The box has the same weight. I think that the stairs does more work because it travels a further distance as it is a less direct path opposed to going straight up.
This might be a stupid question, but why exactly is work a path function?  In school, my teacher said it’s because it depends on the path. She gave an example of walking up a mountain, and said the work you expend depends on the path you take (straight path up or circling up around the mountain). But isn’t the work expended just equal to $E= mgh?$
Do we say "-1 thing" or "-1 things"?  I am interested in both      two things minus one thing(s)    and      minus/negative one thing(s) Can I speed up iCloud photo sync between iPhone and Macbook? I have an iPhone 5 running iOS 9.1 and a Macbook Pro running Yosemite.  Both devices are set up to sync photos to and from iCloud.  When I take a photo on the iPhone (for further processing on the Macbook), it takes an inordinate amount of time until the photo shows up in the Macbook's photos library - sometimes up to 10-20 minutes. Sometimes it seems to work faster if I quit the Photos app on both devices, and start it again.  I often end up sending myself photos through E-Mail because it's quicker. That seems ridiculous!  Is there a way to force a sync on the iPhone, or to speed up the process some other way? I remember reading a sci-fi story where astronauts visit a planet, which is covered in stationary aliens with mile long necks that filter feed from the atmosphere.  It was published between 1960 and 2000.    It was in English and involved a pair of astronauts that went from planet to planet on a tour or something, though I don't know details of any other planets they visited. How do I press Ctrl+Alt+Delete in VirtualBox? I'm running VirtualBox with Windows Vista as host OS and Windows Server 2008 as guest OS. To login to Windows Server I have to press Ctrl+Alt+Delete, but my host OS reacts on that so I can not send it to VirtualBox. How can I do it? How to stop a script from running if it's not root (and echo "Not running as root! Exiting...") How to enable or disable services? How to find roots of $X^5 - 1$? How to find roots of $X^5 - 1$? (Or any polynomial of that form where $X$ has an odd power.) Group theoretic meaning of natural isomorphisms between certain functors So imagine you have a group $G$ and we consider the set of group homomorphisms from $\mathbb{Z}$ to  $G$ specified by  $\forall g$ $\in G$ $\exists$   $\phi(1)=g$. Each of these homomorphisms is in 1-1 relation with the elements of $G$.  Consider groups for a moment in the context of category theory, viewing the groups as one object categories and thereof group homomorphism as functors. What would a natural isomorphism mean in group theory terms for G?  My thoughts are that the natural transformations equate to maps between homomorphisms and since the homomorphisms are in 1-1 relation with the elements of G, then a natural transformation is a map between group elements, i.e another element of the group. I'm not entirely convinced by this.   Anyway continuing my reasoning a natural isomorphism is a map between the homomorphisms that has an inverse, the thing is in relation to the elements of G this is every element? Furthermore I'm looking to find an equivalence class defined by this natural isomorphism, is this just a collection of the elements that are each others inverses?  Thanks in advance for any assistance. I have a Visual Studio 2008 solution with two projects (a Word-Template project and a VB.Net console application for testing).  Both projects reference a database project which opens a connection to an MS-Access 2007 database file and have references to System.Data.OleDb.  In the database project I have a function which retrieves a data table as follows   private class AdminDatabase    ' stores the connection string which is set in the New() method    dim strAdminConnection as string     public sub New()    ...    adminName = dlgopen.FileName    conAdminDB = New OleDbConnection    conAdminDB.ConnectionString = "Data Source='" + adminName + "';" + _        "Provider=Microsoft.ACE.OLEDB.12.0"     ' store the connection string in strAdminConnection    strAdminConnection = conAdminDB.ConnectionString.ToString()    My.Settings.SetUserOverride("AdminConnectionString", strAdminConnection)    ...    End Sub     ' retrieves data from the database    Public Function getDataTable(ByVal sqlStatement As String) As DataTable         Dim ds As New DataSet         Dim dt As New DataTable         Dim da As New OleDbDataAdapter         Dim localCon As New OleDbConnection           localCon.ConnectionString = strAdminConnection          Using localCon             Dim command As OleDbCommand = localCon.CreateCommand()             command.CommandText = sqlStatement             localCon.Open()             da.SelectCommand = command             da.Fill(dt)             getDataTable = dt         End Using      End Function End Class   When I call this function from my Word 2007 Template project everything works fine; no errors. But when I run it from the console application it throws the following exception     ex = {"The 'Microsoft.ACE.OLEDB.12.0'   provider is not registered on the   local machine."}   Both projects have the same reference and the console application did work when I first wrote it (a while ago) but now it has stopped work.  I must be missing something but I don't know what.  Any ideas? I am using pdflatex on a fresh (and current) MikTex 2.9 install with the following MWE:  \documentclass{article} \usepackage{animate} \begin{document}  Test \end{document}   Pdflatex throws the error:  Package: pdfbase 2017/03/23 v0.14 driver independent access to low-level PDF fe atures \g_pbs_page_int=\count175  ! Undefined control sequence. &lt;argument&gt; \luatexversion                            &lt;95 l.924 }   I have read the other posts containing the offending control sequence, especially  but the solutions offered there didn't help in my case.  This problem might have arisen with a recent MikTex update. I have now completely uninstalled, redownloaded, reinstalled and updates MikTex -- with no success. Shear transform a "box" Using the graphicx package, I can make any arbitrary box rotated using the \rotatebox{...}{...} command. Is there a comparable command in any package that lets me shear a box, i.e., producing a kind of general slanting? How to show hidden folders in File Manager (Nautilus) on Ubuntu? How do you show a hidden folder (whose name starts with .) in File Manager a.k.a. Nautilus on Ubuntu?  I am somewhat new to Ubuntu and can't seem to find the "view" menu. After learning about the  datasets I've working with the following layers, from the USA data   Country boundaries State boundaries County boundaries City boundaries ZipCode/Postcode boundaries   What I am trying to find is the equivalent (where appropriate) of the same data for various countries.  Is there any free administrative boundaries available as shapefiles for other countries? I have the following data structure (a list of lists)  [  ['4', '21', '1', '14', '2008-10-24 15:42:58'],   ['3', '22', '4', '2somename', '2008-10-24 15:22:03'],   ['5', '21', '3', '19', '2008-10-24 15:45:45'],   ['6', '21', '1', '1somename', '2008-10-24 15:45:49'],   ['7', '22', '3', '2somename', '2008-10-24 15:45:51'] ]   I would like to be able to   Use a function to reorder the list so that I can group by each item in the list. For example I'd like to be able to group by the second column (so that all the 21's are together)  Use a function to only display certain values from each inner list. For example i'd like to reduce this list to only contain the 4th field value of '2somename'    so the list would look like this   [      ['3', '22', '4', '2somename', '2008-10-24 15:22:03'],       ['7', '22', '3', '2somename', '2008-10-24 15:45:51'] ] My old computer broke down a few days ago, so I'm using a laptop until I can get it fixed.  As a side effect, I no longer have my usual browser cookies, so I had to log back into Stack Exchange.  While doing so, I noticed that I kept having to log in to every Stack Exchange site I visited &mdash; the usual "Welcome back [username], you've been logged in." auto-login banner seemed to be conspicuously missing.  In fact, a quick look at the "network" tab in the developer tools suggested that no requests to stackauth.com were being made at all.  Eventually, I decided to dive into .  Turns out that the code to make the global auth check and bring up the banner is simply:    gauth.checkStackAuth(StackExchange.options.stackAuthUrl);   And, what do you know, running that command from the developer console does auto-log me in.  However, the reason this code isn't being run automatically is because it's disabled in the site config (apparently for all SE sites).  For example, the page I'm typing this question on has the following config options set:  StackExchange.init( {     "locale": "en",     "stackAuthUrl": "https://stackauth.com",     "serverTime": 1408393334,     "networkMetaHostname": "meta.stackexchange.com",     "styleCode": true,     "enableUserHovercards": true,     "site": {         "name": "Meta Stack Exchange",         "description": "Q&amp;A for meta-discussion of the Stack Exchange family of Q&amp;A websites",         "isNoticesTabEnabled": true,         "recaptchaPublicKey": "6LdsB7sSAAAAAAzjgEF_Hd8vXv-C42sa_KyofaGR",         "recaptchaAudioLang": "en",         "enableNewTagCreationWarning": false,         "globalAuthDisabled": true,                // &lt;--- HERE         "isMetaSite": true,         "enableSocialMediaInSharePopup": true,         "useGoogleOAuth2": true     },     // etc.   So, apparently, global auto-login has been deliberately disabled for some reason.  Why is that, and is there any planned timeline for re-enabling it? Let $g(x)\in \mathbb{Z}[x]$, a nonconstant polynomial. Show that the set of primes $p$ such that $p\mid g(n)$ for some $n\in \mathbb{Z}$ is infinite.  I don't know how to start. I have tried asuming that the set is finite but i haven't reached any contradiction. Normal distribution tail probability inequality I am trying to show that $$P(X&gt;t)\leq \frac{1}{2}e^\frac{-t^2}{2}$$ for $t&gt;0$ where $X$ is a standard normal random variable.  Perhaps this is simple.  I have been starting with  $$ \int_{t}^{\infty} \frac{1}{\sqrt{2\pi}} e^\frac{-x^2}{2}dx \leq \int_{t}^{\infty}\frac{x}{t}\frac{1}{\sqrt{2\pi}}e^\frac{-x^2}{2}dx = \frac{1}{t\sqrt{2\pi}}e^\frac{-t^2}{2}$$  but this is not what I want...I am looking for a much stronger inequality.   Any help in the direction of getting the $1/2$? How can I send mail from an iPhone application Why don't wizards always use multiple wands? Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from? I'm curious where the  $p=\frac{h}{\lambda}$ comes from?   I know that for light (which has no rest mass), the following is true:  $E=pc$ and $E=hf$  so,  $$pc=hf \Rightarrow p=\frac{hf}{c}=\frac{h}{\lambda}$$  But how is the expression $p=\frac{h}{\lambda}$ obtained for a massive particle where $E\neq pc$? I've read some people claim that the expression can be derived, and others saying it's an experimentally verified relationship.