The description of the  cantrip reads:  A flickering flame appears in your hand. The flame remains there for the duration and harms neither you nor your equipment. The flame sheds bright light in a 10-foot radius and dim light for an additional 10 feet. The spell ends if you dismiss it as an action or if you cast it again. You can also attack with the flame, although doing so ends the spell. When you cast this spell, or as an action on a later turn, you can hurl the flame at a creature within 30 feet of you. Make a ranged spell attack. On a hit, the target takes 1d8 fire damage.  If I have one hand occupied with a shield and another hand occupied with an arcane focus, can I cast produce flame into one of my occupied hands? If I have the War Caster feat, can I then use the flame as an opportunity attack while my hands are occupied? I'm getting ready for a one-shot battle-royale and want to be able to have a free damage cantrip.  This question is different from the question . The previous question is about casting produce flame with an open hand and then equipping an item. I am specifically talking about having both hands equipped with items and then choosing to cast produce flame.
The text of the  spell reads:      A flickering flame appears in your hand. The flame remains there for the duration and harms neither you nor your equipment. The flame sheds bright light in a 10-foot radius and dim light for an additional 10 feet. The spell ends if you dismiss it as an action or if you cast it again.   Emphasis mine. The druid in our party asked our DM if he is able to cast produce flame in a dark cave, then opt not to attack with it, and wield a shield and sword. The goal is to continue emitting light, since he doesn't have the light spell. He claims that since the flame does not harm his equipment, he is able to hold a shield or sword with the fiery hand with no problem.  Is this okay to do RAW, or are we missing something?  This is specifically not asking about casting spells with a sword in hand. He wants to draw his weapon after casting and holding the flames.  Related, but not the same question: , , .
This is from page 3 of  ().  Copying the relevant segment:     Stirling’s approximation tells us $\sqrt{2\pi n} (n/e)^n \leq n! \leq e^{1/12n} \sqrt{2\pi n} (n/e)^n$. In particular we can use this to say that   $$ {n \choose k} \leq \left(\frac{en}{ k}\right)^k$$   I tried the tactic of combining bounds from $n!$, $k!$ and $(n-k)!$ and it didn't work. How does this bound follow from stirling's approximation? Declaring Text Decorations such as Underline, Strikethrough in a Style How do I include text decorations such as Underline, Strikethrough etc in a Style definition:  &lt;Style x:Key="UnderlinedLabel"&gt;      &lt;Setter Property="Control.FontFamily" Value="Trebuchet MS" /&gt;      &lt;Setter Property="Control.FontSize" Value="14" /&gt;      &lt;!-- Next line fails --&gt;      &lt;Setter Property="Control.TextDecorations" Value="Underline" /&gt; &lt;/Style&gt;   I'm familiar with using the following XAML to underline text:  &lt;TextBlock&gt;    &lt;Underline&gt;        Underlined text    &lt;/Underline&gt; &lt;/TextBlock&gt;   However text decoration is just another style, I want to be able to define it declaritively like FontWeight, FontSize etc.  [Update]  I was applying this style to a Label control.  This was my main problem.  It appears you can't underline text in a Label.  Change to a TextBlock (thanks gix) and all is well. For a given ellipse, find the locus of all points P for which the two tangents are perpendicular.   I have a trigonometric proof that the locus is a circle, but I'd like a pure (synthetic) geometry proof. One can show that $\mathbb{P}^n\times \mathbb{P}^m$ is birational to $\mathbb{P}^{n+m}$ by making note of the Zariski topologies and the canonical isomorphism between affine spaces $\mathbb{A}^n\times \mathbb{A}^m\to \mathbb{A}^{n+m}$.   Question: Does it follow that there is isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$? If so, what is an example of such an isomorphism?   Unfortunately I am having a hard time coming up with one, and haven't seen too many examples thus far. Show all comments if there is just "1" extra comment to show When looking at a question or answer with comments, I think it would be better to just show that one extra comment if the threshold is "Show 1 more comment".  In other words, if there are 6 comments, show all 6 comments.  If there are 7 comments, then show 5 comments and the link "Show 2 more comments".  Etc for more comments. Ugly "Next Privilege" text on user activity page Understanding GeoTIFF tags? Does "She had a brother" mean that her brother is dead? My Friend has sent me this riddle to solve:     "If you solve this, then you are a genius. Mr.Smith has 4   daughters🙍‍♀🙍‍♀🙍‍♀🙍‍♀ and each daughter had a brother.  How many   children does Mr. Smith have now?"   He said the answer is not 5, but 4 only as in the riddle it is mentioned as each daughter had a brother. So their only brother is dead.     Is he right? Sending Email in Android using JavaMail API without using the default/built-in app The divisibility rule for $3$ is well-known: if you add up the digits of $n$ and the sum is divisible by $3$, then $n$ is divisible by three.  This is quite helpful for determining if really large numbers are multiples of three, because we can recursively apply this rule:  $$1212582439 \rightarrow 37 \rightarrow 10\rightarrow 1 \implies 3\not\mid 1212582439$$ $$124524 \rightarrow 18 \rightarrow 9 \implies 3\mid 124524$$  This works for as many numbers as I've tried.  However, I'm not sure how this may be proven.  Thus, my question is:     Given a positive integer $n$ and that $3\mid\text{(the sum of the digits of $n$)}$, how may we prove that $3\mid n$? I know blender can display both orthographic and perspective projection. But, when we look at a cube in blender's viewport, I'm unable to distinguish by eye, if the projection in the viewport is a one-point, a two-point or a three-point perspective. What does blender use, and is this something changeable? A twice differentiable function $f$ satisfies $f′′(x)+f(x)=−xg(x)f′(x)$, $\forall x\ge 0$. Consider $f\in C^2$ so that $$f''(x)+f(x)=-x\,g(x)f'(x), \ \forall x\ge0 $$ where $g(x)\ge 0$. Then ($\forall x\ge 0$)         (A) $f(x)^2+f'(x)^2$ is non-increasing,   (B) $f(x)^2&lt;3f(0)^2+(2f'(0))^2$,   (C) $|f(x)|\le\alpha$, where $\alpha$ is a fixed real constant.   (D) $\lim_{x\to\infty} f(x)\sin\left(\dfrac{1}{x}\right)$ exists.        Answer Given: (A),(B),(C),(D)  What I have tried : I differentiated option (A) and then with the help of the given equation in the question I was able to show that  it is less than zero . Hence I was able to infer that option (A) is correct .   Now coming to option (B).  I assumed the function in option (A) to be $h(x)$.   $$ h(x) = f(x)^2 + f'(x)^2 $$  Since $h'(x)&lt;0$ ,therefore $h(x)$ is a decreasing function   hence for all $x\ge 0$  $h(x)&lt; h(0)$  which implies $(f(x))^2 + (f'(x))^2&lt;(f(0))^2 + (f'(0))^2$  From the above expression we can get the second option .   Is my method correct ?. If not , please show the right method .  I am unable to get the the 3rd and 4th option . Creating a gradient-based legend I have a map with graduated symbology, with 328 unique values. I would like to add a legend to my map (as in the picture), illustrating that light blue indicates low values and dark blue high values.  I have done this in ArcGIS before. Is there a way to do this in QGIS as well? why would curl and wget result in a 403 forbidden? How do I delete Windows after an Ubuntu install? I downloaded Ubuntu 12.04 LTS to my Dell Dimension 4600 with Windows XP installed.  I now have a neat dual-boot system, but I want to get rid of the XP OS and keep Ubuntu as my only OS.  How do I do this? I am new to the telecom simulations system specially multisim, which I am having a project that I want to simulate.  My project in (Analog Communications) is consisting to have FM Transmitter (Modulator) that accepts a generated signal (Sin, Cos) and get me the modulated output as a Graph.  I've found this FM transmitter circuit (3 km range):   ![two muppets][1]  and I am building that circuit on Multisim, and I failed. Because I faced many problems, first of, the variable capacitor symbol is weird here in the multisim, and the regular capacitor doesn't have variable options. Secondly, when I Use signal generator as (Sin, Cos), the output gets weird after 5 second of the simulation.  I want to show the input signal (before modulation) and the output signal (transmitted or modulated).  I guess my output result where not the as expected, as the signal (Sin with phase 90&deg;) is giving weird result of few seconds of simulating.  Below are screenshots of the simulation results within time.          Any ideas how to edit or fix the above circuit to have this output is similar to what it should be? Direction of $d\mathbf{l}$ A solid sphere has charge $q$ and radius $R$. Find the potential at a point a distance $r$ from the center of the sphere where $r&gt;R$, using infinity as the reference point.  My attempt:  From Gauss' theorem we may deduce that $\displaystyle\mathbf{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r'^2}\hat{\mathbf{r}}$ where $r'$ is the distance of an arbitrary point from the center of the sphere provided $r'&gt;R$.  $V=-\int_\infty^\mathbf{r}\mathbf{E}\cdot d\mathbf{l}$  My question: What is $d\mathbf{l}$? Since we are traversing in the direction opposite to $\hat{\mathbf{r}}$, I think it should be $-dr'\hat{\mathbf{r}}$. But when I use it to find $V$, I get a sign error. Please help! In the Monster Manual, gargoyles, golems, helmed horrors, and xorns all enjoy either immunity or resistance to:     bludgeoning, piercing, and slashing damage from nonmagical weapons that aren't adamantine   Is it actually possible to obtain a nonmagical adamantine weapon?   Although the Dungeon Master's Guide describes adamantine armor (p.150) and Daern's instant fortress (p.160) as being made of this metal, and provides an AC for destructible adamantine objects (p.246), there's no mention of adamantine weapons. The creation spell (PH p.229) can produce an adamantine weapon that lasts for a single minute. The true polymorph spell (PH p.283) can't turn a regular weapon into adamantine, but it might be able to  for an hour. The only way to obtain a (somewhat) permanent adamantine weapon in the game seems to be to loot one from drow elves (MM p.127). A PC (perhaps even a drow) with proficiency in smith's tools could presumably craft a nonmagical adamantine sword during downtime at 5gp per day (PH p.187), except that unlike silvered weapons, there's no pricing for adamantine.   It's seeming like mugging an NPC drow is the only by-the-book way to tool up against gargoyles. Tikz: adjusting pin anchor I was looking for a possibility to adjust the anchor of the text of a pin. Tikz does not allow this out of the box.   This question was already asked on the mailing list , Sept. 2009 without any reply till today or feature addition to pgf/tikz:  \documentclass[tikz]{standalone}  \begin{document}      \begin{tikzpicture}[          every pin/.style={anchor=west},          every pin edge/.style={anchor=west}]          \node [pin=60:test] at (0,1) {};          \node [pin={[anchor=west]60:test}] at (0,0) {};      \end{tikzpicture}  \end{document}   There is also a question with a suggested workaround here on  by defining an aligned pin style consisting of another node positioned at the end of the pin using \tikzlastnode:  \tikzset{     aligned pin/.style args={[#1,#2]#3:#4}{         pin={[inner sep=0pt,%               pin distance=#2,% new option, default = 3ex               label={[append after command={%                     node[inner sep=0pt,%                         xshift=-0.1cm,% modified, default = 0                         at=(\tikzlastnode.#3),%                         anchor=#1,%                     ]{#4}%                 }%             ]center:{}}%         ]#3:{}}%     } }   In this code, I have added a second unnamed option for pin distance within the square brackets.  MWE using the workaround showing the desired result:  \documentclass[tikz]{standalone}  \tikzset{     aligned pin/.style args={[#1,#2]#3:#4}{         pin={[inner sep=0pt,%             pin distance=#2,% new option, default = 3ex             label={[append after command={%                     node[%                         inner sep=0pt,%                         xshift=-0.1cm,% modified, default = 0                         at=(\tikzlastnode.#3),%                         anchor=#1,%                     ]{#4}%                 }%             ]center:{}}%         ]#3:{}}%     } } \begin{document} \tikz[pin distance=15mm, every pin/.style={fill=blue,text=white}] \node [circle,draw,     aligned pin={[west,3ex]0:X-Value},%     aligned pin={[west,3ex]45:Y-Value},%     aligned pin={[west,3ex]90:Z-Value}] {my circle}; \end{document}     I would like to add further options such as pin edge to adjust the style of the edge. Another addition would be xshift to finetune the position of the text (and yshift).  Is it possible to change the workaround to allow named options with default values if not specified?  Usage could look like this (without using necessarily all options):  node[aligned pin={[pin anchor=west,pin distance=1cm,pin edge={thick}]90:{txt}}]{};   If someone is interested in the implementation of the pin feature in tikz see  and do a textsearch for pin.  Update after answer by Qrrbrbirlbel:  To achieve almost the same result as my MWE use following code  % use preamble from Qrrbrbirlbel answer \begin{document}  \begin{tikzpicture}[every pin/.append style=draw, every pin edge/.style={thick}] \node[c] [ pin={[pin anchor=south west,pin edge pin anchor=south west,pin distance=6ex]90:Z-Value}, pin={[pin anchor=west,pin edge pin anchor=west,pin distance=6ex]45:Y-Value}, pin={[pin anchor=west,pin edge pin anchor=west,pin distance=6ex]0:X-Value} ] at (0,0) {}; \end{tikzpicture}  \end{document}     However, I would like to finetune the text positioning using inner sep=0 and a slight shift:  \newlength{\xshiftlength} \setlength{\xshiftlength}{0.5\widthof{Z}}   Following works:  \tikzset{   pin inner xsep/.style={tikz@pin@post/.append style={inner xsep=#1}} }   Apparently xshift cannot be added in the same way. It shifts more than only the text. How could a pin text xshift be added? What is the difference between class and instance attributes?