in triangle ABC there satisfies equation: $\cos A \cos B+\sin A\sin B\sin C=1$, determine possible values of $C$
If $\sin(a)\sin(b)\sin(c)+\cos(a)\cos(b)=1$ then find the value of $\sin(c)$
Inner product of two continuous maps is continuous Let f,g be continuous maps of S in $\mathbb{R}^n$, to $\mathbb{R}^m$. Show the inner product h(x) = $\langle f(x), g(x)\rangle$ is continuous.  My attempt: Since f,g are continuous, their product is a continuous mapping, so for $\epsilon \gt 0\: t.e\:  \delta \gt 0$ such that $\parallel x - a\parallel \lt \delta $ implies $\parallel \langle f(x),g(x)\rangle - \langle f(a)g(a)\rangle \parallel \le\parallel f(x)g(x) - f(a)g(a)\parallel \lt \epsilon$ by schwartz inequality. Prevent href="#" link from changing the URL hash What does the above Error mean? What is an installation candidate?  I was trying to do  sudo apt-get install munin-memcached     and I get this message:  Reading package lists... Done Building dependency tree        Reading state information... Done Package munin-memcached is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package munin-memcached has no installation candidate   I googled for the problem and someone said to do a apt-get upgrade but it still did not solve my problem. ICANN charges 18¢ per domain name registered regardless of its extension, but I pay $10 for a domain name per year with my registrar.   What do domain name registrars do for its customers to justify this extra $9.82?  Is there something that they do for our domain names other than registering it with ICANN?   I just read about the 7 people who hold the ICANN database key and got a little bit curious to know what the domain name servers do for us to justify this extra amount (12 times the actual fee)? Execute command in remote active terminal Suppose you have a terminal emulator (T1) open with a PID of 6350.  From another terminal, type this command (C1):  echo "ls\n" &gt; /proc/6350/fd/0   This writes ls and the new line in T1 but does not execute it. Why?  I also tried using cat|bash with echo "ls\n" &gt; /proc/catid/fd/0 but it is still not executed.  How can I echo the command into another terminal and have the command executed?  possible answer :  $ mkfifo toto; $ bash &lt; toto; $ echo "ls" &gt; toto;   In this case you cannot write anymore directly in the terminal (everything is displayed the same way the command (C1) displayed thing in this terminal. Show vote counts on activity>comments page It would be helpful to show vote counts on the activity > comments page, and also allow sorting by votes.  This would make it easy to see what comments other people thought were valuable or at least amusing. Environment variable substitution in sed If I run these commands from a script:  #my.sh PWD=bla sed 's/xxx/'$PWD'/' ... $ ./my.sh xxx bla   it is fine.  But, if I run:  #my.sh sed 's/xxx/'$PWD'/' ... $ ./my.sh $ sed: -e expression #1, char 8: Unknown option to `s'    I read in tutorials that to substitute environment variables from shell you need to stop, and 'out quote' the $varname part so that it is not substituted directly, which is what I did, and which works only if the variable is defined immediately before.  How can I get sed to recognize a $var as an environment variable as it is defined in the shell? Proving that either $2^n-1 $ or $ 2^n+1$ is not prime Reading shapefile using C#? Why does "unisex" mean both sexes? There are some places where men and women are segregated — for example public toilets and public swimming pool changing areas.  By this I mean, for example, that there are "Men's toilets" and "Ladies' toilets".  However, in some more cosmopolitan swimming baths, and other places, there are such things as unisex changing areas, or unisex toilets.  From my understanding uni- implies one, as in universe, unilateral or unicycle.  However when it comes to unisex, this means both sexes, so applies to two things.  How does uni- mean one in unisex? Does it mean one? How compatible are my old Nikon lenses? I'm looking at buying a new SLR body. I have an old film Nikon entry-level SLR (about ten years old) with a kit lens. If I buy a Nikon body, how likely is it that my old lens will work on it? Would I be better off buying a new lens? What control type should I use - Image, MediaElement, etc.? When did the red shirt careers change to yellow shirts in Star Trek and why? How to cite lecture notes? (and should I even do this?) $\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$ Page 105 of D. Burton's A First Course in Rings and Ideals reads     It is not difficult to show that if (I'll call them $n$ and $m$ instead of $n_1$ and $n_2$) $n$, $m$ are square free integers, then $\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ if and only if $n=m$.   Well, it is getting difficult for me, any help or would be appreciated.    My progress so far: Suppose $\phi :\mathbb{Q}(\sqrt{n})\to\mathbb{Q}(\sqrt{m})$ is an isomorphism. Then $\phi(u)=u$ for every $u \in \mathbb{Q}$, so that $\phi(\sqrt{n})^2=\phi(n)=n$. If $\phi(\sqrt{n})=a+b\sqrt{m}$ for some $a,b\in\mathbb{Q}$, then $(a+b\sqrt{m})^2=a^2+b^2m + 2ab\sqrt{m}=n$ implies $$a^2+b^2m = n$$ and $$2ab=0.$$  Then $b=0$ cannot happen since that would imply that $\sqrt{n}\in\mathbb{Q}$, where $n$ is a square-free integer. Also $a=b=0$ cannot happen. Hence $a=0$ and we have $$b^2m=n.$$ If $\psi:\mathbb{Q}(\sqrt{n})\to\mathbb{Q}(\sqrt{m})$ were an isomorphism then there would exist some $s\in\mathbb{Q}$ such that $$s^2m=n,$$ then $s=b$ or $s=-b$. Therefore the only isomorphisms from $\mathbb{Q}(\sqrt{n})$ to $\mathbb{Q}(\sqrt{n})$ are $\phi(u+v\sqrt{n})=u+vs\sqrt{m}$ and $\psi(u+v\sqrt{n})=u-vs\sqrt{m}$.    I don't know if there's an easier way and I don't know if I'm in the correct way here. Thanks beforehand :) Handler frame_change_pre doesn't work in render this works in viewport but not in render.  import bpy from math import *  def frame_handler(scene):     z = scene.objects['Lift'].location[2]     scene.objects['Text'].data.body = str(floor(z / 4.0) - 2)  bpy.app.handlers.frame_change_pre.clear() bpy.app.handlers.frame_change_pre.append(frame_handler)   How to get it working in render? I've read  and changed from "bpy.data.objects" to "scene.objects" as already seen in the script. What am I missing? Blender v. 2.81.16  Edit. Tried that depsgraph thing mentioned in comments and changed to frame_change_post:  import bpy from bpy.app.handlers import persistent from math import *  @persistent  # maybe not relevant but doesn't harm anything? def frame_handler(scene, depsgraph):     z = scene.objects['Lift'].evaluated_get(depsgraph).location[2]     scene.objects['Text'].data.body = str(floor(z / 4.0) - 2)  bpy.app.handlers.frame_change_pre.clear() bpy.app.handlers.frame_change_post.clear() bpy.app.handlers.frame_change_post.append(frame_handler)   Now the Text doesn't show up at all in rendered (but works in viewport). Suppress "In:" biblatex Number of $n^2\times n^2$ permutation matrices with a 1 in each $n\times n$ subgrid I found the following question in a paper I was trying to solve:  The following figure shows a $3^2 \times 3^2$ grid divided into $3^2$ subgrids of size $3 \times 3$. This grid has $81$ cells, $9$ in each subgrid.    Now consider an $n^2 \times n^2$ grid divided into $n^2$ subgrids of size $n \times n$. Find the number of ways in which you can select $n^2$ cells from this grid such that there is exactly one cell coming from each subgrid, one from each row and one from each column.  My try:  Since we have $n^2$ rows, $n^2$ columns and $n^2$ subgrids in total, we have to choose one and only one cell from each of them. Let's choose them one at a time. We can choose the first cell in $n^4$ many ways. Then, we'll have to avoid that subgrid, that column and that row that we've chosen the first one from when choosing the second cell. So, we have $n^4-n^2-2n(n-1)$ choices. We can continue this to get the total number of possible ways. But, I think there's a hole. Say, we've chosen the first cell from the subgrid of the up-left corner and the second from the subgrid just right to it so that it doesn't violate any rules. Then, when finding the number of ways we can choose the third cell, we would have substracted some of the cells twice. I think you get it. Please, if anyone can help me solving this problem, it'd be greatly appreciated. What do you call someone who is supported? Synonym for a supportee (Which doesn't seem to be a word)?  I created products that retail and we sell them and give the proceeds to charities. Trying to figure out a single word to use as a page title for those that we support were we can list the charities (With their permission of course).  Thanks Started new job. Rollover previous employer 401k to new 401k, IRA or Roth IRA?