What is the relative speed of two near-light speed particles headed towards each other?
(Almost) double light speed
18.04: color emoji not showing up at all in Chrome, only partially in Firefox Using both “one’s” and “their” to refer to the same entity How to find the inverse modulo $m$? For example: $$7x \equiv 1 \pmod{31} $$ In this example, the modular inverse of $7$ with respect to $31$ is $9$. How can we find out that $9$? What are the steps that I need to do? Update If I have a general modulo equation: $$5x + 1 \equiv 2 \pmod{6}$$ What is the fastest way to solve it? My initial thought was: $$5x + 1 \equiv 2 \pmod{6}$$ $$\Leftrightarrow 5x + 1 - 1\equiv 2 - 1 \pmod{6}$$ $$\Leftrightarrow 5x \equiv 1 \pmod{6}$$ Then solve for the inverse of $5$ modulo 6. Is it a right approach? Thanks. What if I run a virus/trojan Windows EXE on Ubuntu with Wine? I'm currently in the process of making a custom map and I want to add blocks that can only be placed on a certain colour clay.  This is the command I tried using.  /give @p cobblestone 1 0 {CanPlaceOn:["hardened_stained_clay"],Damage:3}   However, even with this command the cobblestone can be placed on any colour of stained clay. What command can I use for placing only on a certain block? TikZ externalization with absolute path and MiKTeX distribution This code:  \documentclass[11pt,openright]{book} \usepackage[T1]{fontenc} \usepackage[latin9]{inputenc} \usepackage[british]{babel}  \usepackage{tikz} \usetikzlibrary{external} \tikzexternalize[prefix={"C:/Users/MyName MySurname/Documents/LaTeX/Figures/"}]  %\tikzexternalize[prefix={Figures/}]   \begin{document} \begin{tikzpicture}     \draw (0,0) circle (1cm); \end{tikzpicture} \end{document}   gives me the error:     ! I can't write on file `"C:/Users/MyName   MySurname/Documents/LaTeX/Figures/MyMWE-figure0.md5"'.   I'm working with Windows 10, MiKTeX 2.9 distibution.  Following the advice Tarass gave me on a comment of this question:  and as indicated here:  I've registered a user-managed TEXMF directory but I still get the same error.  With \tikzexternalize[prefix={Figures/}] all works perfectly but, since I'm using LyX, the files are stored in a LyX temp dir, hence I loose them when I close the program (making externalization useless), so I need to use an absolute path. addtocontents not working with certain other packages I understand the proof that  $$Var(aX+bY) = a^2Var(X) +b^2Var(Y) + 2abCov(X,Y), $$  but I don't understand how to prove the generalization to arbitrary linear combinations.  Let $a_i$ be scalars for $i\in {1,\dots ,n}$ so we have a vector $\underline a$, and $\underline X = X_i,\dots ,X_n$ be a vector of correlated random variables. Then $$ Var(a_1X_1 + \dots a_nX_n) = \sum_{i=1}^n a_i^2 \sigma_i^2 + 2 \sum_{i=1}^n \sum_{j&gt;i}^n a_i a_j \text{ Cov}(X_i,X_j)$$  How do we prove this? I imagine there are proofs in the summation notation and in vector notation? Identifying pin numbers from PCB Consecutive days missed I visited Stack Overflow for about 82 days in a row (starting January 21st), including yesterday (April 13th) and today (April 14th).  All times UTC of course (I thought that was clear but I've now added it to my question as a relevant info).  All visits are in a logged-in session of course.  I've just discovered that SO didn't "see" the April 13th visit, so my consecutive days visits were zeroed !!  It's a bug for sure. I have open tabs which my browser's history shows that are from April 13th. More than 20 of them. I saw this one:  , and it's clearly what happened to me. Please help! I'm so close to getting the Fanatic badge... If $A$ is a non-empty set, then $A \notin A$ Exercise 3.2.2 Use the axiom of regularity and the singleton set axiom to show that if $A$ is a set then $A \notin A$.  Axiom of Regularity: If $A$ is a non-empty set, then there is at least one element x of A which is either not a set, or is disjoint from A.  Singleton Set Axiom: If $a$ is an object, then there exists a set $\{a\}$ whose only element is $a$, we refer to $\{a\}$ as the singleton set whose element is $a$ Furthermore, if $a$ and $b$ are objects, then there exists a set $\{a,b\}$ whose only elements are $a$ and $b$    I think I can give the proof when A is the non-empty set which contains finite elements. However, can anyone give any hint for the general case?  Suppose $A \in A$   Then eixsts $x$ such that either $x$ is not a set or $x \cap A$=$\emptyset$  Then it is clear thar $x \ne A$ (if $x = A$, then $x \cap A \ne \emptyset$)  We observe that as an element, $A$ $\ne$ $x$, $A$ $\in$ $A$  Then $A$ $\in$ $A-x$   Define the new set $A-x$ as $A_1$  then exists $x_1$ such that $A \in A_1-x_1$  After finite steps  we find that $A \in \emptyset $  which leads to contradiction. How can I change an element's class with JavaScript? How can I change the class of an HTML element in response to an onclick or any other events using JavaScript? If $f$ is bounded and $\lim_{x \to c} g(x) = 0$, then $\lim_{x \to c}g(x)f(x) = 0$ How to prove that $L=${$a^p$: p is prime} isn't regular? I tried using pumping lemma or finding infinite equivalence classes, but I didn't succeed.  It's clear to me that there is no automata that accepts this language, but I just can't formally prove that this language isn't regular.  How can you prove it? How can I deduce/identify an app from a notification icon? Engines that play Mangala? Which is more idiomatic in a bash script: `|| true` or `|| :`? I don't do terribly much shell scripting, so I was a little surprised when I was reading  and I saw the syntax they used in this documentation:     A non-zero return from the command in any submodule causes the processing to terminate. This can be overridden by adding || : to the end of the command.   I had to look up that || : was a shorthand for forcing a command to exit successfully.  Anytime I've had to make a command exit successfully, I used || true.  Is || : considered to be more idiomatic? Player looses boot after tackle $\Delta U$, $C_p$, $C_v$ for an ideal gas process Show that $\cot \frac{\pi}{2m}\cot \frac{2\pi}{2m}\cot \frac{3\pi}{2m}...\cot \frac{(m-1)\pi}{2m}=1$