I've been given this question for homework, and I've made a bit of progress but I'm not sure what to do next. I called the intersection of the two lines $P$, and let $BP=x$ and $FP=y$. Thus, $PG=6-y$ and $PC=14-x$. I then used Power of a Point to get that $y=\frac{7x}{3}-\frac{40}{3}$, but I don't know where to go from here.
On a plane, there are two congruent circles, $O_1, O_2$. One line intersects $O _1$ and A and B and $O_2$ at C and D such that AB=BC=CD=14. Another line intersects $O _1$ and E and F and $O_2$ at G and H such that EF=FG=GH=6. What is the radius of the circle.   The configuration was hard to draw. . You can reflect the lines over the centers, but it is still the same. Cleary, $\widehat{AB}=\widehat{CD}$ and $\widehat{EF}=\widehat{GH}$. I have no idea how to proceed.
Necromancy In Harry Potter How is Necromancy accomplished in the Harry Potter universe?  I thought that people cannot be raised from the dead in Harry Potter.  Were bodies just use as puppets that can only do simple tasks, for instance when Dumbledore and Harry were getting the locket, the  were there to guard the locket.  Also, besides Inferi were there any Zombies in Harry Potter? My Notes has Title-Task2 and Content is "Talk to customers"  When I run following query:  SELECT Title,Content FROM ContentNote  Output is:  ('Title', 'Task2'), ('Content','/services/data/v42.0/sobjects/ContentNote/0692x000000WFDKAA4/Content')])]  how to get my actual content from this? In iOS 8.4.1, if a caller who has 6 numbers, calls you and you see a missed call. Then, clicking the "i" symbol next to the missed call showed you all the 6 numbers of the caller and the number from which he called, was indicated with blue. This helped in knowing exactly what number he called me from and I could call back on the same number.  iOS 9.0.1 call log does not indicate the number the caller called from with blue (if the caller has more than one number). So, it becomes impossible to call the person back on the same number.  This was one very important feature that made iOS 8 very useful. Apple has taken away a very important feature. Converting LiDAR files from LAZ to LAS format I'm trying to convert LiDAR files from the LAZ format (the compressed version) into LAS (the uncompressed version) using  software.   However, I am not really sure how it works. I created a new output folder as I entered in the app interface, but it is totally empty.  I also had tried the following code in the command prompt window:   D:\LiDAR\Laszip\laszip.exe *.laz    and got a message saying 'no input specified'.  In my folder, there are about 100-ish.laz files as well as one imu.laz. Any suggestions? I'm using Ubuntu 16.04 and there's no fglrx! creating a diagonal matrix with a variable amount of parameters I have the following annoying problem with Excel 2010. I use Conditional formatting to apply bold formatting to each line of the spreadsheet that meets a condition expressed by a formula. In the "applies to", I write =$A$2:$Q$149, which is the current extent of my spreadsheet. But I want this range to grow with my spreadsheet, i.e., I want the formatting to permanently apply to the whole spreadsheet. Regularly, my "applies to" field is transformed into a complex range, that selects most lines of spreadsheet, but not all, like =$A$2:$Q$138;$A$140:$Q$147. Have you ever encountered such a problem? Is there a solution? What are the advantages and limitations of dynamic type languages compared to static type languages?  See also:  (a far more argumentative thread...) I am a software engineer but try to keep up with maths as I really enjoyed the subject at school. I just saw a great TED talk:   The talk states that the current largest known prime is $2^{57885161}-1$  This got me thinking - how does one actually prove whether a number this large is prime or not?  Is it just done by brute force via a computer algorithm or are there any well known mathematical techniques for doing so?  I would be really grateful for any pointers as I am eager to learn about these techniques (if they exist). Why is the edit button disabled? Taylor Expansion $\log(\frac{1+z}{1-z})$ Taylor Expansion of $\log(\frac{1+z}{1-z})$ around $z=0$  But $\log(1+z)=\sum_{n=1}^{\infty}(-1)^{n+1}\frac{z^n}{n}$  How can I continue from here? Traditional statistical tests, like the two sample t-test, focus on trying to eliminate the hypothesis that there is no difference between a function of two independent samples. Then, we choose a confidence level and say that if the difference of means is beyond the 95% level, we can reject the null hypothesis. If not, we "can't reject the null hypothesis". This seems to imply that we can't accept it either. Does it mean we're not sure if the null hypothesis is true?   Now, I want to design a test where my hypothesis is that a function of two samples is the same (which is the opposite of traditional statistics tests where the hypothesis is that the two samples are different). So, my null hypothesis becomes that the two samples are different. How should I design such a test? Will it be as simple as saying that if the p-value is lesser than 5% we can accept the hypothesis that there is no significant difference? What is "angle of view" in photography? I read on the :     Focal-length determines the angle-of-view seen through a lens for a   given sensor-size. With a full-frame sensor a lens gives the same   angle-of-view as it would on a 35mm film camera. With a smaller   sensor, the angle-of-view becomes smaller. The crop-factor, also   called FLM, is the ratio representing the difference in equivalent   focal-lengths. So a 150mm on a full-frame DSLR such as the Nikon D700   gives the same angle-of-view as a 100mm on a D7000 since its FLM is   1.5X.      Short focal-lengths show a greater angle-of-view compared to longer   ones. [...]   In layman's terms, what is angle-of-view? Is it the same as focal length? If not, how is it different? How is it used? Why do I need to know about it? Sensor for ultralow (to -85°C) freezer monitor text processing rows to columns for a block I have a file containing lists on Solaris:  List A hi hello hw r u  List B Hi Yes  List C Hello   I need to transpose the lists as shown below:  List A    List B    List C hi        Hi        Hello hello     Yes hw r u   How can I do this on Solaris? Display Custom Fields in a SharePoint 2010 Content Query Web Part Using SharePoint 2010, Having Custom List With 4 Columns, Now I am Using Content Query Web-part To Display List Data ,But Currently It Display Only First Column, SO How to Display Custom Fields in a SharePoint 2010 Content By Query Web Part Is the set of real matrices diagonalizable in $\mathcal M_n(C)$ dense in the set of all companion matrices? Let $\mathcal E=\{A \in \mathcal M_n(\mathbb R): A \text{ is of companion form} \}$. That is, $A$ has the following form \begin{align*} A=\begin{pmatrix}  0 &amp; \cdots &amp; 0&amp; -a_{0} \\  1 &amp; \cdots &amp; 0 &amp; -a_{1}\\ \vdots &amp;\ddots &amp; \vdots &amp;\vdots \\ 0 &amp;\cdots &amp; 1 &amp; -a_{n-1} \end{pmatrix}. \end{align*} Let $\mathcal D = \{A \in \mathcal M_n(\mathbb R): A \text{ is diagonalizable in $\mathcal M_n(\mathbb C)$}\}$. We know $\mathcal D$ is dense in $\mathcal M_n(\mathbb R)$. I am wondering whether $\mathcal E \cap \mathcal D$ is dense in $\mathcal E$. The set $\mathcal E$ is closed. It is not clear to me whether this statement is true. I have a site with Google Maps on most of the pages. When inspecting content keywords in Google Webmaster tools, content keywords identified by Google-bot for the site include "imagery", "sorry" and "here". These turn out to be part of an error message returned by Google Maps: "Sorry, we have no imagery here". I cannot reproduce this error with normal clients, nor does "fetch as Google" show it. The problem is presumably that Google-bot tries to execute some of the Google Maps Javascript but then shoots itself on the foot and records the error message.  A  shows that this problem is endemic to sites across the internet, including Yelp and many others.  I'd like to convince Google that my site is not about imagery and being sorry, but I'd also like to keep the maps in place. I guess one option would be to transition to , but that's not a great alternative.  There's some , no resolution. How to create bootable ISO from an installed OS? Say I have two systems A and B.  I have installed Ubuntu 12.04 on system A and need same set of settings in system B, for which I am thinking to make a bootable iso from System A(creating as a backup). so that I can make Live USB from the generated iso and boot the System B which will be now the replica of System A.  Could you please tell is there any method or tool in doing this process? What is "Best Practice" For Comparing Two Instances of a Reference Type? I came across this recently, up until now I have been happily overriding the equality operator (==) and/or Equals method in order to see if two references types actually contained the same data (i.e. two different instances that look the same). I have been using this even more since I have been getting more in to automated testing (comparing reference/expected data against that returned). While looking over some of the  I came across an  that advises against it. Now I understand why the article is saying this (because they are not the same instance) but it does not answer the question:  What is the best way to compare two reference types? Should we implement ? (I have also seen mention that this should be reserved for value types only). Is there some interface I don't know about? Should we just roll our own?!  Many Thanks ^_^ Update Looks like I had mis-read some of the documentation (it's been a long day) and overriding  may be the way to go..  If you are implementing reference types, you should consider overriding the Equals method on a reference type if your type looks like a base type such as a Point, String, BigNumber, and so on. Most reference types should not overload the equality operator, even if they override Equals. However, if you are implementing a reference type that is intended to have value semantics, such as a complex number type, you should override the equality operator.