For a map my friend was making, I was trying to make grenades but they failed. I need a data tag that can make it so that as soon as it touches the ground it explodes.
I am trying to make a snowball that triggers a command when it hits a player in 1.15, but I don't know how to do that. When I do execute at @e[type=snowball] run gamemode spectator @a[distance=..2] it only runs the command if it goes right next to them.
Bounty not awarded automatically — bug? Question on showing a bijection between $\pi_1(X,x_0)$ and $[S^1, X]$ when X is path connected. I am trying to do this question taken from Hatchers algebraic topology and I am struggling to understand the notation and the concepts.  As far as I know $\pi_1(X,x_0)$ is the set of end point preserving homotopy classes of loops in X based at $x_0$ and a loop is just a path    $f:I \rightarrow X$ with $f(0)=f(1)$. The question says we can regard $\pi_1(X, x_0)$ as the set of basepoint preserving homotopy classes of maps $(S^1, s_0) \rightarrow (X, x_0)$.   This confuses me, does it mean the set of basepoint preserving homotopy class on maps $g:S^1 \rightarrow X$ which map loops in $S^1$ based at $s_0$ to loops in X based at $x_0$?  Then how can $\pi_1(X,x_0)$ be regarded as this set?  If someone could explain this it would be really useful Grandi's Series; tends to $1/2$, but why is this considered a valid sum? Two figures side by side How can I put two figures side-by-side? Not two sub-figures, but two actual figures with separate "Fig.: bla bla" captions.  A figure is supposed to spread over the entire text width, but I have two figures which are narrow and long, and I need to save the space in order to withstand the pages limit. I sold an investment in a standard brokerage account at a small loss because I needed the money for a down payment.  I still think it is a good investment, can I buy the same investment in a standard IRA without running into wash sale problems?  I will probably just wait the 30 days any way to avoid any headaches, but I want to know if there is a definitive answer on this.    Being as the cost basis in the traditional IRA doesn't matter, I wouldn't think there would be a problem. unzip error "End-of-central-directory signature not found" I try to unzip a zip file, but got an error:  $ unzip COCR2_100.zip  Archive:  COCR2_100.zip   End-of-central-directory signature not found.  Either this file is not   a zipfile, or it constitutes one disk of a multi-part archive.  In the   latter case the central directory and zipfile comment will be found on   the last disk(s) of this archive. note:  COCR2_100.zip may be a plain executable, not an archive unzip:  cannot find zipfile directory in one of COCR2_100.zip or         COCR2_100.zip.zip, and cannot find COCR2_100.zip.ZIP, period.   I googled but didn't find a solution. I was wondering why it is and how I should fix it? Thanks!  The zip file can be downloaded from . It is an application, and here is its website .  My OS is 10.10. Filling in new field in attribute table based on values of another field in ArcGIS Desktop? I have added a new field (Category) in an attribute table of a shapefile and I would like to fill it with numbers, 0 or 1, based on the numbers of another field (Calorific value) of the same attribute table.   That means that if the Calorific value is higher than 15, then I would like to fill in the corresponding cells of the (new) Category field with 1. If the Calorific value is less than 15, then the rest cells of the (new) Category field to be filled in with the number 0.   Is there a way to do this automatically rather than manually? Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$ During our studies on Riemann Integrals we were given the following question in my Calculus II course: $$ \forall n\in\mathbb{N}: \text{let } f_n(x)=(1+\cos(x))^n, f_n:[0,1]\to \mathbb{R}$$ $$\text{ Find}: \lim_{n\to\infty}\int_0^{\frac{1}{2^n}}f_n(x)\, dx $$ I have tried finding the limit using the squeeze theorem. I noticed that the function is defined on $[0,1]$, where $\cos(x)$ is positive and decreasing. I used the following boundaries: $$ 1\leq f_n\leq 2^n \implies \frac{1}{2^n} = \int_0^{\frac{1}{2^n}}1 \leq \int_0^{\frac{1}{2^n}}f_n(x) \leq \int_0^{\frac{1}{2^n}}2^n = 1  $$ but $ \displaystyle{\lim_{n\to\infty}}\frac{1}{2^n} = 0 $ which means I'm unable to apply the squeeze theroem. I've tried using tighter lower boundaries such as $1+\cos(1)$ But it didn't seem to work. I did some trial and error by calculaing the integrals manually for different values of $n$ and it does seem like $\displaystyle{\lim_{n\to\infty}}\int_0^{\frac{1}{2^n}}f_n(x) dx = 1 $ This means that somehow I should find a lower bundary which tends to 1 when $n\to\infty$. Any ideas on how to go forward from here are welcome. Can you raise a number to an irrational exponent? How do you factorise $x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3$? I'm trying to factorise $$ x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3 $$ into four linear factors.  By plugging it into WolframAlpha I've learned that it's $$-(x-y)(x-z)(y-z)(x+y+z)$$  My question is: what are the steps involved in factorising the expression? Is there a method I don't know about that I'd have access to with my limited maths?  Really appreciate any help! What makes frictional force the centripetal force of a car turning along a curve? As friction is the opposing force and acts anti-parallel so there is no component of frictional force towards the center,right? Then how can frictional force be centripetal force? Why is $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X > k)$ true? I'm working through a problem regarding expected values in Markov chains, and at some point it says:     Recall from probability that if $X$ is a positive integer valued random variable, then $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X &gt; k)$.   I know that by definition $\mathbb{E}[X] = \sum_a a\mathbb{P}(X = a)$, but I can't see how the above equality follows from this, nor am I sure if this is how to approach the problem. From my old HD (Ubuntu 16.04) I copied ~/.thunderbird and other programs to the new disk with Ubuntu 18.04 installed. All went good. I tried to install Opera. The installation was unsuccessful, a window asking something was held. After that Thunderbird Local Folders -> Inbox (only) was invaded by large icons like this screenshot  Flowers, plants, trucks and others. I restarted but those images are still there. Opera was successfully installed. What can I do to remove them? I sadly haven't been able to answer this questions using Google. In beamer, I'd like to make the default font for the entire title page, as well as frame titles, to be the default font from the old  (example ). Possible to change where Android Virtual Devices are saved? Processor: PIC18F66K22 Compiler:  C18 (XC8 is fine also)   I've just made (and succesfully tested) code to measure the voltage on AN4 analog pin.  Now I want to try something else, not quite sure if it's theoretically possible.  My test-board has a PIC processor, with VDD,AVVD connected to a supply (ranging from 0(if the battery is empty/disconnected) to 4,2(full battery).  Can I use ADC to measure the VDD(-in) of my board?  Why not?:   It's not an ANx pin, not sure how to make the ADC measure it? (Channel?) If the voltage on VDD(-in) drops, will my ADC reference voltage also drop? (So when my PIC only gets 3,3V the ADC will still say it's 100% (as the max Voltage on the chip, also the reference is 3,3V).   Why/what do you ask?:   Can I just measure Channel 30 (VDDCORE)? Could I set my Vref to Vdd and measure a precision voltage reference with the A/D converter. (Not sure how) Or I could add a wire from VDD-in to an ANx pin? Will Internal VREF+ (4.096V) stay 4+V when the VDD-in is around 3,4V? Is there some kind of transformator that makes it so? Internal VREF+ (4.096V) is a bit lower than the max of the battery (4,2V), does this mean I can damage the ADC? Or just that the result will be max when the battery is full. (4,2V out of 4,096V)     Please mind that my knowledge of Electronics is "low". I've learnt way more about the software part in my education, but I'd like to know more about (Embedded) Electronics as it's a crucial part in Embedded Engineering. (It's sad how my school doesn't see this.) Validity of naively computing the de Broglie wavelength of a macroscopic object Many introductory quantum mechanics textbooks include simple exercises on computing the de Broglie wavelength of macroscopic objects, often contrasting the results with that of a proton, etc.  For instance, this example, taken from a textbook:     Calculate the de Broglie wavelength for      (a) a proton of kinetic energy 70 MeV      (b) a 100 g bullet moving at 900 m/s   The pedagogical motivation behind these questions is obvious: when the de Broglie wavelength is small compared to the size of an object, the wave behaviour of the object is undetectable.  But what is the validity of the actual approach of applying the formula naively? Of course, a 100g bullet is not a fundamental object of 100g but a lattice of some $10^{23}$ atoms bound by the electromagnetic force. But is the naive answer close to the actual one (i.e. within an order of magnitude or two)? How does one even calculate the de Broglie wavelength for a many body system accurately? $\chi(G)+\chi(G')\leq n+1$ How to prove, that the sum of chromatic numbers of graph and it's complement is smaller then the number of vertices incremented by one?  $\chi(G)+\chi(G')\leq n+1$  The notes from my classes say to color the first graph using sequential algorithm with vertices ordered by their degrees (the ones with lowest appear first). We would get $k_1$ colors, then we color the graph $G'$ in the backwards order and get $k_2$ colors, and the sum $k_1+k_2$ in my notes is magically smaller than $n+1$, but I just don't see why... I have the following recurrence that I've been pounding on:  $$ a(0)=1\\ a(1)=1\\ a(2)=2\\ a(2n)=a(n)+a(n+1)+n\ \ \ (\forall n&gt;1)\\ a(2n+1)=a(n)+a(n-1)+1\ \ \ (\forall n\ge 1) $$  I don't have much background in solving these things, so I've been googling around looking for different techniques. Unfortunately, I haven't been able to correctly apply them yet. So far I've tried:   Characteristic equations Generating functions Plugging it into Wolfram Alpha Telescoping Observation   I'm sure that one or more of these is the way to go, but my biggest problem right now is figuring out how to deal with the idea that there are different equations for odd and even values of $n$. I'm not necessarily looking for a solution (though it would be gratefully accepted), but any nudges in the right direction would be much appreciated.    To follow up, it turned out that the speed problem described in my comment, below was related to the Decimal implementation in Python 2.7. Switching to Python 3.3 (and Java) made everything many orders of magnitude better. Are battery packs allowed in hand luggage?