How can I change owner back to root?
What if I accidentally run command "chmod -R" on system directories (/, /etc, ...)
How do you use plural or singular form of an adjective? Change installed AppleScript version Trying to plot the sin(x) function, I get this result:    The MWE is here:  \documentclass{standalone} \usepackage{ pgfplots} \begin{document} \begin{tikzpicture} \begin{axis} \addplot[samples=500]{sin(x)}; \end{axis} \end{tikzpicture} \end{document}   cos(x) looks like an inverted parabola and tan looks just like sin.  I'm using pdflatex and MiKTeX. Any ideas? How can I modify title page so that it looks like it is in  video. Please seek to 16 seconds and watch title page. I do not have permission to post images. I liked this theme and I want to make a beamer theme that looks similar. I tried with beamercolorbox but I failed to position the box to the bottom.      Edit: Here is my minimum working example  \documentclass[xcolor=dvipsnames]{beamer} \defbeamertemplate*{title page}{customized}[1][] { \usebeamerfont{subtitle} \usebeamercolor[fg]{subtitle}  {\flushright \setbeamercolor{author}{bg=white,fg=Red} \usebeamerfont{author} \insertauthor\par \usebeamerfont{institute}\insertinstitute\par }  \vspace{0.2in}  \setbeamercolor{postit}{fg=white,bg=YellowOrange}  \begin{beamercolorbox}[sep=1em,wd=1.062\textwidth,ht=3cm,dp=3cm,right]{postit} \usebeamerfont{title} {\huge \inserttitle}\par \usebeamerfont{subtitle} {\insertsubtitle} \end{beamercolorbox} } \usecolortheme[named=YellowOrange]{structure} \useoutertheme{infolines} \setbeamertemplate{navigation symbols}{}  \institute{Harvard College Professor and\\ Johnstone Family Professor in Psychology, Harvard University}  \title{SAY WHAT?} \subtitle{Linguistics as a Window to\\ Understanding the Brain} \author{Steven Pinker}  \begin{document} { \setbeamertemplate{footline}{} \begin{frame} \titlepage \end{frame} } \end{document} We have duplicates in our all contacts in Marketing Cloud. To solve this, we want to delete all contacts (audience builder).   We use the Marketing Cloud connector, and send emails to synchronized data extensions. Because of this connector the all contacts will be filled with fresh data after 15 minutes right?  Is there any reason not to do this? What can go wrong? How do I prove/disprove that $F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$, where $F_n$ is the $n$th Fibonacci number? I was looking at the Fibonacci sequence:  $$1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,\ldots, F_n : F_n + F_{n - 1} = F_{n + 1} \land F_0 = 0$$  Here I noticed something; $\qquad F_n^2 + F_{n\pm1}^2 = F_{2n\pm1} : n\in \mathbb{N}$  For example; $$\ \ F_3^2 + F_{3 + 1}^2 = F_3^2 + F_4^2 = 2^2 + 3^2 = F_{2\times3 + 1} = F_{6 + 1} = F_7 = 13$$ $$F_3^2 + F_{3 - 1} = F_3^2 + F_2^2 = 2^2 + 1^2 = F_{2\times3 - 1} = F_{6 - 1} = F_5 = 5$$ However, no matter how true this can seem, I cannot seem to prove/disprove it.    My Attempt: $$\because (a + b)^2 = (a + b)(a + b) = a^2 + ab + ba + b^2 = a^2 + b^2 + 2ab : (a,b)\in \mathbb{Z}$$ $$\implies F_n^2 + F_{n\pm 1}^2 = (F_n + F_{n\pm 1})^2 - 2F_nF_{n\pm 1}$$ $$\implies F_n^2 + F_{n - 1}^2 = F_{n + 1}^2 - 2F_nF_{n - 1} : F_n + F_{n - 1} = F_{n + 1}$$ $$\implies F_n^2 + F_{n + 1}^2 = F_{n + 2}^2 - 2F_nF_{n + 1} : F_n + F_{n + 1} = F_{n + 2} \iff F_n + F_{n - 1} = F_{n + 1}$$ $$\implies F_{2n\pm 1} + 2F_nF_{n\pm 1} = F_{n + 2\lor1}^2 : F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1} \tag{+2 if +, +1 if -}$$ $$\implies F_{2n\pm 1} + 2\sqrt{F_{2n\pm 1} - F_{n\pm 1}^2}\sqrt{F_{2n\pm 1} - F_n^2}= F_{n + 2\lor1}$$ $$\implies F_{2n\pm 1} + 2\sqrt{(F_{2n\pm 1} - F_{n\pm 1}^2)(F_{2n\pm 1} - F_n^2)} = F_{n + 2\lor1}^2$$ $$\implies F_{2n\pm 1} + 2\sqrt{F_{2n\pm 1}(F_{2n\pm 1} - F_n^2 - F_{n\pm 1}^2) - (F_nF_{n\pm 1})^2} = F_{n + 2\lor1}^2$$.  $$\because F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$$ $$\implies F_{2n\pm 1} + 2\sqrt{-(F_nF_{n\pm 1})^2} = F_{n + 2\lor1} \neq F_{2n\pm 1} + 2\sqrt{\big(-(F_nF_{n\pm 1})\big)^2}$$ $$\therefore F_{2n\pm 1} + 2F_nF_{n\pm 1}i = F_{n + 2\lor1} : i = \sqrt{-1}$$  I have looked over every step and cannot see where I am wrong. The only part that must be wrong is that:  $$F_{2n\pm 1} + 2F_nF_{n\pm 1}i = F_{n + 2\lor1} \iff F_n^2 + F_{n\pm1}^2 = F_{2n\pm 1}$$  I can seperate $F_{2n\pm 1}$ as $F_n^2 + F_{n\pm 1}^2$ (if true) so I turn the equation into:  $$F_n^2 + F_{n\pm 1}^2 + 2F_nF_{n\pm 1}i = F_{n + 2\lor1}$$ $$\therefore (F_n + F_{n\pm 1})\bigg(\frac{F_n}{F_{n\pm 1}} + \frac{F_{n\pm 1}}{F_n} + 2i\bigg) = F_{n + 2\lor1}$$ Now I know that the greater the value of $n$, one of the fractions in the above equation (depending on which sign is used in $F_{n\pm 1}$) will get closer to the golden ratio $φ = \frac{1 + \sqrt{5}}{2}$ but $i = \sqrt{-1}$ is not a "real" number, although $F_n$ is.  I then searched for other formulae for finding $F_n$ and came across the one below (being Binet's Formula):  $$F_n = \bigg\{\frac{φ^n - ψ^n}{φ - ψ} : ψ = φ - \frac{\sqrt{20}}{2} = \frac{1 - \sqrt{5}}{2} \ \land \ φ - ψ = \sqrt{5}\bigg\}$$  But I do not know what how to turn that into $F_{n\pm 1}$. Could you please show me where I went wrong (because I must have gone wrong somewhere), and also if you wish, could you please show me how to turn the above fraction into $F_{n\pm 1}$ (if possible).  I only used the $(a + b)^2$ expansion rule because my skill level in mathematics is not particularly high compared to most of the users on this site (especially when logging into the MSE and finding fancy symbols like $\nabla$ and $\partial$ and $\sum$ which all look Greek to me, however the only "fancy" thing I know is that $i = i^5 = \cdots = \sqrt{-1}$) so if you used any other techniques in trying to prove this formula, could you please show me step by step?  Much appreciated. Thank you in advance.    Edit: I believe this question is a duplicate of this other question $\longrightarrow$   and I can go here to serve as a little hint $\longrightarrow$ How do I install Ubuntu? Industry standard file format deliverables for logos? Site.createPortalUser() returning null in test context Two figures side by side How can I put two figures side-by-side? Not two sub-figures, but two actual figures with separate "Fig.: bla bla" captions.  A figure is supposed to spread over the entire text width, but I have two figures which are narrow and long, and I need to save the space in order to withstand the pages limit. Symmetry condition for continuous coordinate transformations Is spacetime discrete or continuous? How can I concatenate two arrays in Java? I need to concatenate two String arrays in Java.  void f(String[] first, String[] second) {     String[] both = ??? }   What is the easiest way to do this? Installing windows to dual-boot I'm looking to install 32-bit windows with IIS to dual-boot with my 64-bit edition of windows on a laptop. I have a ten gig partition on my harddrive - is this large enough for a simple Windows install and a few programs?   I've never dual booted before, so I'm not quite sure how easy it is to mess up the process. Can you recommend any tutorials on how to set up a dual-boot configuration on Windows? Why is $2\pi i \neq 0?$ Intuition on the Kullback–Leibler (KL) Divergence Inverse of a Positive Definite Let K be nonsingular symmetric matrix, prove that if K is a positive   definite so is $K^{-1}$ .   My attempt:  I have that $K = K^T$ so $x^TKx = x^TK^Tx = (xK)^Tx = (xIK)^Tx$ and then I don't know what to do next. How to switch window controls to the left (Gnome Shell)? Is there a way to the switch gnome-shell window buttons to the left? I've gotten so used to them being on the left that them being on the right has thrown me way off.  (gnome shell has them defaulted to the right corner) Why is df -h size, util and dispo not corresponding to each other When I'm using the command "df -h" I'm having the following output :   Filesystem                 Size   Used  Avail Use% Mounted on /dev/mapper/fedora-root    20G    9,4G  8,8G  52% / devtmpfs                  1,9G       0  1,9G   0% /dev tmpfs                     1,9G    1,2M  1,9G   1% /dev/shm tmpfs                     1,9G    1,0M  1,9G   1% /run tmpfs                     1,9G       0  1,9G   0% /sys/fs/cgroup tmpfs                     1,9G    108K  1,9G   1% /tmp /dev/sda1                 477M    129M  319M  29% /boot /dev/mapper/fedora-home   916G    279G  591G  33% /home   Or it says my root is of 20G with 9.4 used and 8.8 still available it's 2G that disappeared. I know a very similar question as been answered here  and I'm just wondering if the reason could be the same here since I'm using LVM.  If not is there any way to reclaim that space that disappeared because for home there is an amazing 46G that disappeared. I came across a phrase for a type of question which is designed to discover someone's religious background, particularly in the context of sectarianism and divided societies but can't for the life of me remember it.   For example, if you are in Scotland and I ask you what football team you support, that may reveal your religion. Or in N.Ireland, if I ask what school you attend, likewise that may do the same.  It's like a 'veiled question' only that's not the term I'm looking for. Any help appreciated.  I've a feeling that the second part of the phrase is (question) as in, a INSERT TERM question, but not 100% sure.