How do I merge these three triangle faces, which are all on the same plane, into a single pentagonal face? Thanks!
I'm a beginner with blender so this is probably a very basic question.  I have this basic model below. I've ended up with a lot of unwanted geometry that I want to simplify. I wanted to start by merging the two selected faces below but no matter what I try to delete or merge it just destroys the geometry.  How can I achieve what I want to do (which is combining all of the unwanted geometry, either starting with this merge or some other way?)
If we pick randomly two points inside a circle centred at $O$ with radius $R$, and draw two circles centred at the two points with radius equal to the distance between them, what is the expected area of the intersection of the two cirlces that contain the origin $O$. Except when we use right to denote direction, what is the difference between these two terms?  Also, which one is the preferred construction between these two     Am I right?   or     Am I correct? Can we have a list of all the Stack Exchange domains somewhere, for firewall purposes? I work behind an really annoying firewall, and I just want the net admin to add all the SE websites to the whitelist. Right now I've lost access to Stack Overflow's authentication, but not Meta's... so I have to come here before I log in there.  It's driving me nuts. Basically I just want to add an exclusion rule for all SE domains; not only the website domains, but also the content domains such as gravatar.com, quantserve.com, the domain that holds static content, etc... I have a Virtual machine using centos 7 with 200GB disk.For some reason my layout is:  df -h Filesystem               Size  Used Avail Use% Mounted on /dev/sda1                100GB  95GB  5GB      Running fdisk -l:  Disk /dev/sda: 204.8 GB, 204803670016 bytes,400007168 sectors  Units = sectors of 1 * 512 = 512 bytes  Sector size(logical/physical): 512 bytes / 512 bytes I/O size(minimum/optimal): 512 bytes / 512 bytes Disk label type: dos Disk identifier: 0x0006c283  Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048   199997439    99997696     Linux   I would like to increase my space on my partision /dev/sda1. Ping a site in Python? Show a,b,c congruences when $a^2+b^2=c^2$ i would like to know how to prove that if $a^2+b^2=c^2$ then   a) $3|a$ or $3|b$  b) $5|a$ or $5|b$ or $5|c$  c) $4|a$ or $4|b$   Also that $a^2+b^2+c^2+1$ can't be divisible by 8  Thank you very much! Change multiple filenames by replacing a character I would like to be able to execute a SOQL query that will allow me to see which users have access to a certain record type for a certain object.  For example, if I have a case record type called Phone Team, I would like to make a query that returns the names of all the users that have been assigned the Phone Team record type, as can be seen in the native user interface in a profile's Object Settings page.  So far I have managed to get a query that can get the names of all the users that have, for example, read access to the case object:  SELECT Assignee.Name FROM PermissionSetAssignment      WHERE PermissionSetId IN          (SELECT ParentId FROM ObjectPermissions WHERE SObjectType = 'Case'               AND PermissionsRead = true AND Parent.IsOwnedByProfile = true)   However, there doesn't seem to be any way to access record type assignment in the same way that you can object permissions.  I see from  that the info can be obtained via the metadata API, but I would much prefer to do it by SOQL if possible.  Thanks What is a Generic Handler in asp.net and its use? Why didn't Palpatine publicly change his name once he became Emperor? Anakin Skywalker was known as Darth Vader (this was already his Sith name) after the creation of the Galactic Empire.  So why did Palpatine remain "Emperor Palpatine"? Why didn't he embrace his persona as Darth Sidious?  I started wondering after reading one of the answers to Change default CSS of Google Chrome I would like to be able to change the default CSS used by chrome, such as removing the underlines for links, etc. However, I cannot find the default CSS file used by Chrome. Does anyone know where it is? Unable to resume after suspend I'm using Ubuntu 12.04 &amp; everything about it is great except that it just won't resume after suspend. I've tried the suggestions listed in this thread  but none worked. I'm using Lenovo Y510P. I'm new to Ubuntu, or unix for that matter, so please let me know if there's anymore  information that I should be posting. Thanks.  update  I tried the suggestion by Dima on this post . The machine wakes up from hibernation but immediately the screen gives a screen like this     Wondering if this is an issue with the graphics card or something. I have been studying the pronunciation of Greek-derived words in English, and I've found an odd anomaly. There are (at least) two possible pronunciation patterns for plural word-forms that end in -&#8288;mata (which correspond to singular word-forms that end in -&#8288;ma).   Antepenult stress (expected)  It appears that it is always possible to place the stress on the antepenult (third-to-last) syllable, such as:    /ˈlɛmə/, /ˈlɛmətə/  /ˈskiːmə/, /ˈskiːmətə/  /ˌtɛrəˈtoʊmə/, /ˌtɛrəˈtoʊmətə/~/ˌtɛrəˈtɒmətə/  /ˈstɪɡmə/, /ˈstɪɡmətə/   This is what would be expected from  (I believe most or all of these words came through Latin before entering English), since the penultimate "a" in the original Greek words is short.  Maybe Latin vowel quality and stress rules are not very relevant; certainly, few English speakers know about them nowadays. And even with antepenult stress, some of these pronunciations do not seem to follow all of the traditional rules for pronouncing Latin-derived terms in English. I was reminded by some comments in this  that  in antepenult stressed syllables, we would expect tense ("long") vowels to be shortened due to  (TSL), yielding pronunciations like /ˌtɛrəˈtɒmətə/ (which I just noticed is in fact listed in the Oxford English dictionary) and ?/ˈskɛmətə/ (which is not). (Compare to genus~genera /dʒiːnəs/~/dʒɛnərə/, and perhaps opus~opera /oʊpəs/~/ɒpərə/). However, there are other Latinate plural forms that typically don't have trisyllabic laxing (matrices, also I think helices), or where both the lax- and tense-voweled pronunciations coexist (codices, apices), so I guess the apparent lack of it in schemata should not be surprising. (There are even some exceptions to TSL in singular nouns like obesity.)  Penult stress (unexpected)  The other pronunciation seems to exist only for a couple of words, in which the penultimate "a" is commonly stressed and broadened: stigma ~ stigmáta  (listed by both the Merriam-Webster dictionary and the ), and also sometimes schéma ~ schemáta /skiːˈmɑːtə/ (listed only by the ). (Neither the Merriam-Webster dictionary nor the Oxford Learner's Dictionaries list *"lemmáta").  I'm wondering why this pronunciation exists. It's an irregular plural either way, and putting the stress on the penultimate syllable creates a stress change between the singular and the plural forms.  (It's true that all of these words are rare, and some people might pronounce some of their plurals differently. The pronunciations I give here are simply the ones listed in dictionaries.)  The plural form "stigmata" is probably most common in religious or theological contexts (where it refers to the wounds of Christ), so at first I wondered if the penultimate stress was supposed to be closer to the original Greek pronunciation, but according to , the stress is on the antepenult in Greek as well.  So, what's up with this? Did the stress perhaps change in Latin over time, is this a tradition of Greek accentuation that I'm not familiar with, is this a simple matter of ignorance of the original position of the stress that has now become entrenched with time and usage, or is this somehow explainable by established English stress patterns? (For example, do English speakers have some natural preference for a penultimate stress on polysyllabic words?)  If nobody knows of a reason, I suppose I can just put it down to people encountering the word mainly in text, not knowing which syllable to stress, and choosing the penult because it sounds better to them.  (I asked this question a while back on , but nobody knew of any reason.) At least two questions (, ) on this site indicate that in more than a few isolated cases at least, letters of recommendation are in fact written by the applicant and only signed off (or perhaps rephrased somewhat) by the recommender, who would actually be responsible for writing the letter.  Is there any evidence about the prevalence of this practice that goes beyond anecdotes? I realize that cross-country (cultural) difference may play a role. Cross-reference packages: which to use, which conflict? Inspired by my earlier question , here is another similar question.  There are many different packages for making cross references. Among them , , , , … The  package defines its own cross-referencing command for theorems…  Which collection of packages provides which kind of functionality, and which packages cause conflicts with each other? Is $\int \frac{1}{2x} \, dx $ equal to $\frac{\ln|2x|}{2}+ C$ or $\frac{\ln|x|}{2}+ C$ Reasoning for $\frac{\ln|x|}{2}+ C$ :  $$\int  \frac{1}{(2x)}  \, dx = \frac{\ln|2x|}{2}+ C$$   Check: By taking derivative we get $\frac{1}{x}$  Reasoning for $\frac{\ln|x|}{2}+ C$ :  $$\int  \frac{1}{2x}  \, dx = \frac{1}{2}\int  \frac{1}{x}  \, dx =\frac{\ln|x|}{2}+ C$$  Check: By taking derivative we get $\frac{1}{x}$  Question: Is  $\int  \frac{1}{2x}  \, dx $ equal to $\frac{\ln|2x|}{2}+ C$ or $\frac{\ln|x|}{2}+ C$? I have created multiple objects, while testing I applied a drop shadow style on one object and its looking very good. Now I want to apply the same style to all other objects (around 20). Is there any way like global color to create a style once and apply to other objects with single click automatically?  Or I have to apply that drop shadow effect on each object one by one manually? Cheap/free tool to view/convert Canon CR2 RAW format photo files on Windows? Align cell height of the tabularx rows The following latex code prints rows one at a time. However all the cells of the rows don't come out aligned. How can I fix it.   \documentclass{beamer}     \usepackage{tabularx}    \begin{document}  \begin{frame}{}  \begin{tabularx}{3.50in}{lXX}           \hline           &amp; Observation &amp; Conclusion \\           \hline             \uncover&lt;2-&gt;{1.} &amp; \uncover&lt;2-&gt;{Observation 1 } &amp; \uncover&lt;2-&gt;{Conclusion 1} \\   \uncover&lt;3-&gt;{2.} &amp; \uncover&lt;3-&gt;{Observation 2} &amp; \uncover&lt;3-&gt;{Conclusion 2} \\           \end{tabularx}      \end{frame}   \end{document}   The output looks as follows :    As we can see cells in first column do not align with the rest of the rows. Will appreciate any input as to how to fix this. Find all $x$ such that $x^6 = (x+1)^6$.