How Do I Connect PVC Pipe to a Toilet Waste Pipe?
How do I replace this cast iron toilet flange?
Fiber from $S^1$ to $\mathbb{R} P^1$ that does not admit a section. Consider the map $q:S^1 \to \mathbb{R} P^1$ given by $v \mapsto \mathbb{R} v$. I want to show that this map does not admit sections. I've previously shown that $S^1$ is diffeomorphic to $\mathbb{R} P^1$ but this doesnt seem to be of much help. I've also shown that $TS^1$ is trivial, however I don't see how to use this. My only idea is that such a section wouldn't be well defined since it could go to either antipidal points when composing with $q$. Any hint or help with this would be amazing! We have previously determined that  or  can attune to magic items, but one of those is a sapient creature, and the other "always obeys your commands".  A paladin's steed (per the Find Steed spell) is also 'unusually intelligent' and falls within the score range for sapient creatures.  But what about a regular old animal? If my ranger has a wolf companion, can he make that wolf attune to, say, an Amulet of Health? According to the Beast Master archetype, a companion animal "obeys your commands as best it can".  Is spending an hour 'focused only on the item' (as required for attunement) something a beast can manage?  Or what if it's not an Animal Companion, but just a riding horse, a pet dog, a trained magpie?  I know, probably this is going to be down to the DM to determine, but is there any guidance we can use to help decide whether my cat can attune to an item, and whether rubbing it with catnip would help? Converting string of 1s and 0s into binary value I'm trying to convert an incoming sting of 1s and 0s from stdin into their respective binary values (where a string such as "11110111" would be converted to 0xF7). This seems pretty trivial but I don't want to reinvent the wheel so I'm wondering if there's anything in the C/C++ standard libs that can already perform such an operation? Animated textures don't work in Blender viewport playback I am trying to animate in 2d. I do it with planes that have textures on them. I recently came up with the idea of having a plane with an image sequence of mouths because animating actual lip syncing by hand takes too long and isn't really necessary for what I'm trying to acomplish. However, when playing back the animation in textured viewport shading the animated texture stays at the last frame until the animation stops. I can use the arrow keys and it works fine as well as scrubbing through the timeline, just not when playing back the animation with alt+a. Can anyone help me with this problem? How do I remap multi-key sequences to individual keys? I just bought an IBM Model M keyboard. While awesome, it lacks a windows key and multimedia keys. While there are many programs out there that can map one key to another, or one key to a key sequence, are there any programs that will map a keyboard sequence to a single key?  Edit: OS = Win7 How do you get the footer to stay at the bottom of a Web page? How long can eggs be unrefrigerated before becoming unsafe to eat? A friend of mine accidentally left a carton of eggs on her counter, unrefrigerated, for three days. The eggs had been previously refrigerated both at the store and at home. Now she's planning to do some more cooking which requires eggs, and is wondering if it's still safe to use them for baking. I believe she is planning on baking cookies with them, so they would be baked at fairly high temperatures for probably at least 10 minutes. Would this be safe, or are eggs left unrefrigerated for that long not safe for consumption? What's the best way to use SOAP with Ruby? A client of mine has asked me to integrate a 3rd party API into their Rails app.  The only problem is that the API uses SOAP.  Ruby has basically dropped SOAP in favor of REST.  They provide a Java adapter that apparently works with the Java-Ruby bridge, but we'd like to keep it all in Ruby, if possible.  I looked into soap4r, but it seems to have a slightly bad reputation.  So what's the best way to integrate SOAP calls into a Rails app? We have given isosceles triangle $ABC$ with baseline $AB$. Point $M$ is midpoint of AB. Draw perpendicular line to side $AC$ through $M$ which intersects $AC$ in point $H$. Let $P$ be midpoint of $MH$. Show that lines $BH$ and $CP$ are perpendicular to each other.  I also have "hint": Construct height $BD$ to side $AC$ and look at the triangles $ABD$ and $MCH$.  Analytically there is no problem but I get stuck in geometrical approach to solution. How can I block app and game invitations once and for all in Facebook? I want to block app and game invitations once and for all in Facebook. How can I do it so they cannot disturb me anymore? Input impedance of Arduino Uno analog pins? I'm using the  on some small robotic arm motors, and reading in the analog voltage with an Arduino Uno.  I've had reasonably good results, but only after putting in an RC filter on the output.  However, in the application note on the datasheet, it says not to do that:  "the addition of an RC filter to the output of a sensor IC can result in undesirable device output attenuation — even for DC signals."  Then it gives a formula to calculate attenuation, but it depends on knowing the input impedance of whatever is reading the signal, so that's what I'm after here. How to add readable text to a light and dark image? I'm trying to add text to a photo of a city but the colors in the background make it difficult to read light and dark text. I've tried several light and dark colors but they all looked overpowered by the colors in the image. What colors could I use or what can I do to the text to make it show but also make it so you can still see the background?  Here is the image I'm trying to use: Why is the empty set considered an interval? What is the definition of an interval and why is the empty set an interval by that definition? $$\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$$  $$\sin(x)=\frac{e^{ix}-e^{-ix}}{2i}$$  $$z=\alpha(x)=e^{ix}$$   $$\sin(x)=\frac{z^2-1}{2zi}$$ $$2+\sin(x)=\frac{4zi+z^2-1}{2zi}$$ $$\frac{1}{2+\sin(x)}=\frac{2zi}{4zi+z^2-1}$$    $$\int_\alpha \frac{2zi}{4zi+z^2-1} \ \ \frac{1}{zi}$$    $$4zi+z^2-1=0$$ $$z_1=\frac{-4i+2\sqrt{3}i}{2}$$ $$z_2=\frac{-4i-2\sqrt{3}i}{2}$$    $$\rvert z_1 \rvert &lt;1$$ $$\rvert z_2 \rvert &gt;1$$   Using Residue theorem:   $$\int_\alpha \frac{2}{4zi+z^2-1}=2 \pi i \ \lim_{z\rightarrow-2i+\sqrt{3}i} \ \frac{2}{z+2i+\sqrt{3}i}=\frac{2 \pi}{\sqrt{3}}$$    Is it correct?  Thanks! How to negate a specific symbol? I want to negate the symbol whose code is \models (this would be specific to Formal Logic). How can I do that? I tried a number of combination, but didn't find how this could be done. I tried \neqmodels, \nemodels, \notmodels, \nmodels  but all of them are wrong.  Is there a general way to negate symbols? stackoverflow.com without OpenID is it possible to login/create user in stackoverflow.com without creating/login using OpenID? i hate using OpenID, it's really confusing if you create different user/account on different websites :(     Note: the following text was submitted as an edit suggestion. I approved it, giving the user the benefit of the doubt and assuming that it was the OP's other account. -   even when i want to post this question under my new openid, i still logged as the old user, so i can't view my own question when i logged under my userid How can I convert an integer into its verbal representation? Is there a library or a class/function that I can use to convert an integer to it's verbal representation?  Example input:     4,567,788`   Example output:     Four million, Five hundred sixty-seven thousand, seven hundred eighty-eight Having problems with listings and UTF-8. Can it be fixed? I'm having some problems with listings and UTF-8 in my document. Maybe someone can help me? Some characters work, like é and ó, but á and others appear at the beginning of words...  \documentclass[12pt,a4paper]{scrbook} \KOMAoptions{twoside=false,open=any,chapterprefix=on,parskip=full,fontsize=14pt}  \usepackage[portuguese]{babel} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{listingsutf8}  \usepackage{inconsolata} \lstset{     language=bash, %% Troque para PHP, C, Java, etc... bash é o padrão     basicstyle=\ttfamily\small,     numberstyle=\footnotesize,     numbers=left,     backgroundcolor=\color{gray!10},     frame=single,     tabsize=2,     rulecolor=\color{black!30},     title=\lstname,     escapeinside={\%*}{*)},     breaklines=true,     breakatwhitespace=true,     framextopmargin=2pt,     framexbottommargin=2pt,     extendedchars=false,     inputencoding=utf8 }  \begin{document} \begin{lstlisting} &lt;?php  echo 'Olá mundo!'; print 'Olá mundo!'; \end{lstlisting}  \end{document} \end{lstlisting} Do ideal gases at zero Kelvin have potential energy? Possibility of recovering files from a dd zero-filled hard disk I have "zero filled" (complete wiped) an external hard disk using dd, and from what I have heard: people said you should at least "zero fill" 3 times to be sure that the data are really wiped and no one can recover anything.  So I decided to scan the disk once again after I've zero filled the disk. I was expecting the disk to still have some random binary left. It turned out that it has only a few sequential bytes in the very beginning. This is probably the file structure type and other headers stuff. Other than that, it's all zeros and nothing else.  So if we have to recover any file from a zero filled disk, ...how? From what I've heard, even you zero fill the disk, you should still have some data left. ...or could dd really completely annihilate all data?