I've recently had some issues with my Dell Vostro laptop and Dell sent me out some OS discs to reinstall Windows 7 Ultimate SP1. I expected to get 64-bit discs in the mail, but instead received 32-bit.   So I called up Dell and asked what type of processor I have. The person on Dell's side said 32-bit. So I looked up my processor: Intel Core i3 CPU M370 @ 2.4GHz, and the documentation I found online says it's a 64-bit instruction set.   So I'm guessing it actually is 64-bit. Should I request new discs?
How can I determine whether my processor is 32-bit or 64-bit? My processor is AMD Phenom 8450 triple-core.
Ignore python multiple return value Say I have this file:  hello world hello world   This program  #!/bin/bash  for i in $(cat $1); do     echo "tester: $i" done   outputs  tester: hello tester: world tester: hello tester: world   I'd like to have the for iterate over each line individually ignoring whitespaces though, i.e. the last two lines should be replaced by  tester: hello world   Using quotes for i in "$(cat $1)"; results in i being assigned the whole file at once. What should I change? print IP address with interface name I want to show the IP address like below  lo : 127.0.0.1  eth0 : 192.168.5.123 eth1 : 192.172.0.212 wlan0 : 10.1.0.124   I'm able to print all IP address by ifconfig | awk '/inet addr/{print substr($2,6)}'. But it is only printing the IPs. Every system have their own interface names and addresses. So my script has to show their interfaces with respect to IP addresses. How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$? Prove that for any positive integer $n$, $$2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$$ Progress I think Riemann sum should be used for the middle term. I got the limit as $n\to \infty$ of the function inside using Riemann sum but what I cannot get are the lower and upper bound. I am writing a few rather large pseudocode functions using algorithm and algorithmic, i.e. my code looks something like:  \begin{algorithm}                      \caption{Coolest Algorithm ever}           \label{findme}                           \begin{algorithmic} [1]                   % enter the algorithmic environment \REQUIRE    Here are a few variables \\             variable 2 \\             variable 3  \ENSURE     this is the output \\             output 2  \STATE $some cool code here$ \STATE $some cool code here$ \STATE $some cool code here$ \STATE $some cool code here$ \end{algorithmic} \end{algorithm}   Unfortunately this code does not fit on one page and I am definitely not able to split it into some subfunctions or so (I already did that as far as possible).  So now I need to split up the algorithm into two pages, but I have no idea how.  The easiest way I can imagine is just to start a new algorithm on the new page, but this time letting the line counter start at line 35 or so instead of 1. But how can I do that?  Please not that there is already a similar question here on this site, but it deals with the package algorithmicx. Six simple tips to get Stack Overflow reputation fast Hydrogen radial wave function infinity at $r=0$ When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts: $$\psi(r,\phi,\theta)= R(r)Y_{\ell,m}(\phi,\theta).$$ I understand that the radial part usually has a singularity for the $1s$ state at $r=0$ and this is why you remove it by writing: $$R(r) = \frac{u(r)}{r}$$ But what is the physical meaning of $$R(r=0) = \infty~?$$ Wouldn't this mean that the electron cloud is only at the centre of the atomic nucleus? Find generator of multiplicative group of $\mathbb{F}_{27}$ I have a finite field $\mathbb{F}_{27}$. I need to find an element of order 13. I know that multiplicative group of this field is cyclic with order 26. So I want to find a generator $g$ of this cyclic group, then $g^2$ will have order 13. Also I know that all elements of this field can be represented by polynomials from $\mathbb{F}_3[t]$, where t is root of irreducible polynom $x^3-x-1$.  Probably we can find generator of $\mathbb{Z}_{26}$ and than build an isomorphism to $\mathbb{F}_{27}\setminus 0$.  Anyway I don't know were to start.  Thanks! Is there an easy way to limit user bandwidth usage? Seeking QGIS tutorials and web resources? I wish to familiarize myself with the capabilities of QGIS up to and beyond QGIS version 3.0.   Can you recommend some good web resources and tutorials that would show me QGIS' capabilities?   I am interested in both using QGIS through its GUI and in developing applications using QGIS. I am executing my ./shell.sh which contains   eval "$(pyenv init -)" pyenv shell 3.8.2   But nothing happens. If i run this code in bash manually it works fine and shell version of python switches from 2.7.10 to 3.8.2.  I am in the right directory and I gave the .sh file execution permissions. Find the number of solutions of $a_0+a_1+a_2=17$ if $2\le a_0\le 5$,   $3\le a_1\le 6$, $4\le a_2\le 7$.   This is an exmaple given by my professor, and his solution is:       The number of solutions to this equation satisfying the given   constraints is equal to the coefficient of $x^{21}$ in the expression   $$\left(\sum_{n=2}^5x^n\right)\left(\sum_{n=3}^6x^n\right)\left(\sum_{n=4}^7x^n\right)=x^9\left(\sum_{n=0}^3x^n\right)\left(\sum_{n=0}^3x^n\right)\left(\sum_{n=0}^3x^n\right).$$   This must be 3, since the coefficient of $x^8$ in $(1+x+x^2+x^3)^3$ is   3.   I understand actually nothing here. The expression of summation just pops up, and then comes the answer. What I only know that the idea of generating function is used here. Can someone help explain how the steps in the solution come? Foreword  This question was inspired by initial mistakes in . I wanted to explore the strange circle with $A&gt;\pi r^2$ and got lost into geometrical jungle.  A  is usually described by it's height $h$, radius of the base $a$ and radius of the sphere $r$. Besides we have a relation $a^2+(r-h)^2=r^2$ so the cap actually only has two degrees of freedom.  When considering a case of circle on a sphere (like the Earth), it's the surface of a spherical cap, but we can't see the height or other classic parameters of this spherical cap. Instead we encounter parameters like area $A$, perimeter $C$ and diameter $d$. I will try to write formulae for these: $$A=2\pi rh$$ $$C=2\pi a$$ $$d=2r\theta$$  Where $\theta$ is introduced with $\sin\theta=\frac{a}{r}$ or $\cos\theta=(1-\frac{h}{r})$.  As the cap only has two degrees of freedom, it should be a good problem with unique solution if only two values are known.  A-C Problem  The simple example: $A$ and $C$ are given. I show this only as example before the other tasks.  We can easily find $a=\frac{C}{2\pi}$ and then solve:  $$A=2\pi rh = 2\pi r (r-\sqrt{r^2-a^2})$$  to obtain  $$r=\frac{A}{2\sqrt{\pi(A-\pi a^2)}}$$  Parameters $a$ and $r$ are now known and it is straightforward to find $h$, $d$, $\theta$ and anything else.  C-d Problem  $C$ and $d$ are given.  First step once again is easy: $a=\frac{C}{2\pi}$. The knowing of $a$ suggests that we might prefer the $\theta$ definition with the sine. We obtain: $$d=2r\theta=2r\arcsin\frac{a}{r}$$  That's where I got stuck. Is there an easy way to solve this? Is there a hard way to solve this?  I tried solving numerically with Wolfram Mathematica and it went into complex numbers. When solving the geometrically equivalent $\sin\frac{d}{2r}=\frac{a}{r}$ I got some roots, but the search seemed very unstable and not finding the root closest to initial value. Besides it was finding a lot of different roots while I am pretty sure that there should only be one $r$ for each pair of $d$ and $a$. What would be the right formulation to solve this problem numerically?  A-d problem  $A$ and $d$ are given. This seems the hardest one. We obtain a system of equations:  $$A=2\pi r h$$ $$d=2r\arccos\left(1-\frac{h}{r}\right)$$  (The first equation suggested solving the problem in $h$ and $r$).  Is this system solvable analytically? Or numerically? My experiments with Wolfram Mathematica never converged.   Of course, I could express $h$ or $r$ from the first equation and leave only the second in one of these forms: $$d = 2r\arccos\left(1-\frac{A}{2\pi r^2}\right)$$ $$d = \frac{A}{\pi h}\arccos\left(1-\frac{2\pi h^2}{A}\right)$$  But I have no idea how to solve these either. Drawing text and line-dasharray Is it possible with TileMills and CartoCSS? How to Create a Vinyl Plastic Toy Shader? How can I make one of the vinyl toy plastic material like this?    Video: Hello. I was trying to make a bootable flash drive from the startup disk creator, and when I went to erase the flash drive I accidentally erased the wrong drive, a 1TB removable drive. The operation took less than a second and gave no warning. I tried erasing the flash drive and it took about a minute, but it took but a second to erase the 1 TB drive, which is very surprising.  Please help, Gabriel Looking to identify a short story I read in a sci-fi anthology as a child, about an angry, bullied somewhat misanthropic boy who is given immense near-omnipotent powers by an alien intelligence. I read this in English, sometime in the late 1990s/early 2000s. He goes on to use this power to destroy the human race, which causes him to age terribly in a very short amount of time. At the end of the story he is a lonely old man stripped of the powers he held briefly, and is alone on an isolated Earth. The aliens then proceed to invade Earth. Is there a difference in disenchanting strong items vs. weak ones? Possible Duplicate:           states that the strength of the enchantment doesn't matter when disenchanting items to learn new enchantments.  Am I reading that right? If I have novice robes with 50% faster regen and disenchant it and my enchantment skill is at 5/5, when I enchant that item will it be the same result as disenchanting master robes with 150% faster regen? Because if you do the math, 5/5 enchanting will give you 100% better enchantment.   Therefore wouldn't it be better to disenchant more powerful items than weaker ones? Proving normality of affine schemes One of the exercises in Ravi Vakil's algebraic geometry notes, Ex. $5.4.$I(b), is to show that    $$ \operatorname{Spec}\left(k[x_1, \ldots, x_n]/(x_1^2 + \cdots + x_m^2)\right) $$   is normal, where $k$ is any field of $\operatorname{char}(k)\neq 2$, and $n \geq m \geq 3$.    I have absolutely no idea how to get started on this. Is there anyone that could give a hint as to how one would approach this problem? Number Theory: Prove that $m | \phi(a^m - 1)$