Why are these two variables synced together
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Why does $F=ma$? Is there a straightforward reason? Why is force = mass $\times$ acceleration? I have searched in many sites but didn't actually get at it. Simply I want to know that if a mass in space moves (gains velocity thus further accelerates), how can I think, postulate and further believe that force = multiplication  of mass and its acceleration ? A ring $R$ is a Boolean ring provided that $a^2=a$ for every $a \in R$. How can we show that every Boolean ring is commutative? Can I travel to the USA while working remotely for my non-US employer? How to monitor bandwidth use of each device on wifi network Volume of bounded region between sphere and a plane I forgot my iPhone 5 passcode when I was changing the code. A window appeared on the device screen saying that iPhone is disabled.  I have Apple ID and password for it. After signing in to iCloud I have erased the device in order to remove the passcode from my iPhone but it still says that device will be erased when device will connect to internet. What would i have to do? What does Pirsig mean by "Quality"? I tried to install OracleJDK 8 using   sudo add-apt-repository ppa:webupd8team/java   But it's not working.   I searched the problem and found that      "The Oracle JDK License has changed for releases starting April 16, 2019." And  "Oracle Java (JDK) 8 Installer PPA (DISCONTINUED)"   So I installed the OpenJDK8 .   But why oracle cancelled the license of oracle 8 installer? I recently discovered that my computer is 64-bit. I have backed up my Home folder, and reinstalled Ubuntu. The reinstall wasn't nearly as painful as I thought. There is one thing that I can't quite seem to figure out: how do I get the 64-bit Firefox Beta build? I always get the Beta builds, but I want to take advantage of the 64-bit architecture of my computer.  says that Mozilla has come out with a 64-bit version of Firefox, but I can't seem to find it.  I do understand  of using a 64-bit browser, but I've decided to jump right in and do it anyway. (Flash and Java are already 64-bit, and who cares about Silverlight, since it's not for Linux anyway?)  There's only one issue, and it's a big one: I can't find the 64-bit Beta PPA!!! (I really hate using .tar.gz files, but I'd be willing to do that as long as I could still access Firefox via the Launcher. Oh, speaking of which, I don't understand .tar.gz files. Once, I managed to run one (the Dropbox Beta build,) but I have no idea whatsoever on how to install them: as in, click on the icon and go.) Where does gravitational waves' energy go? Following the measurement of gravitational waves, many sources described them and explained they carry energy away. What I don't get is how this energy will get transfered back to anything else.  If the fabric of space-time itself is vibrating, it would seem to be in impossible for any physical object to gain this energy.    What am I missing?  How would one hypothetically get energy out of gravitational waves?  If impossible, does the universe end up with nothing but GW? 80's pop song with lyric "It's the story of my life if you wanna know" I'm trying to identify a song by a female 80's pop group.   Here are the lyrics I remember:     It's the story of my life if you want to know   a play where everything is meant to be   you're the story of my life and I can't let you go How does RNA transcription determine which half of the DNA to use? I feel that I might have a complete misunderstanding here. If DNA has two strands, how does the machinery of RNA transcription determine which one to transcribe? What's so special about standard deviation? Do particles ever touch each other during a collision? Is the “sum of all natural numbers” unique? A while ago, there was a great hype about the “identity” $$\sum_{n=1}^{\infty} n = -\frac{1}{12}.$$  Apart from some series manipulations where the validity seems to be at least questionable, the derivation of this always goes through the zeta function:  Where the series converges, the zeta function is defined by $$\zeta(s) = \sum_{n=1}^{\infty}\frac{1}{n^s}$$ and outside that range by analytic continuation. And it turns out that inserting $s=-1$ formally results in $$\zeta(-1) = -\frac{1}{12} = \sum_{n=1}^\infty n$$  However looking at the series in isolation, there is no indication that the zeta function should be chosen.  An obvious way to get an analytic function that at one point gives the sum of all natural numbers is $$f(x) = \sum_{n=1}^{\infty} nx^n$$ at $x=1$, however (not surprisingly) that function diverges at $1$.  Therefore my question:     Is it possible to get another finite value for the series by analytic continuation of another series?   Concretely, do there exist continuous functions $f_1, f_2, f_3, \ldots$ such that   On some non-empty open subset $S$ of $\mathbb C$, $f(x)=\sum_{n=1}^\infty f_n(x)$ converges to an analytic function. At some point $x_0$, $f_n(x_0) = n$ for all positive integers $n$. The analytic continuation of $f$ is well defined and finite at $x_0$. $f(x_0) \ne -1/12$   What if we demand the functions $f_n$ to be analytic rather than just continuous? $A$ is an $n\times n$ matrix of complex numbers. Prove that if $\lambda$ is an eigenvalue of $A^2,$ then $\sqrt{\lambda}$ or $-\sqrt{\lambda}$ is an eigenvalue of $A.$    If $\lambda$ is an eigenvalue of $A^2,$ we have $\lambda\alpha=A^2\alpha$ for some $\alpha.$ Then how can we find a $\beta$ s.t. $\sqrt{\lambda}\beta=A\beta?$ How to hide quoted text in Lion Mail? In Mail's conversation view, by default, quoted text is hidden and can be shown by clicking "See More from XXX" in the bottom of each message. After clicking that, how can quoted text be hidden again? Probability that a quadratic polynomial with random coefficients has real roots The following is a homework question for which I am asking guidance.     Let $A$, $B$, $C$ be independent random variables uniformly distributed between $(0,1)$. What is the probability that the polynomial $Ax^2 + Bx + C$ has real roots?   That means I need $P(B^2 -4AC \geq 0$). I've tried calling $X=B^2 -4AC$ and finding $1-F_X(0)$, where $F$ is the cumulative distribution function.  I have two problems with this approach. First, I'm having trouble determining the product of two uniform random variables. We haven't been taught anything like this in class, and couldn't find anything like it on Sheldon Ross' Introduction to Probability Models.  Second, this strategy just seems wrong, because it involves so many steps and subjects we haven't seen in class. Even if I calculate the product of $A$ and $C$, I'll still have to square $B$, multiply $AC$ by four and then subtract those results. It's too much for a homework question. I'm hoping there might be an easier way. How to disable pagebreak on \hline in longtable? How to disable pagebreak on \hline in longtable?  This is an example illustrating my problem:  \documentclass[12pt,a4paper,oneside]{letter}  \usepackage{longtable}  \begin{document}  \begin{longtable}{ | p{5cm} | } \hline Table header\\* \hline Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris pharetra porttitor turpis, id egestas neque congue in. Nam sed lorem lorem, ac tristique tellus. Nunc ornare feugiat orci, a blandit turpis facilisis ut. Aenean pharetra ornare ante. Sed tempus leo in dolor eleifend placerat. Integer at enim augue. Ut nisl tortor, interdum ac porttitor ac, sagittis quis libero. Vivamus nibh metus, ornare vel pulvinar nec, fringilla nec orci. Maecenas mollis nulla a nibh fringilla nec convallis augue varius. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere   cubilia Curae. \\ Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris pharetra porttitor turpis, id egestas neque congue in. Nam sed lorem lorem, ac tristique tellus. Nunc ornare feugiat orci, a blandit turpis facilisis ut. Aenean pharetra ornare ante. Sed tempus leo in dolor eleifend placerat.  Integer at enim augue. Ut nisl tortor, interdum ac porttitor ac, sagittis quis libero. Vivamus nibh metus, ornare vel pulvinar nec, fringilla nec    orci. Maecenas mollis nulla a nibh fringilla nec convallis augue varius.   Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere   cubilia Curae. \\ \hline Table header\\* \hline Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris pharetra porttitor turpis, id egestas neque congue in. Nam sed lorem lorem, ac    tristique tellus. Nunc ornare feugiat orci, a blandit turpis facilisis ut. Aenean pharetra ornare ante. Sed tempus leo in dolor eleifend placerat.    Integer at enim augue. Ut nisl tortor, interdum ac porttitor ac, sagittis  quis libero. Vivamus nibh metus, ornare vel pulvinar nec, fringilla nec    orci. Maecenas mollis nulla a nibh fringilla nec convallis augue varius.   Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere  cubilia Curae. \\ \hline \end{longtable}  \end{document}   I'd like to have second header on page 3. I do not control table contents, so I can not do page breaks manually. I once saw watch a sci-fi movie or an episode of a tv series (not sure) in which:   Every police officer was a judge, and hence could act by themselves on the streets. Each "judge" had a gun, which appended their DNA to the bullet. This was used later in investigations about a crime scene, and I think was confidential before the trial was held. Only a judge could use the gun, try to use it and you've been electrified. Also the guns had a self-destruction feature. The main villain was an ex-judge who purchased and activated a very old "killer robot" which was a residue of a long-ended war. When a judge was exiled, they were given a copy of the book of law, and sent outside the city to enlighten the people outside cities.   Can you help me find it?  PS: It was difficult to select a title