I am given the following riddle with complex numbers. But I can't figure what is wrong here:  $1=\sqrt{(-1)\cdot (-1)}=i\cdot i=-1$
I know there must be something unmathematical in the following but I don't know where it is: \begin{align} \sqrt{-1} &amp;= i \\\\\ \frac1{\sqrt{-1}} &amp;= \frac1i \\\\  \frac{\sqrt1}{\sqrt{-1}} &amp;= \frac1i \\\\  \sqrt{\frac1{-1}} &amp;= \frac1i \\\\  \sqrt{\frac{-1}1} &amp;= \frac1i \\\\  \sqrt{-1} &amp;= \frac1i \\\\  i &amp;= \frac1i \\\\  i^2 &amp;= 1 \\\\  -1 &amp;= 1 \quad !!? \end{align}
Evaluation of OptionValue[] Mirror modifier is not working, no mirrored object? I'm very new to Ubuntu, and have come to this point that I can't boot back to my Windows Vista anymore.  I thought that I would get some kind of dual boot in the beginning when booting my computer, but this doesn't seem too happen and I don't have the slightest idea on how to fix this. I was looking for help here at askubuntu, but I couldn't seem to find anything. I'm too new with this software.  I'll need hints and tips on how to fix this  Thanks for your time folks! Does "Erase Disk and Install Ubuntu" replace the default boot screen? I am new here. And I may replace a laptop's hard disk with Ubuntu. It's an HP Compaq notebook which has Windows 7 installed. So If I choose that install option, will it replace the screen that says F12 for boot options [actually it was esc]. I am just asking. I know that choosing that options erases your other partitions. I am assuming it gets replaced by grub2? Create UEFI bootable USB stick to install Windows AND Ubuntu from it I know how to make a UEFI bootable stick to install Ubuntu (explained ) and I know how to make one to install Windows 7 (, sorry). I guess for Win 8 the procedure would be similar, but I haven't looked into it.  I also know how to make a legacy bootable stick from which I can install Windows and Ubuntu using YUMI. I have failed so far though at creating a UEFI bootable stick that can do this. When I do a UEFI boot from my YUMI multiboot stick it gives me no option to choose between Ubuntu and Windows (hardly surprising I guess) and instead simply UEFI boots Windows (which I find kind of surprising to be honest but maybe this is due to the fact that I added the Windows image after the Ubuntu image and this simply replaced Ubuntu's EFI boot files).  So how would I proceed to create such a bootable stick? "debconf: DbDriver "config": config.dat is locked by another process: Resource temporarily unavailable" while installing packages I have cobbled together a command to return the process ID of a running daemon:  ps aux | grep daemon_name | awk "{ print \$2 }"   It works perfectly and returns the PID, but it also returns a second PID which is presumably the process I'm running now. Is there a way I can exclude my command from the list of returned PIDs?  I've tested it a few times and it appears my command is always the second PID in the list, but I don't want to grab just the first PID in case it's inaccurate. Stack Overflow provides good tools in the question editor, like "Links" and "Styling".  Another thing that for me would be nice is a color selector. Although an HTML editor is available, a direct click on tool would be good, and users can select different colors, as for marking errors in their program with red, and more important data with blue. I've already defeated the Big Bug.   I see the hint that the small bugs disguised as cursors are vulnerable to the three words "Charity", "Uganda", and "Bram".  I think I have all keys available, I've tried undoing with the bugs on the three words, I've tried motions which include the three words in their range, I have each of the three words stored in a named register, but I haven't figured out how to defeat the three small bug minions underground in Level 14 of Vim Adventures.  I suspect I should have defeated them before defeating Big Bug, maybe even before finding 'undo'. Is there instead something I should do in the 'lorem' buffer where I found the three cursors (Blue, White, and Pink) at the beginning of the level?  How does one defeat the three small bug minions in Level 14? Image viewer without large window borders I am looking for an image viewer software without very large window borders. I don't need any type of toolbar, just a simple image viewer.   It would also be fine if there is no top bar to close, minimize or maximize window. Why are there scenes that will not render on GPU but will render fine on CPU? I've already tried GPU Rendering and it seem to be twice as fast as the CPU. However I have some situation where tried to render on the GPU, but it doesn't do anything. When I switch to CPU it renders.  I have some fur texture/materials using particle systems. I wonder if that causes the GPU not to render, I'm not really sure. Left inverse implies right inverse in a finite ring Let $R$ be a finite ring with identity $1$, and assume $\exists x,y\in R$ such that $ xy=1$. How can I show it implies $yx=1$? Can I recover app data after the phone has been Factory Reset? I have a lot of 3D objects of various sizes, shapes in blender 2.76b and I would like to set the origin to the bottom center of the objects bounds.  I cannot select the bottom edge and snap to cursor etc as each shapes edges are in different X/Y positions.  Is there a script or tool that will allow me to set the origin to the lowest edge z position? Creating all possible line segments between all points using QGIS I want to connect all points in a point feature with every possible line segment using QGIS. For example, how a pentagon has five points with ten line segments connecting them all to form a pentagram inside. Alternatively phrased: How do I make spokes when all the points are hubs? I don't care about the order, I just want every connection between two points as one line each. Is there a tool or script that can do this in QGIS? This topic () is the closest to what I want but the plugins are no longer supported. Find asymptotic of recurrence sequence Given a sequence $x_1=\frac{1}{2}$, $x_{n+1}=x_n-x_n^2$. It's easy to see that it limits to $0$.  The question is: is there exists an $\alpha$ such, that $\lim\limits_{n\to\infty}n^\alpha x_n\neq0$.  I tried to find explicit formula for $x_n$, but did not succeed. I stucked at that point: if $a_1=(\frac{1}{4})^2$, $a_n=(a_{n-1}+\frac{1}{4})^2$, then $x_n=-a_{n-2}+\frac{1}{4}$ for $n\ge3$.   Thanks for any ideas and help. Consecutive/Rolling sums in a vector in R Do I need visa for UK visit if I have a work permit for Ireland? When I'm generating a List of Figures in my project, all figures are grouped by chapter. I would like to have the whole list without any additional new lines between different chapters.  How it looks like:  Figure 1.1  Figure 1.2  Figure 2.1  Figure 3.1  Figure 3.2   How it should:  Figure 1.1  Figure 1.2 Figure 2.1 Figure 3.1  Figure 3.2   I tried to apply the following solutions but failed completely :        My main file:  \documentclass[12pt,oneside,titlepage,utf8x]{report}  \usepackage{times,a4wide,multirow,tabularx,graphicx}  \usepackage{psfrag,fancyhdr,longtable}  \usepackage[T1]{fontenc} \usepackage{float} \usepackage[utf8]{inputenc}  \usepackage{url} \usepackage{color} \usepackage{verbatim} \usepackage{fancyvrb} \usepackage{natbib} \usepackage{relsize}  \usepackage{caption} \captionsetup[longtable]{belowskip=10pt}  \usepackage[left=4cm,top=2cm,right=3cm,bottom=2.5cm]{geometry}  \renewcommand{\chaptermark}[1]{\markboth{\nouppercase{\thechapter.\ #1}}{}} \pagestyle{fancy} \headheight 30pt \rhead{} \lfoot{} \cfoot{\thepage} \rfoot{}  \setlength{\parindent}{2em} \setlength{\parskip}{1em} \linespread{1.3}   \begin{document}  \begin{titlepage} \maketitle \end{titlepage}  \tableofcontents  \chapter{First} \label{sec:First} \input{chapter1/chapter1}  \chapter{Second} \label{sec:Second} \input{chapter2/chapter2}  \chapter{Third} \label{sec:Third} \input{chapter3/chapter3}  \relsize{-1} \listoffigures \normalsize  \bibliography{praca_mgr} \bibliographystyle{plain} \nocite{*}  \end{document} How to lead a moving target from a moving shooter I saw this question: .  My situation is a little different though.   My target moves, and the shooter moves.  Also, the shooter's velocity is added to the bullets' velocities, i.e. bullets fired while sliding to the right will have a greater velocity toward the right.   What I'm trying to do is to get the enemy to be able to determine where they need to shoot in order to hit the player.  Using the linked SO solution, unless the player and enemy are stationary, the velocity difference will cause a miss.  How can I prevent that?      Here is the solution presented from the stack overflow answer.  It boils down to solving a quadratic equation of the form:  a * sqr(x) + b * x + c == 0   Note that by sqr I mean square, as opposed to square root. Use the following values:  a := sqr(target.velocityX) + sqr(target.velocityY) - sqr(projectile_speed) b := 2 * (target.velocityX * (target.startX - cannon.X)       + target.velocityY * (target.startY - cannon.Y)) c := sqr(target.startX - cannon.X) + sqr(target.startY - cannon.Y)   Now we can look at the discriminant to determine if we have a possible solution.  disc := sqr(b) - 4 * a * c   If the discriminant is less than 0, forget about hitting your target -- your projectile can never get there in time. Otherwise, look at two candidate solutions:  t1 := (-b + sqrt(disc)) / (2 * a) t2 := (-b - sqrt(disc)) / (2 * a)   Note that if disc == 0 then t1 and t2 are equal.