How to write this formula in LaTeX?
How to typeset asymmetrical confidence level limits / uncertainties?
Change the location of saved screenshot when screenshot taken by printscreen button in GNOME 3 .bash_history does not update in Git for Windows (git bash) Why does inductor current lag the applied voltage at its terminal by 90 degrees? I studied electromagnetism and I am currently working with Inductors.  I could not figure out the physical reason based on electromagnetics on why inductor current lags the applied voltage by 90 degrees?  Everywhere I find the Formula as the starting point of explanation which is partially satisfying.    Induced EMF =L di(t)/dt    From the above equation, I understood that when there is a change in current there will EMF induced in the coil terminals. But How this induced EMF makes the current to lag the supply voltage V(t) = Vm*sin(wt)? (Please don't just differentiate and say there is a lag, I am looking for a physical sense on why this happens)  Lets us consider the AC voltage is applied across the terminal at time t=0; At this time there is almost no current. From this transient state how the steady-state is reached where the current is delayed with respect to the voltage?  Can someone help me to figure out why the current lags the Supplied voltage by using electromagnetism, the motion of Charges or any other basic concepts? Is it possible to find power armor in the wasteland? If you send somebody out in the wasteland for long enough with good enough luck, is it possible to find power armor or any other legendary gear? 403 error after upgrading to apache2.4 After upgrading from Ubuntu 13.04 server, the www pages won't display themselves.     Error 403 Forbidden You don't have permission to access / on this server.   I've changed access control saves from apache2.2 to apache2.4, but that didn't work. What else could I do? Using OR comparisons with IF statements When using IF statements in Python, you have to do the following to make the "cascade" work correctly.  if job == "mechanic" or job == "tech":         print "awesome" elif job == "tool" or job == "rock":         print "dolt"   Is there a way to make Python accept multiple values when checking for "equals to"? For example,  if job == "mechanic" or "tech":     print "awesome" elif job == "tool" or "rock":     print "dolt" What is the difference between g++ and gcc? What is the difference between g++ and gcc?  Which one of them should be used for general c++ development? Controlling Volume Mixer Can I read the hash portion of the URL on my server-side application (PHP, Ruby, Python, etc.)? I´m trying to model a race track using a bezier curve, but, when I add modifiers -> array -> curve I get this :    What should I check for to get the mesh following the curve correctly ? Thankyou Proof for SSS Congruence? Combine 4 cells in a table Here is a simple table.  I want to merge 4 cells. I want to combine the three "this" cells area in this table. I thought I have to use multirow and multicolum at same time. However, I could not find how to use it.  If possible, could you post the modified LaTeX source code?     My LaTeX code:  \documentclass{article} \usepackage{multirow}% http://ctan.org/pkg/multirow \usepackage{hhline}% http://ctan.org/pkg/hhline \begin{document}  \begin{table}[ph] \begin{center} \begin{tabular}{c|c|c|c|c} \hline \multirow{2}{*}{Raaa (k)} &amp; \multicolumn{4}{c}{C ()} \\ \hhline{~----}  &amp; 3.3 &amp; 2.5 &amp; 1 &amp; 0.5 \\ \hline \multirow{2}{*}{Raaa (k)} &amp; \multirow{2}{*}{this} &amp; this &amp; 0.5 &amp; 0.6\\ \hhline{~~~--}            &amp;                       &amp; this &amp; 0.7 &amp; 1.2 \\ \hline \end{tabular} \caption{R, C ripple size} \label{T:peak} \end{center} \end{table} \end{document} Interior of cartesian product is cartesian product of interiors I have to prove that:  $$Int(A\times B) = Int(A)\times Int(B)$$  Where $A\subset M$ and $B\subset N$, both $M$ and $N$ metric spaces.  The problem is that the exercise does not specify the metric, so I need to try to prove it using a generic metric.  If $x\in Int(A\times B)$, then an open ball can be centered at $(x,y)$ such that it is contained in $A\times B$. Therefore, this open ball, $B((x,y),r)\subset A\times B$. It means that $d((x,y),a)&lt;r$ for any $a\in A\times B$ for some $r&gt;0$. I guess that if I can take from here that $d(x,a)&lt;r$ and $d(y,a)&lt;r$ I can prove thhat $Int(A\times B)\subset Int(A)\times Int(B)$, but I still have to prove the other way around.   Any ideas? Proof on Catalan numbers How far do you go with const?  Do you just make functions const when necessary or do you go the whole hog and use it everywhere?  For example, imagine a simple mutator that takes a single boolean parameter:  void SetValue(const bool b) { my_val_ = b; }   Is that const actually useful?  Personally I opt to use it extensively, including parameters, but in this case I wonder if it's worthwhile?  I was also surprised to learn that you can omit const from parameters in a function declaration but can include it in the function definition, e.g.:  .h file  void func(int n, long l);   .cpp file  void func(const int n, const long l)   Is there a reason for this? It seems a little unusual to me. How to replace one char with another in all filenames of the current directories? What does the Recycle Bin in Windows actually do?  Is it just a glorified folder and a holding place for soon to be deleted files, or does it do something specific?  Specifically, are files that are "moved" to the Recycle Bin actually moved on the hard disc, or are just the pointers to the files moved?  I am a fairly experienced user, I just wanted a more depth explanation of the Recycle Bin. The problem is, when I open applications I need to always right click, select run as admin.     When I don't do it getting unexpected application errors. BTW, I turned off UAC.   It's annoying. Is there any way to change behavior of double left-click to act as "Run as administrator" action? I mean to make "Run as administrator" action by default. Thx in advance Show that $\prod (1- P(A_n))=0$ iff $\sum P(A_n) = \infty$ Tile Edge Challenge I've been having a problem with these problems for a week now so I thought I'd post it on MSE. Read the text below. . I've also typed it up:  Annabel made a shape by placing identical square tiles in a frame as shown in the diagram above. The tiles are arranged in columns. Each column touches the base but no columns touch the side or top. There are no empty gaps between columns. The frame can be enlarged as needed.  These are the questions. I've also typed them up.    A. Show that it is possible to arrange $7$ tiles so that the ant walks $8,9,10,11,12,13,14,15$ tile edges.   B. Show 6 ways of arranging 7 tiles so that the ant walks a total of 9 tile edges.  C. Show it is possible to arrange 49 tiles so that the ant walks a total of less than 21 tile edges.  D. Show four arrangements of 137 tiles, each arrangement with a different maximum height, so that the ant walks a total of 34 tile edges.  For question $a$, is there a formula relating the number of tile edges exposed to the number of tiles. These are my answers for $a$    For the above picture, it's the left hand side which has the $a$ answers.  However, I'm having a bit of trouble with $b$. I've already got four answers down but where are the other two. My four current answers are in the right hand side of the last image. Also, I'll also appreciate a formula to show the relationship.  I'm also having trouble with $c$. I found out that you get 21 tile edges exposes when you make a $7*7$ square but the answer is asking for less than 21. Can anyone help me. Also, as in the previous questions, a formula to show the relationships would be great.  And for $d$, I am totally lost. I have no idea where to start, and I certainly can't find out four arrangements. So can anyone help me? And as always, a formula is nice  P.S. Please explain this in an understandable formula, as I'm only a Year 7 with the ability to understand linear algebra and parts of quadratics and trigonometry. Also, sorry about the poor imaging.