Show that mapping cones are homotopy equivalent.
Homotopic maps have homotopy equivalent mapping cones
Backup to Azure Storage Container: Shared Access Signature the only way? RESTORE FILELISTONLY FROM URL = '' WITH CREDENTIAL = '' fails in SQL Server 2016.  Copied script from SQL Server 2012 environment, successfully restoring from Azure Storage Container, with create credential statement, and it failed in 2016.  Error message "Forbidden".  Only after logging into the Azure Portal, creating a Shared Access Signature for the container, could I execute the restore, and only by not specifying the credential did the restore work.  No documentation advises that a SAS (Shared Access Signature) is required in SQL Server 2016 for Azure container backup / restore.  Is there another way to use T-SQL to access blob backups on Azure storage containers in SQL Server 2016, than using SAS?    Looking at the MSDN tutorial on how to configure the backup service SQL 2016 introduces, a SAS is used. Refer "I saw one of my classmates who was/were?" heat weighting: failed to find solution for one or more bones Here is the .  Picture:   It's nothing special but I cant figure out why I get problems rigging this mesh. It would be important and a great Help! Thanks for reading and I know there are a lot of guides answering this question but I tried all and it doesn't seem to work. Does the Rogue's Assassinate feature grant criticals on multiple attacks? Does the Rogue's Assassinate feature (auto-crit on surprised targets) allow for multiple crits if you make multiple attacks that round, either through two-weapon fighting or extra attacks gained through multiclassing?  As an example: my 3rd level Human (Variant, TWF feat) Rogue-Assassin rolls high on his stealth roll, and gets up behind his target.  With two daggers, he gets 2 attacks per round if he uses his bonus action as well.  Do both of these attacks qualify for Assasinate's auto-crit feature?  That is: would I do 2 criticals for       4d4+4d6+2*DEX damage   or a single critical and a non-critical for       3d4+4d6+2*DEX damage?   Additionally, if I gained the Extra Attack feature through multiclassing, would I get crits on all 3 of my attacks, or just the first one? It would seem that one way of proving this would be to show the existence of non-algebraic numbers. Is there a simpler way to show this? Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$ $$\lim_{x \to \frac{2}{\pi}}\lfloor \sin \frac{1}{x} \rfloor=0$$    I need to prove the limit of this using the $\epsilon - \delta $ way but I don't know how to find $\delta$ when I'm given a trigonometric function I know only how to do it with polynomial functions At what speed does our universe expand? Cross-thread operation not valid: Control accessed from a thread other than the thread it was created on Outlook Rule - Move mail that is READ and Older than X days Outlook 2010. Want to create a rule that moves all mail from my inbox to another folder:   Has been read Is older than X days   I was looking at Auto-archiving, but it does not seem to let me be this specific with my criteria. How to interpret the margin of error in a poll? Recently the media reported on a political poll that stated that "46% of Republican voters in Mississippi think that interracial marriage should be illegal".  One example story (of many around the 'net) is this one from the NY Daily News: .  From that article:     A survey conducted last month shows 46% of GOP voters in the state   believe interracial marriage should be illegal - a plurality of the   people questioned   Given that I know many people in interracial marriages (including in my own family) I was motivated to track down the full story rather than fall to the obvious hysteria.  I located the press release on the poll from Public Policy Polling  (PDF)  which has:     46% of these hardcore Republican voters believe interracial marriage   should be illegal, while 40% think it should be legal. With Barbour   included, Huckabee gets more support (22%) from the former than the   latter (15%), as does Palin (13-6). The support for Bachmann (10-2),   Gingrich (13-8), and Pawlenty (4-1) works the opposite way.   And at the end of the first page they state:     PPP surveyed 400 usual Mississippi Republican primary voters from   March 24th to 27th. The survey’s margin of error is +/-4.9%.   Now what I don't understand is how to interpret the results especially the margin of error value.    From the raw numbers, 46% (~50%) of 400 voters is 200 voters who responded who think that interracial marriages should be illegal.  But from stats of Mississippi in the 2008 Federal election, McCain polled about 725,000 Republican votes (to Obamas 556,000). My gut feeling is that you can't extrapolate that 46% number to the other 724,600 Republican voters and still retain a 5% margin of error.  So is the media misrepresenting the numbers (really? the media would do that?!?!?!) Or are there statistics at work that I don't understand?  Thanks for your help! executing web service using postman I'm trying to create record Type selection screen in LWC, but getting this error  afterRender threw an error in 'c:createContact' [Cannot read property 'recordTypeInfos' of undefined]  HTML:  &lt;template&gt;     &lt;lightning-combobox name="recordType" label="Record Type" placeholder="Choose Status"                         value={value}                          options={recordTypeId}&gt;      &lt;/lightning-combobox&gt; &lt;/template&gt;   JS:  import { LightningElement, track, wire, api } from 'lwc'; import { getObjectInfo } from 'lightning/uiObjectInfoApi'; import CONTACT_OBJECT from '@salesforce/schema/Contact';  export default class CreateContact extends LightningElement {      @track statusOptions;     @track value;     @api objectApiName;      @track objectInfo;      @wire(getObjectInfo, { objectApiName: CONTACT_OBJECT,})     objectInfo;       get recordTypeId() {         // Returns a map of record type Ids          console.log(this.objectInfo);         const rtis = this.objectInfo.data.recordTypeInfos;         return rtis;     }  } How do I determine the result of a Saving Throw? I'm a pretty new player, and I'm building a bard in D&amp;D 5e. I understand how saving throws work in general, but I am a little confused about one thing. Say I cast Blindness/Deafness on a humanoid. They must then make a Constitution saving throw. My question is: what value do they have to roll in order to make the save? Does their roll (plus their constitution modifier) have to beat my constitution (plus my modifier)? This is more of a general player question than one specific to the Bard or that spell. I don't want to do this through trial and error, and the best way I have found so far was to start dividing from 1.     $n! = \text {a really big number}$   Ex. $n! = 9999999$   Is there a way to approximate n or solve for n through a formula of some sort?  Update (Here is my attempt):  Stirling's Approximation: $$n! \approx \sqrt{2 \pi n} \left( \dfrac{n}{e} \right ) ^ n$$  So taking the log:     $(2\cdot \pi\cdot n)^{1/2} \cdot n^n \cdot e^{-n}$       $(2\cdot \pi)^{1/2} \cdot n^{1/2} \cdot n^n \cdot e^{-n}$       $.5\log (2\pi) + .5\log n + n\log n \cdot -n \log e$       $.5\log (2\pi) + \log n(.5+n) - n$   Now to solve for n:     $.5\log (2\pi) + \log n(.5+n) - n = r$       $\log n(.5+n) - n = r - .5 \log (2\pi)$   Now I am a little caught up here. According to Hubble's Law, how can the expansion of the Universe be accelerating? Scientists today think the expansion of the universe is accelerating.   According to Hubble's law, objects further away are moving faster than objects closer to us. The further away an object is, the further back in time we are seeing, so in the past objects moved faster (is this sentence correct?).  So because objects moved faster before than they do now, surely that's deceleration not acceleration?  my textbook says "if Scientists today think the rate of expansion of the Universe were decreasing then distant objects should appear different to Hubble's Law predictions: universe is accelerating. More distant objects would seem to be receding faster (since expansion was faster in the past)" How can we prove that $D(f)\backsimeq\operatorname{Spec} A_f$? Let $$D(f)=\operatorname{Spec}A - V(f)=\{p\in \operatorname{Spec} A:f\notin p\}$$ be the principal open subsets of $\operatorname{Spec}A$ with the Zariski topology. I'm trying to prove that $D(f)\backsimeq \operatorname{Spec} A_f$, where $A_f$ is the localization of $A$ at $f$.  If we consider the canonical homomorphism $\varphi:A\to A_f$ given by $\varphi (a) = \frac {a}{1}$, we can define $\varphi':\operatorname{Spec} A_f\to \operatorname{Spec} A$, given by $\varphi'(p)=\varphi^{-1}(p),\forall p\in \operatorname{Spec}A_f$.  I'm having trouble proving that this map is surjective.  Thanks. Verify the identity: $\tan^{-1} x +\tan^{-1} (1/x) = \pi /2$ Verify the identity: $\tan^{-1} x + \tan^{-1} (1/x) = \frac\pi 2, x &gt; 0$  $$\alpha= \tan^{-1} x$$  $$\beta = \tan^{-1} (1/x)$$  $$\tan \alpha = x$$  $$\tan \beta = 1/x$$  $$\tan^{-1}[\tan(\alpha + \beta)]$$  $$\tan^{-1}\left [{\tan\alpha + \tan\beta\over 1 - \tan\alpha \tan\beta} \right]$$  $$\tan^{-1}\left[ {x + 1/x\over 1- x/x }\right]$$  $$\tan^{-1}\left[{x + (1/x)\over 0} \right]$$  I can't find out what I'm doing wrong.. Make the enter key send message on iPad How to make applications open on the correct monitor when using multiple monitors? I'm using Windows 8.1, which has much better multiple monitor support than Windows 7 (sort of). However when I'm in a full-screen app on one monitor, and I go to the Start menu on the other and open a desktop app, it opens on the opposite monitor because of it being on that one last time the app was used.  This suspends the full-screen app and switches to the desktop view on that monitor. I then have to drag the desktop app to the other monitor which I didn't have my mouse pointer near in the first place, then switch back to the full-screen app on that monitor by going to the upper-right corner.  This is so incredibly irritating, every time I plug in my laptop to my second monitor and try to use it, this happens. Not to mention whenever I have Netflix or any kind of video in the second monitor and it just randomly stops playing when I'm trying to work on the other screen.  Most likely there is going to have to be a third-party application to install to do this, right? I would really prefer if it was free, as this was less annoying in Windows 7 when the application would only open on top of the other that was on that monitor. This is one of the maybe two annoying things I don't like about Windows 8/8.1. Everything else is fantastic, to be honest. The ability to undo reviews