Can you use Twinned Spell on Fireball and target the same creature with both attacks? Can a sorcerer use the Twinned Spell metamagic on the fireball spell and target the same creature with both attacks?  Also, if you can target one with both, would it be double damage?
Can you use twinned spell on the same target? So me and my DM have been arguing on how Twinned spell works. Twinned spell:  When you cast a spell that targets only one creature and  doesn't have a range of self, you can spend a number of  sorcery points equal to the spell's level to target a second  creature in range with the same spell (1 sorcery point if  the spell is a cantrip).  I argued that &quot;a second creature&quot; can be a the same target as it is not worded as &quot;another creature&quot; For this example counter spell with twinned spell.  A wizard casts fireball on me I use CounterSpell#1 with Twinned Spell Wizard casts CounterSpell on my CounterSpell#1 I use him as the same target for my twinned Spell CounterSpell#2  Result countered Is this possible?
[Probability]need help to understand the following expression So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively.  assume c is a constant.  I am having huge trouble to understand the integration of the following expression.  $P(Y&lt;c/u(X))$  $=\int_{t}^{\infty}f_X(x)\int_{0}^{c/u(x)}f_Y(y)dydx +\int_{0}^{t}f_X(x)\int_{c/u(x)}^{\infty}f_Y(y)dydx$  where t is the cross-point that $u(x)$ change sign    here $c/u(x)$ is given by the plot below, t is the point crossing the zero:   Confusion:   I don't understand the second integration of the second term "$\int_{c/u(x)}^{\infty}f_Y(y)dydx$", this isn't right because Y an X only defined for y>0, and x>0. So it's the first quadrant in this plot. The  is the stuff of legend () and is . My question is two-fold, really: Is the Golden Ratio really a good tool used in modern design (defined here as 20th century on forward), and if so, how often is it used outside of the aforementioned known uses?  EDIT: To @e100's first comment, examples of modern use of the Golden Ratio would be a great thing to add here if there any documented or arguably conclusive uses of it. How to effectively use the man pages? I am looking forward to mastering linux. I have been repeatedly told to refer to man pages when you are in doubt.   Though I am very comfortable with the commandline, I find it very difficult to quickly and efficiently use man to find help with commands. Hence I end up googling up how to get things done. It is even more painful when the system I am using does not have internet access and I have to walk back to my office to get help from the internet.  How does one master man pages? What are the most common tricks that can be used to quickly get whatever you want from the man page? What are the most commonly used keyboard shortcuts? Add an Image Upload button to the Mobile Site With the release of iOS 6, the most commonly used mobile browser now supports standard generic image upload buttons. This is actually really handy.  I can take screenshots on my phone or iPad, and use them to answer questions about apps made to run on those devices (or ) to answer questions. Until the release of iOS 6 however, the only way to use these images in my answer was to either sync them over to my computer, and then answer from a desktop, or use a specialized app to upload the images, such as PicUp or DropBox, and then manually write out the markdown code.  After iOS 6, the Image Upload button works just fine, if I switch to viewing the full site from my iDevice, rather than the mobile view. I can upload images directly, and the markdown is handled for me. It's awesome, except for the fact that the non-mobile site is decidedly non-awesome on the small screen of my phone.  Which brings me to my feature request: Add the Image Upload button (and other markdown shortcuts, as deemed worthwhile) to the ask/answer editors on the mobile version of SE sites. Newton's third law does not apply to the kinetic energy formula? Here is a classic problem:     A 60kg boy and a 40kg girl are sitting in front of each other on skateboards on a frictionless horizontal surface. The boy pushes the girl and the girl gains a velocity of 0.3m/s during the 0.5s the boys hand was in contact with her. What is the boy's resulting velocity?   Considering Newton's Third Law, the best way is to find the total force applied and rearrange the formula to find the boy's speed.  Newton's Law Method:  $F = m*a$  $a=\frac{0.3m/s}{0.5s}$  $F = 40kg * 0.6m/s^2$  $F = 24N$  Therefore the boy's speed will be:   $\frac{24N}{60kg} = a$  $a = 0.4m/s^2$  $v = 0.4m/s^2 * 0.5s$  $v = 0.2m/s$  Kinetic Energy Method:  $E_{k}=\frac{1}{2}*m*v^2$ the girl's kinetic energy  $E_{k}=\frac{1}{2}*40kg*(0.3m/s)^2$  $E_{k}=1.8J$  Since every action has an equal and opposite reaction the boy should have the same amount of kinetic energy.  $E_{k}=\frac{1}{2}*60kg*(0.2m/s)^2$  $E_{k}=1.2J$  As you can see, using Newton's Third Law, the kinetic energy was not the same. So what's going on here? I thought that in this case they should both have the same amount of kinetic energy due to Newton's Law. I must be missing something since there is more energy going in one direction than the other after meeting. My book used the first method as the answer and, well, it feels wrong. How do you get the current time in milliseconds (long), in VB.Net? How to calculate $\int_0^{\pi/2} \sin^a x \cos^b x \,\mathrm{d} x$ Example of a ring with an infinite inclusion chain of ideals I'm trying to track down an example of a ring in which there exists an infinite chain of ideals under inclusion. (i.e. $I_1 \subsetneq I_2 \subsetneq I_3 \subsetneq...$) Is there to make the login screen appear on the external display in 18.04? What is the difference between test set and validation set? I found this confusing when I use the neural network toolbox in Matlab. It divided the raw data set into three parts:   training set validation set test set   I notice in many training or learning algorithm, the data is often divided into 2 parts, the training set and the test set.  My questions are:   what is the difference between validation set and test set?  Is the validation set really specific to neural network? Or it is optional. To go further, is there a difference between validation and testing in context of machine learning? How to set up RAID 1? Colors and legend in groupplots/barplot In order to compare three items I use the groupplot command. For each item I have n different criteria to compare.    Is it possible to set the color for each criteria itself? Meaning the first bar in every group goes gray, the second pink etc.. The legend than should contain the n compared criteria.  And... how do I manage to let the whole tikz-picture have a width of 0.9\textwith  \documentclass{standalone} \usepackage{pgfplots,pgfplotstable} \usetikzlibrary{pgfplots.groupplots}  \pgfplotstableread{ nr  fii faa foo a   10  15  12 b   12  18  14 c   13  19  15 d   9   13  10 e   7   11  8 f   10  15  12 }\datatable  \begin{document} \begin{tikzpicture} \begin{groupplot}     [group style={columns=3},         ybar,         ymin=0,         ymax=20,         xtick=\empty,         tickpos=both]  \nextgroupplot[xlabel=fii] \addplot [fill=blue] table [x expr=\coordindex, y=fii] {\datatable}; \nextgroupplot[xlabel=faa] \addplot [fill=green] table [x expr=\coordindex, y=faa] {\datatable}; \nextgroupplot[xlabel=foo] \addplot [fill=red] table [x expr=\coordindex, y=foo] {\datatable};  \end{groupplot} \end{tikzpicture} \end{document} Let $a_1=1$ and $a_n=n(a_{n-1}+1)$ for $n=2,3,\dots$. Define $$P_n=\left(1+\frac{1}{a_1}\right)\left(1+\frac{1}{a_2}\right)\dots\left(1+\frac{1}{a_n}\right)$$Find $$\lim_{n \to \infty}P_n$$   Trial: $$1+\frac{1}{a_n}=1+\frac{1}{n(a_{n-1}+1)}\;.$$ But I can't simplyfy.Please help. Parentheses vs. double commas vs. dashes to provide additional detail When do you use commas and when do you use parentheses to provide more detail about something?  For example:   The suspect, Tom Wilson, is now being charged with murder. The suspect (Tom Wilson) is now being charged with murder. John Smith, a member of the jury, agreed with the verdict. John Smith (a member of the jury) agreed with the verdict. The first example, the one about the fox, is the more valid one. The first example (the one about the fox) is the more valid one.   I realize that the first example, the one that uses parentheses, is probably more valid in this case (if anyone has a better example, please include it), but when, if ever, would you favor parentheses?  Update: I realize that dashes are sometimes used for similar situations, so I'd appreciate information on these as well.  For example:   The children—who are wearing shoes—will go on the trip The children, who are wearing shoes, will go on the trip The children (who are wearing shoes) will go on the trip Hide and seek game $A$ and $B$ go to the Senate to play a game of Hide-and-Seek. There are $100$ rooms in the Senate, and $B$ picks one of them and hides there till the game ends.  $A$, at the beginning of every turn, picks one room and searches in it. Since he is human and thus fallible, he only has a $60\%$ chance of finding $B$ if she is in fact hiding in the room. If he fails to find her in the room, $B$'s score increases by one, and the next turn starts, whereupon $A$ must pick another room to check (he can also check the same room again). $B$ remains in the room she initially chose.  Given that $A$ and $B$ play with perfect strategies, what is the expected value of $B$'s score at the end of the game?  I tried with $1$ room. There is only one hiding place for $B$. So the expected score of $$B = \sum_{n=1}^{\infty}0.4^{n-1}0.6(n-1)=\frac{2}{3}.$$ How do you interpret a significant but weak correlation? C++ preprocessor __VA_ARGS__ number of arguments What's a big-vocabulary word for someone with a big vocabulary? What's a big-vocabulary word for someone with a big vocabulary?  I'd like to say I'm looking for a "_____". Recommended books for advanced undergraduate electrodynamics What books are recommended for an advanced undergraduate course in electrodynamics? How can I get an email message's text content using Python?