac{x \sin rx }{a^2+x^2} dx,\quad a,r \in \mathbb{R}. $$  Edit: I was able to solve the integral using complex analysis, and now I want to try and solve it using only real analysis techniques. Rootspaces are $\mathop{ad}$ nilpotent Solving ODE with negative expansion power series I am solving a series of ODE, such that each DE is equal to some degree of term that I'm expanding to. For instance, one DE is this:  $\xi^r\partial_r g_{rr}+2g_{tt}\partial_t\xi^t=\mathcal{O}(r)$  $g_{ii}$ are given, from metric, but that's not important. I need to assume that the solution (since I'm looking for components of $\xi^\mu$, which is a vector with components $\xi^t,\xi^r,\xi^\phi$) is given with power series of the form:  $\xi^\mu=\sum\limits_{n}\xi^\mu_n(t,\phi)r^n$, and this is to be seen as expansion around $1/r$ (expansion around $r=\infty$).  Now when I plug this in the ODE I get this  $\frac{2}{l^2}\sum_n\xi^r_nr^{n+1}+2\sum_n\xi^t_{n,t} r^n+\frac{2}{l^2}\sum_n\xi^t_{n,t}r^{n+2}=\mathcal{O}(r)$, where   $\xi^\mu_{n,i}$   is the derivative with the respect to i-th component.   What troubles me is, how to expand this? Do I set n=0,-1,-2,... until my $\mathcal{O}(r)$ terms cancel each other out? Or?  I'm kinda stuck :\ How to install Internet Explorer (multiple versions)? I am developing one site which has chat feature in Rails. I am using Ubuntu 12.04 LTS. I need to check that the site is IE9 because the chat feature using socket io of HTML5. I want to know that how to install IE9 in Ubuntu. I have looked at Chrome and Firefox extensions but if any standalone is available then please give me suggestion. What are examples of two non-similar invertible matrices with same minimal and characteristic polynomial and same dimension of each eigenspace? How can I avoid name mangling in C++? Extracting numbers from string field using Python Parser of ArcMap Field Calculator? I am trying to calculate field test2 with only the numeric values from a string field test. The entire script is like:    def makestr(test)      list=[]      for s in test:          if s.isdigit():              list.append(s)      for a in list:          str=''.join(list)     But I keep getting an error:    Any ideas?