Find the inverse of $5$ under multiplication modulo $11$ on $Z_{11}$  Please help me with problem. Can't show any work because I don't know how to proceed.
I need to find out the modular inverse of 5(mod 11), I know the answer is 9 and got the following so far and don't understand how to than get the answer. I know how to get the answer for a larger one such as 27(mod 392) but am stuck because they are both low numbers.  11=5 (2)+1  5=1 (5)
Integrate $\int \frac{25 - x^2}{x^4} \operatorname d\!x$ I think we use trig substitution for this. But I'm not sure where to even begin with this   $$\int \frac{25 - x^2}{x^4} \operatorname d\!x$$ I am flying from New Orleans to Dulles (IAD) on United Express, and from IAD to Frankfurt on United. I have a short connection (45 minutes) in IAD.   I'm trying to figure out how can I make it:  Will I need to go throughout security and border check since I'm leaving the US? How big is IAD airport? and are there different terminals for domestic and international flights? If so, how long would it take to walk between them? Increase the visibility of the association bonus by documenting it with the other privileges Additive group contains exactly three elements of the set $\{p,p+q,pq,p^q,q^p\}$ Let $p$ and $q$ be distinct primes. There is a proper subgroup $J$ of the additive group of integers which contains exactly three elements of the set $\{p,p+q,pq,p^q,q^p\}$. Which three elements are in $J$?  I know the solution is $\{p,pq,p^q\}$. However I do not understand why. I thought $J$ can not even be a finite group. Maybe there is serious misunderstanding of the problem. Can anyone give me a hand? Thanks. Ubuntu in VirtualBox wants to install on every boot Is Cyclops’ mutant power just an organic version of Iron Man's repulsor tech? They occupy the same universe so we have to assume the same physics apply. Iron Man's repulsor tech is described as an inertia-less one-way kinetic blast. At higher energy levels, it can can even disintegrate matter in front of it. Cyclops’ eye beams are described exactly the same way. Is there any place in comics or the animation where the two beams are shown to have different powers? Consider the partial sum of the divergent Harmonic series $H_n = \sum\limits_{k = 1}^{n}\frac{1}{k}$. I recently saw a question which required finding out the asymptotic bounds of $H_n$. Now, I could not find any bound closer than $O(n)$. So I looked up the series and found  Wikipedia article which says that $H_n - \ln n$ approaches a constant (the ). This clearly shows that $H_n = \Theta(\log n)$.  However, considering the question was in an beginners undergraduate algorithms course in CS, I was wondering if there is a simpler proof of this? Is there some clever proof requiring elementary mathematics to show $H_n = \Theta(\log n)$?  PS: This is not homework in the sense that it is not my homework, and the actual question does not ask for a proof, but rather asks a lot of functions to be arranged asymptotically. Why are "south" and "southern" pronounced with different vowels? I was wondering why we pronounce the vowels in the words south and southern. They seem to be very closely related to each other. Both refer to the same direction. South is a noun and Southern is an adjective, which I don't think caused them to have a different vowel. Oxford Dictionary shows that south is /saʊθ/ and southern is /ˈsʌð(ə)n/. In short, south has a long vowel and southern has short. What's the difference between Google Chrome and/or Chromium? What are the advantages/disadvantages to each? I used Google Chrome in Windows, and am now using Chromium in Ubuntu.  Is there any difference to the two programs?  What are the advantages and disadvantages to each program?  Which one seems better? computing the orbits for a group action Can't read code blocks from the Stack Exchange android app Why did the slaver in Astapor think Daenerys wouldn't do exactly what she did? Spoilers! (do I have to even say that here?)  I recently rewatched the episode of Game of Thrones where Daenerys is in Astapor. She makes the deal with the master slaver guy, where she trades him one of her dragons for 8,000 of his very tough slaves. I immediately thought this was stupid for two reasons:   Why would he think the dragon would immediately obey him rather than her? Maybe he doesn't quite believe the 'Mother of Dragons' lore, but it's still basically a pet at the very least. This one isn't as bad though, as... Why would he possibly think she wouldn't betray him and use her freshly bought slaves to take back her dragon? He just traded her literally all his slaves and he has not been kind to her so far. He has motivation to not go back on the deal -- he's running a business, basically... but she has no reason not to.   I guess you could argue that he was blinded by greed, but I think that would be poor writing -- he's in a vicious trade, I can't imagine he would've survived long thinking so naively.  Does anyone have a good explanation? A regular function can contain a call to itself in its definition, no problem.  I can't figure out how to do it with a lambda function though for the simple reason that the lambda function has no name to refer back to.  Is there a way to do it?  How? Simplify a combinatorial sum Why is $\sum_{k=0}^n (_k^n) 2^k$ simplified as $3^n$ and not just $2^n$ ? The answer uses the binomial theorem as a solution: let $a=1$ and let $b=2$. So $1+2 = 3$. But since $1+2 = 3$ why do we not use $1+1 = 2$? I know that $\operatorname{Spec} \mathbb{C}[x]$ can be identified with the set $\mathbb{C}\cup *$, where $*$ is a generic point via the correspondence  $$ \prod_{i}(x-a_i) \leftrightarrow \{a_i\}_i , \ \ \ \ (0)\leftrightarrow *. $$ This correspondence holds for any $\operatorname{Spec} k[x]$ with algebraic closed field $k$.   When $k$ is not algebraic closed, how should one understand $\operatorname{Spec} k[x]$? Two columns with different background color and height of whole page I want to create page with two columns with different background color and height of whole page. What I was able to do is two columns with different background color but I can't set proper height and there is small gap between two columns and another gap between top of the page and top of the columns. I want to remove these gaps. Also I want to create vertical line between two columns. Right now I have minipages packed inside \colorbox which allows me to create all four borders but I only want one.   Final effect should look like this:    This is what I figured out for now:  \documentclass{article} \usepackage{blindtext} \usepackage{xcolor} \usepackage{geometry} \geometry{margin=0in}  \begin{document} \noindent \fcolorbox{black}{red}{ \begin{minipage}{.3\textwidth}   test \end{minipage} } \fcolorbox{yellow}{yellow}{ \begin{minipage}{.7\textwidth}   test \end{minipage} } \end{document} How to change css property using javascript Review option on mobile phone not available? Show address bar w. full path in Nautilus instead of breadcrumbs bar Enable Wireless Monitor mode for traffic sniffing I need to sniff all the wifi traffic that I can capture using wireshark in Ubuntu. My wireless interface is named as eth1 in the interfaces list. When I select that interface in Wireshark and start new sniff, I got following error;    As  thread says, I tried to installed the mentioned driver but I got an error in installation saying that that driver is not supported by my device. After that I tried the second answer in the same thread and run following command to enable monitor mode in my wireless card.  echo 1 &gt; /proc/brcm_monitor0   Then I saw a new Ethernet interface (not a wireless interface ) called prism0 in wireshark interface list. I couldn't start a sniff using that interface using monitor mode because in that interface settings, monitor mode check box has been disabled.  I have installed a broadcom wireless driver in Additional Drivers as follows:    Is there an error listing my Wifi interface as eth1 rather than wlan0 in the interfaces list? How can I start my wireless interface in monitor mode for sniffing?   Thank you.