The day before yesterday, I tried to update my OSX from macOS Cataline to Big Sur. I tried 3 times and all time after downloading some MB / 1 GB , it says operation failed.  Then I stop to update. But after this process , my macbook space is showing more 3 GB as used. Are there any was to find those files? It's urgent for me to free up those space.  In the same day , Xcode archive for app was also not working. Was giving some error. So this failed archive also took some space. I tried to find that unsuccessful archive folder under Library/Developer/Xcode/Archive . But I didn't find anything.  Does anybody help me in finding those files??  are there any other way to free up my storage. My macbook is running out with space.  This is the storage details  Anyone kindly help me. Any help would be appreciated...
Every few days I get notices on my MacBook that it's running or run out of hard drive space. Curiously, restarting the computer will enable me to recover gigabytes of space (this past time, it was able to recover about 2.2GB). However, I can't identify anything in my personal activity that consumed that space.  It's possible that it's a rogue iTunes podcast or a huge software update that my Mac is automatically downloading - would either of these reclaim the space upon a restart?  One possibility that I can think of is that FileVault has some sort of disk leak, allocating but not freeing files. Does this make sense? Is there a tool that I can run to determine where this space is going? Assuming it is FileVault, should I try to disable it? What's the best way to turn of FileVault on a nearly full computer?
Are there rules for using manacles in combat? I can't quite find in the PHB or DMG how to slap manacles onto someone during combat. PHB 152 describes how to break out of mundane manacles, while DMG 165 shows how Dimensional Shackles work (they are essentially magic manacles -- use 1 action to bind an Incapacitated target).  Is there an official rule on how to use manacles in combat, or do we have to use house rules? How do I resolve a recurrence relation when the characteristic equation has fewer roots than terms? I know how to solve "simple" recurrence relations. For instance, say you have:  $$c_0 = 20$$ $$c_1 = 30$$ $$c_n = 3 c_{n-1} - 2 c_{n-2}$$  We can write the characteristic equation as:  $$3x^{n-1} - 2x^{n-2} = x^n$$  Solving this with $n=2$, we get $x = 1$ or $x = 2$. This lets us write the relation $c_n = \alpha_1 1^n + \alpha_2 2^n$, and we can solve for $\alpha_1$ and $\alpha_2$ with the initial states $c_0$ and $c_1$.  However, this depends on the fact that $3x^{n-1} - 2x^{n-2} = x^n$ has two roots.  Now, I'm stuck on another problem where the characteristic equation has fewer roots than terms.  Say I have this recurrence relation instead:  $$a_0 = 0$$ $$a_1 = 2$$ $$a_2 = −1$$ $$a_n = 9a_{n-1} - 15a_{n-2} - 25a_{n-3}$$  The characteristic equation would be:  $$9x^{n-1} - 15x^{n-2} - 25x^{n-3} = x^n$$  However, solving with $n=3$, we only get two roots: $x=-1$ or $x=5$. There are not enough roots to write a relation in the form of $a_n = \alpha_1 r_1^n + \alpha_2r_2^n + \alpha_3r_3^n$. How do I proceed? Can't see a glass object through another glass object in Eevee I was just testing Eevee and found that you cannot view a glass object through another glass. Is there any workaround? It works fine only If I rotate the glass window or put my camera to the back side of the scene General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$. If $k=1$, we have \begin{align} \sum_{n\ge1}\frac{1}{\binom{2n}{n}}&amp;=\frac12\sum_{n\ge1}n\mathrm{B}(n,n)\\ &amp;=\frac12\int _{0}^{1}\sum_{n\ge1}n(t-t^2)^{{n-1}}{\mathrm  d}t\\ &amp;=\frac12\int _{0}^{1}\frac{1}{(t-t^2-1)^2}{\mathrm  d}t\\ &amp;=\frac13+\frac{2\sqrt3\pi}{27} \end{align} I wonder if there exists a general formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$ with $k\in\Bbb N^*$. This may involve some ${}_pF_q$ functions. Sum of real numbers that multiply to 1 I've seen a question in my math book with this explanation above it: "If the product of n positive real numbers is 1, then the sum of these numbers must be more than n". I was wondering if this is correct, and if it is, could someone give an explanation or a proof for it? Delayed erasure experiment Do all accepted students in top-tier engineering programs get invited to interview before getting admitted? What's the thing with $\sqrt{-1} = i$? Do they really teach this in the US? It makes very little sense, because $-i$ is also a square root of $-1$, and the choice of which root to label as $i$ is arbitrary. So saying $\sqrt{-1} = i$ is plainly false!  So why do people say $\sqrt{-1} = i$? Is this how it's taught in the US? I don't know what I've done, but all of a sudden I am unable to compile any document which uses the geometry package. Minimal (non)-working example:     \documentclass[11pt]{article}      \usepackage{geometry}  \begin{document} test \end{document}   doesn't produce any output, and this is what I see in my error summary screen in TeXnicCenter:    The red arrow points to what seems to be the problem: something about the bundle "oberdiek" and its package "ifvtex" is causing pdflatex.exe (which, while I don't really know what it does, sounds pretty important) to "not be initialized". I , and it's relevance here is a mystery to me.  I've confirmed that all of my files without the geometry package compile just fine; however, that doesn't mean that the problem is with the geometry package - what seems more likely is that there is some hidden cause of the error, and geometry happens to be one way to induce that. By the way, I've tried compiling a document which includes the ifpdf and ifvtex packages separately, and they do just fine; it's only when I include the geometry package (which for some reason requires these ifpdf and ifvtex packages) that the error occurs.  I've tried the only things I can think of:   going into MiKTeX Package Manager (by the way I am using 2.8), and removing + reinstalling both geometry and oberdiek refreshing the file name database ("FNDB") deleting all automatically generated files, as well as simply starting over in a new document   So I'm stuck now. I've considered attempting to just get rid of all traces of MiKTeX and TeXnicCenter from my computer and starting over, but that seems a bit excessive - after all, the geometry package was working for me . I honestly am not sure what I did to cause this; I've spent today trying to make a better template file for myself, and so I've been trying out new packages, but if I'm not loading these new packages there shouldn't be any conflicts, right?   Actually, I've just now thought of something that I think I did between the last time it worked and now, so is a possible candidate for the cause: I had to install some package manually, as it wasn't available on MiKTeX, and so I created a folder and pointed MiKTeX to it (i.e. the second option ). The package didn't do what I wanted, so I deleted the folder and removed it from the list of folders I told MiKTeX to check. Perhaps it's still trying to reach it for some reason? Reset or remove the BIOS password on my laptop So, I know that $\max(-X_{(1)},X_{(n)})$ is a sufficient statistic for the parameter $\theta$. But can I also say that $(X_{(1)},X_{(n)})$ are jointly sufficient for the parameter $\theta$ ?  In other words, can a single parameter have jointly sufficient statistics? In a file with lots of lines I want to delete lines that starts with HERE IT IS.  How can I do this using only command-line tools? Please let me know how to change the size of the camera view. The red dotted line of the square is too small for me. Virus added .mbed File Extension The files on my PC's 2 drives have been altered by a virus; all files on both drives now have an extra extension of ".mbed"  Here you have a screenshot to get my point:   So what is the shortcut way for me to correct all these file extensions? How is the equation of motion on an ellipse derived? I would like to show that a particle orbiting another will follow the trajectory   \begin{equation} r = \frac{a(1-e^2)}{1 + e \cos(\theta)}. \end{equation}  I would like to do this with minimal assumptions. Any pointers? I've read that this is nothing but the equation for an ellipse, as defined from the focus of the ellipse. But I'm not satisfied in just taking the result, I mean why should I assume that orbits are elliptical? I guess it should be derivable from energy and angular momentum considerations... Is Ghost Adventures real or fake? What happens to spirits/souls of other creatues than Elves and Men after their death? My try, using $x = \sec(u)$ substitution:  $$ \begin{eqnarray} \int \frac{\sqrt{x^2-1}}{x} \mathrm{d}x &amp;=&amp; \int \frac{\sqrt{\sec^2(u) - 1}}{\sec(u)}\tan(u)\sec(u) \mathrm{d}u \\ &amp;=&amp; \int \tan^2(u) \mathrm{d}u \\ &amp;=&amp; \tan(u) - u + C \\ &amp;=&amp; \tan(arcsec(x)) - arcsec(x) + C \end{eqnarray} $$  However, according to , the answer should be: $$ \int \frac{\sqrt{x^2-1}}{x} \mathrm{d}x = \sqrt{x^2-1}+\arctan \left( \frac{1}{\sqrt{x^2-1}} \right)+C $$ When I derive this last answer I don't get back the integrand, but rather: $$ \frac{\mathrm d}{\mathrm d x}\left(\sqrt{x^2-1}+\arctan \left( \frac{1}{\sqrt{x^2-1}} \right)+C\right) = \frac{x}{\sqrt{x^2-1}}- \frac{x}{(x^2-1)^{3/2}\left(1+\frac{1}{x^2-1}\right)} $$  I don't know how to simplify this expression more. Also, I am unable to check whether my answer is correct because I don't know how to find the derivative of $arcsec(x)$.  Can someone check my calculations and tell me where I've done something wrong and how one can simplify the last expression to get back the integrand? Clicking on tags in global search results is broken If you search for something on "all sites" (using the searchbox at the top of , you'll reach the search results, e.g.  .  If you click directly on a tag on that page, e.g.        You get 404 Page Not Found error, e.g.     Steps to reproduce   Go to  and enter e.g. "keyforge" into the "Search all sites" field. Arrive at  Click on the "keyforge" tag below a search entry. Reach  (404 page not found)   Expected behaviour  Reach   System Info  Happens in both Firefox and Vivaldi browsers on Windows 10. Can QGIS preserve layers when exporting to PDF?