Solving this trigonometric task: $\sqrt{3}\cos{\theta}-\sin{\theta}=R\cos(\theta+\alpha)$
Express $\sqrt{3}\sin\theta - \cos\theta$ as: $a\cos (\theta + \alpha) $
It is known that a superconductor is a material with electrical resistance zero. My question is, it is exactly zero, a theoretical zero, or for practical realistic reasons it is effectively zero? Pass a PHP string to a JavaScript variable (and escape newlines) What is the easiest way to encode a PHP string for output to a JavaScript variable?  I have a PHP string which includes quotes and newlines.  I need the contents of this string to be put into a JavaScript variable.  Normally, I would just construct my JavaScript in a PHP file, à la:  &lt;script&gt;   var myvar = "&lt;?php echo $myVarValue;?&gt;"; &lt;/script&gt;   However, this doesn't work when $myVarValue contains quotes or newlines. Fixed point, union of $\aleph_0, \aleph_{\aleph_0},\aleph_{\aleph_{\aleph_0}}\dots$ [see Noah's comment on notation] I was editing a curve for hair, and pressed W to bring the specials menu and Subdivide it, but instead everything but the curve I had active dissapeared, and my cursor turned into a circle like the one from the circle select mode.  I'm guessing they changed the specials menu and I'm inside some unknown to me function, but I'm not sure how to turn everything back to normal. RAM not clearing, alway in standby I'm having a problem with my ram on windows 7. The ram is clearing or programs are using and dumping it faster than it can clear. I have 8gb of ram I'm only using 4gb and the rest is in Standby. At best time I can get 100mb of free but its mostly at 15mb or less. I suspect a memory leak but I have no way to figure out what program it is. I have not installed any new hardware recently and newly installed programs have bin closed. Does any one have an idea of what is going on and how to fix it?   I'm sorry this is so little information but that is all I have as well.  Edit: I tried RamMap and found out the my "Mapped File" has 3,291,784k ram in standby how do I figure out what program and how do I limit it's ability to set ram in standby?  Edit: I keep getting a problem when I will have 0 free ram and my computer will stop working properly. It will become outrageously slow where it will take 3-4 minutes to start task manager so I can close some programmes. When I free up some ram by closing some programmes every thing runs normally. It does not matter which programs I closes only that I free up some ram. I know a lot of you say it's supposed to be like that and that's how windows works. But its obviously a problem and my computer has never worked that way neither has any of my other computers. I would like to fix this please help me. Why do some Unicode text messages crash the iPhone OS? Recently a new "glitch" has surfaced over the Internet over the last few weeks where if an iPhone user is sent:    effective.        Power            لُلُصّبُلُلصّبُررً ॣ ॣh ॣ ॣ  冗   via iMessage it crashes the phone OS temporarily and force restarts the receiving phone.  Why does this work? Where do the files go if you mount a drive to a folder that already contains files? I just accidentally mounted a new drive to a folder that already contained files.  I don't care about them and have them somewhere else, but that folder appears empty now.  I'm curious what happened to the files.  Are they simply deleted by Linux? How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion? How can I test for a player wearing specific armor? How can I test for a player that is wearing an iron helmet named "test1" and an iron chestplate named "test2" in Minecraft Version 1.12? proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$ I am currently working through Velleman's book How To Prove It and was asked to prove the following  $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$  This is my work thus far  $(P \to Q) \wedge (Q \to P)$  $(\neg P \vee Q) \wedge (\neg Q \vee P)$ (since $(P \to Q) \equiv (\neg P \vee Q)$)  $\neg[\neg(\neg P \vee Q) \vee \neg (\neg Q \vee P)]$ (Demorgan's Law)  $\neg [(P \wedge \neg Q) \vee (Q \wedge \neg P)]$ (Demorgan's Law)  At this point I am little unsure how to proceed.   Here are a few things I've tried or considered thus far:  I thought that I could perhaps switch some of the terms in step 3 using the law of associativity however the $\neg$ on the outside of the two terms prevents me from doing so (constructing a truth table for $\neg (\neg P \vee Q) \vee (\neg Q \vee P)$ and $\neg (\neg P \vee \neg Q) \vee \neg (P \vee Q)$ for sanity purposes)  I can't seem to apply the law of distribution since the corresponding terms are negated.  Applying demorgans law to one of the terms individually on step 2 or 3 doesnt seem to get me very far either.  Did I perhaps skip something? Am I even on the right track? Any help is appreciated Why is $\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}$? It seems as if no one has asked this here before, unless I don't know how to search.  The Gamma function is $$ \Gamma(\alpha)=\int_0^\infty x^{\alpha-1} e^{-x}\,dx. $$ Why is $$ \Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}\text{ ?} $$ (I'll post my own answer, but I know there are many ways to show this, so post your own!) Cross product term in linear regression why is it zero I'm trying to see why this is the case. I have taken  the LHS and added $X\hat{\beta}$ and subtracted $X\hat{\beta}$.  From this I can get both terms on the right but I end up with a cross product term  $2(y-X\hat{\beta})^T(X\hat{\beta} - X\beta)$  that I can't prove equals to zero. I think there is some trick I'm missing, anybody remember it? DML is not allowed in a constructor. Is there a known reason behind this limit?  I have been searching for the answer &amp; haven't found anything which addresses the question. May be it's not documented anywhere(Or google doesn't know where it is). Find index of nested item in python I'm using +[NSUserDefaults standardUserDefaults] to store application settings. This consists of roughly a dozen string values. Is it possible to delete these values permanently instead of just setting them to a default value? How can metagaming retries on poor skill checks be prevented? Why is Ubuntu 14.04 so slow on my laptop? I just installed Ubuntu 14.04 on a Dell laptop with 1.7Ghz Pentium M and 1Gbyte memory.  Graphics are Intel® 852GM/855GM x86/MMX/SSE2, OS type is 32bit.  The whole system is VERY slow. When I launch the applications manager, for example, I need to wait in order to see the letters I typed appear!  It is as if the CPU was overloaded and no memory available, but I only have Firefox running.  How can I make the system run smoother? It used to have Windows XP installed and it worked fine. Global inbox message not updated after comment edit At the moment, I have the latest notification in the global inbox, content of which does not correspond either to the comment itself or the copy of it on "recent responses" page. This seems like the comment was edited and the updated version was not copied to the global inbox.    ETA: OK, now this looks more coherent. I have upgraded from Ubuntu 16.04 LTS to Ubuntu 18.04 LTS. I was surprised to see that the context menu entry "Make Link" (keyboard shortcut Ctrl+M) in Nautilus doesn't seem to exist anymore. It used to appear upon right mouse click on a file or folder and allowed the user to create a symbolic link. Displacement currents, aren't really currents?