Assume a player with two weapons: a whip and a dagger.  A hostile creature stands right next to the player. On the creature's turn, it moves away 5ft. So the creature left the reach of the dagger, but is still in the reach of the whip.  Does this movement provoke an opportunity attack?   I am interested in an RAW answer, not in speculation about what a (any) sensible DM would rule.  Note: Assume Mearls' interpretation of reach provoking OAs in general, as discussed .
Assume I wield a Whip in one hand and a dagger in the other.  If a creature moves from 5ft to 10ft it has technically moved out of my reach (dagger), but at the same time it is still inside my reach (whip). When does it provoke opportunity attacks from me?  I am fully aware that this would not enable me to make off-hand attacks since the whip is not a light weapon, just to cut that issue out of the question.
I'm having the same problem as it was questioned   I can't get throught the step where I need to show that $\nabla_{E_i}E_j (p)=0$. It only leads to $$ \nabla_{E_i}E_j(p)=\sum_{lk}^n a_{il}(0)\dfrac{\partial b_jk}{\partial x_l}(0)\partial x_k(p) $$ which I can't show that equals zero.  On the linked question, there is also the indication that $\nabla_{E_i}E_j (E_k)=\Gamma^k_{ij}$. This could lead that $\nabla_{E_i}E_j (E_k)(p)=\Gamma^k_{ij}(p)=0$, but $\nabla_{E_i}E_j (E_k)(p)$ is not equal to $\nabla_{E_i}E_j (p)$ which is the one I need.  Can someone help me? I am currently facing a "performance problem" while using grep. I am trying to locate the occurrences of many (10,000+) keywords in many (think Linux kernel repository size) files. The objective is to generate a kind of index for each keyword:   keyword: my_keyword filepath 1 filepath 2 ------ keyword: my_keyword2 ...   Being fairly new to shell scripting, I have tried a few naive approaches:  while read LINE; do     echo "keyword: "$LINE &gt;&gt; $OUTPUT_FILE     grep -E -r --include='Makefile*' "($LINE)" . &gt;&gt; "$OUTPUT_FILE"     echo "-----" done &lt; $KEYWORD_FILE   This takes about 45 minutes to complete, with the expected results.  Note: all they keywords I search for are located in a file ("KEYWORD_FILE", so fixed before anything starts), and the files in which to search can be determined before the search starts. I tried to stored the list of files to search in before the search like that:  file_set=( $(find . -name "Kbuild*" -o -name "Makefile*") )   and then replace the grep call by  echo {$file_set[*]} | parallel -k -j+0 -n 1000 -m grep -H -l -w "\($LINE\)" &gt;&gt; "$OUTPUT_FILE"   It takes about an hour to complete&hellip;  Question: considering I can use whatever technique I want, provided it's sh compliant, how can this be done "faster" and/or more efficiently ?  Perhaps grep is not the tool to use, and my use of parallel is wrong&hellip; any ideas are welcome! Prove $\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$ I am trying to prove  $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$  This problem is a classic, but I seem to be missing one step or the understanding of two steps which I will outline below.   $$I_n := \int\cos^n x \ dx = \int\cos^{n-1} x \cos x \ dx \tag{1}$$  First question: why rewrite the original instead of immediately integrating by parts of $\int \cos^n x \ dx$?  Integrate by parts with $$u = \cos^{n-1} x, dv = \cos x \ dx \implies du = (n-1)\cos^{n-2} x \cdot -\sin x, v = \sin x$$  which leads to  $$I_n = \sin x \ \cos^{n-1} x +\int\sin^2 x (n-1) \ \cos^{n-2} x \ dx \tag{2}$$  Since $(n-1)$ is a constant, we can throw it out front of the integral:  $$I_n = \sin x \ \cos^{n-1} x +(n-1)\int\sin^2 x \ \cos^{n-2} x \ dx\tag{3}$$  I can transform the integral a bit because $\sin^2 x + cos^2 x = 1 \implies \sin^2 x = 1-\cos^2 x$  $$I_n = \sin x \ \cos^{n-1} x + (n-1)\int(1-\cos^2 x) \ \cos^{n-2} x \ dx \tag{4}$$  According to Wikipedia as noted , this simplifies to:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) \int \cos^{n-2} x \ dx - (n-1)\int(\cos^n x) \ dx \tag{5}$$  Question 2: How did they simplify the integral of $\int(1-\cos^2 x) \ dx$ to $\int(\cos^n x) \ dx$?  Assuming knowledge of equation 5, I see how to rewrite it as  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x  - (n-1) I_{n} \tag{6}$$  and solve for $I_n$. I had tried exploiting the fact that  $$\cos^2 x = \frac{1}{2} \cos(2x) + \frac{1}{2} $$  and trying to deal with $\int 1 \ dx - \int \frac{1}{2} \cos (2x) + \frac{1}{2} \ dx$  which left me with $\frac{x}{2} - \frac{1}{4} \sin(2x)$ after integrating those pieces. Putting it all together I have:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x \left(-(n-1) (\frac{x}{2} - \frac{1}{4} \sin 2x) \right) \tag{7}$$  but I'm unsure how to write the last few terms as an expression of $I_{something}$ to get it to match the usual reduction formula of   $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$ What recourse do I have if I believe a moderator has abused their privileges? I am having difficulty in how to calculate the Pearson's $\chi^2$ statistic for a contingency table with entries: (3, 0) and (0, 3) (row-wise).  I was studying Agresti's categorical data analysis and found this table. He calculated it as 6.  Through what calculation did he reach this answer? What is the logic behind the timer of the Sojourner Badge? Does the 24 hours timer start:     when you hack a portal on a particular day     or     does it use the calendar days and check if you did hack a portal on a particular day   or     does it simply use a fixed international timezone to calculate the 24 hour cycle   or     does it use the agent's hacking cell's timezone to start it?   If it's the calendar days method than the explanation of the badge would be a little bit misguided because you could hack a portal on 00:01 on Saturday and then hack another one on 23:59 on Sunday and it would be practically two days between two hacks.  If it's based on the agent's last hack for a particular day then the explanation still would be problematic?  The third option would be a little bit unfair (or timezone racist) for the rest of the world.  The last option (the cell's timezone) would/could be both unfair for travellers and/or non-travellers.  Does anyone know any details about it? The Problem For a small mass a distance $R_i$ away from the center of the Earth, how long would it take for the object to fall to the surface of the Earth, assuming that the only force acting upon the object is the Earth's gravitational force?  Relevant Information The following discussion seems to have solved exactly the same problem:   However, upon working out the mathematics, I'm not exactly sure how to evaluate the constant of integration.   A Partial Solution $$ F=\frac {-GMm}{s^2} $$ $$ a=\frac {-GM}{s^2} $$ $$ \frac {dv}{dt} = \frac {-GM}{s^2} $$ Multiplying by $v$ and then integrating by $dt$ on both sides, we have $$\frac {1}{2} v^2=\frac {GM}{s} +c_1$$ where $c_1$ is a constant of integration. Substituting initial conditions of $v=0, s=R$, we have $$\frac {1}{2} v^2=GM(\frac {1}{s}-\frac{1}{R})$$  At this point of time, when I use Wolfram Alpha, I get  $$c_2+\sqrt{\frac{2}{R}}t=\frac{\sqrt{s}(s-R)+R\sqrt{R-s}\times{\tan^{-1}(\sqrt{\frac{s}{R-s}})}}{\sqrt{GM(R-s)}}$$  where $c_2$ is a constant of integration. Substituting initial conditions of s=R, t=0, we find that the term $$\tan^{-1}(\sqrt{\frac{s}{R-s}})$$ is undefined. At this point, I'm stuck. Any ideas on where I've made the mistake here?  (For those interested, this question was inspired by the Greek myth which states that a bronze hammer dropped from heaven would take 9 days to hit the Earth and would reach on the tenth). How can I reinstall GRUB to the EFI partition? I want to reinstall GRUB 2 and I found these instructions: . In my case, the boot loader is installed in the EFI partition. If I use the commands provided in this guide, will GRUB be reinstalled to the EFI partition automatically, or will it be installed into the root partition where Ubuntu is installed ? Obviously, I do not want this to happen. Not able to calculate sum of multiple column where file data in different format .csv I have a scenario where i want to calculate sum of column   SAL|CAL|TAG|VAL 12.11"|"1.1"|"2.1"|"1.1 13.11"|"1.1"|"2.2"|"2.2 14.11"|"1.1"|"2.4"|"2.4   My below code not giving output giving output as 0.00  I need output for this column CAL VAL  awk -F'|' '{T+=$2} END { printf "%.2f\n", T }' demo.txt   output :  6.7 5.7 Homework question on whether two quotient spaces are homeomorphic "Home page" or "homepage"? Is there a convention for the spelling of the name of the main page of a website? Should it be home page, with a space between the two words; or homepage, all one word? Can a single vertex be rotated? In the duplication options for the dupli verts there is a option for Rotation. Witch brings me to my question, is there anyway to rotate a vertex? Vertex's have normals, is there any way to control which way the normal of a single unconnected vertex points? The series $\sum_{n=2}^{\infty }\frac{1}{\log (n!)}$ I'm trying to find out whether this Series $\sum_{n=2}^{\infty } a_{n}$ converges or not when $$a_{n}=\frac{1}{\log (n!)}$$  I tried couple of methods, among them: d'Alembert $\frac{a_{n+1}}{a_{n}}$,   Cauchy condensation test $\sum_{n=2}^{\infty } 2^{n}a_{2^n}$, and they both didn't work for me.  Edit: I can't use stirling, and integral.  Thank you apt-get update only for a specific repository When I add a PPA and I want to install some of its content, it is quite annoying to re-update all my apt list using apt-get update.  Is it instead possible to only sync the content of a given repository? Tag scores update is supposed to happen at 03:00 UTC every day. Tag scores are updated by a scheduled job that is time consuming and often times out  (see for example the answers for  and ).  In the past month or two, the issue with not updating the scores has gotten much worse. Tag scores are now regularly not updated for 2-3 days in a row. The job fails more often than it runs which obviously lowers usability and appeal of tag badges (which are not awarded when the script fails) and scores to some extent.  I can also guess that if a job fails on consecutive days, it only makes it harder to make it work as it has more and more tags and answers to recount.  This issue happened in the past but not to the extent it's happening now.  Please do not close it as duplicate. I'm creating a separate post as I've been asked to do it by Adam Lear in a comment for the answer for the first of the linked questions. Other posts reporting this issue have accepted answers which makes them difficult to track for the SE team.  UPDATE  I've been writing down whether the scores were updated or not every day in April.  The results are:  Day      1   2   3   4   5   6   7   8   9   10  11  12  13  14  15   Updated  -   -   -   ✓   -   ✓  -   -   -   -   -   ✓   -   -   -   Day      16  17  18  19  20  21  22  23  24  25  26  27  28  29  30 Updated  ✓   -   ✓   -   ✓   -   -   ✓  ✓   -   ✓  -   ✓   -   -   The update succeeded on 10 days, failed on 20. The situation got somewhat better in the second half of the month. Has something been done about it? Does an ability or spell grant me the bonus action with which to use it? The  description of casting times says that spells with a casting time of &quot;bonus action&quot; require a bonus action to cast (p. 79, emphasis mine):  Most spells require a single action to cast, but some spells require a bonus action, a reaction, or much more time to cast. Bonus Action A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven't already taken a bonus action this turn. You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.  It's pretty clear that bonus actions aren't automatic (p. 69):  You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. You otherwise don't have a bonus action to take.  So to cast a spell like Healing Word (p. 93), do I  need to be granted a bonus action that I can use, or do I have a bonus action I can use?  I guess I'm unclear on whether I need to have a bonus action before I can spend it on something, or whether having an ability, spell, or whatnot that can be done as a bonus action grants me the bonus action I need to use it. Deleting a comment (mine) shouldn't count as a comment vote How to disable or uninstall Microsoft Edge in Windows 10 When to use "If I was" vs. "If I were"? I am in the process of creating a LaTeX template for a conference submission, and up until now I've been working only with the anonymous submissions. Now I need to create the "camera-ready" version, which means I need to add authors to the document.   The template is based on article.cls, with some tweaks to meet the font and formatting specifications. The following image contains the examples from the Word template for the conference:    Basically, I need to be able to bold the author's name (which could I suppose be done manually in the document rather than in the template) and more importantly: divide the authors into two columns, with an optional centered last column with an odd number of authors. The font size of the author block corresponds to my \LARGE defined in the class file.  Are there any packages that facilitate this type of conditional formatting, either in a document, or in a .cls file? How can I use those packages to achieve the formatting I require?