How to Calculate Point on an Arc (Given: Center, Arc Endpoints, Direction, and Distance along the Arc)?
How to find an end point of an arc given another end point, radius, and arc direction?
Can wizards create their own spells? In the Harry Potter series, are wizards capable of creating their own spells, or are they limited to the spells that they're taught/learn?  I seem to remember something about Snape creating sectumsempra, but I'm not sure if that really is the case. How are percentiles calculated in Careers 2.0? I noticed that a percentile is placed at the top of my resume in Careers 2.0.    How are these percentiles calculated? Is there a certain threshold you need to be over in order for it to be displayed? I often have to write up reports based on the analysis of some data. I use R to analyse the data and export tables, figures, and text. This is then included into a LaTeX document either using input or Sweave ().  However, when I collaborate with others, I sometimes need to provide a document in Open Office / MS Word format.  Question:  Thus, assume the simplest scenario   I have a LaTeX document with text, tables, and figures I need to export this reliably into Open Office or MS Word format: this includes mathematical formulas, table formatting, and quality figures) I don't need to go back from MS Word to LaTeX   What is a reliable, efficient, and preferably free process?  Initial Thoughts:   Export to HTML,  LaTeX - LyX - ODF Use odfWeave  that deals with some specific issues associated with LaTeX to Open Office conversion    I was hoping that there is an expert out there who has worked out a good system already. Multiple WHERE clause in Linq How can I replace spaces with new lines on an input like:  /path/to/file /path/to/file2 /path/to/file3 /path/to/file4 /path/to/file5 etc...  To obtain the following:  /path/to/file /path/to/file2 /path/to/file3 /path/to/file4 /path/to/file5   Note  I'm posting this question to help other users, it was not easy to find a useful answer on UNIX SE until I started to type this question. After that I found the following:  Related question How to use custom icons with mapKit framework? Will Canadian citizens be denied entry to Canada during COVID-19 border closure? examples:         Gift (German) = poison   poisson (French) = fish   embarazada (Spanish) = pregnant   sauce (Spanish) = willow   triviale (Italian) = vulgar   parentes (Portuguese) = relatives   slim (Dutch) = smart Generate the smallest $\sigma$-algebra containing a given family of sets My teacher gave me an example of performing the subject:     Example      Let $\Omega = \Bbb R$ and $\mathcal R = \{(-\infty,-1),(1,+\infty)\}$.   Then $\sigma(\mathcal R) = \{\emptyset, \Bbb R, (-\infty,-1),  (1,+\infty), [-1, \infty), (-\infty,1],  (-\infty,-1)\cup(1,+\infty),[-1,1]\}$.   There was a different example, where she also generated the smallest  $\sigma$-algebra for the family of sets $\mathcal A = \{A,B\} \subset 2^\Omega$ in the same way: $\sigma(\mathcal R) =  \{\emptyset, \Omega, A, B, A^C,B^C,A\cup B, (A\cup B)^C\}$.   I certainly understand why $\emptyset$, $\Omega $ and a family of sets itself are there, and I certainly know that $\sigma$-algebra is closed under the operations of complement and union. What I don't understand about the other elements of generated $\sigma$-algebras: why we are taking exactly them? Does this work in a general case? Remove suggested apps option in iOS 10 As far as I can tell, suggested apps show themselves based on location.  There are two places where these suggested apps show themselves to me:   At the bottom left of the multitask screen when I double press the home button At the bottom left of the lock screen    article describes how to get rid of the small app icon appearing in the bottom left. However, this method is for iOS 8, and I am now on iOS 10, where I am unable to find iTunes and App Store > Suggested Apps.   How can I get rid of these (in my opinion) annoying little things? What are the increased possibilities (if any) of being able to crack a private key given the following:   The associated bitcoin (ECDSA Secp256k1-based) public key is known. The private key has been used to generate a public key from a different ECDSA curve and that public key is also known. It is known that the two public keys are derived from the same private key. It is known which ECDSA curves were used to generate the public keys. It is known which ECDSA curve was used to generate which public key.   Does it make any more difference if there is data that is known to have been signed by the private key and the signature(s) are known and the raw data is known?  EDIT: I should have pointed out that the conditions are ANDed, I.e. All conditions are known. Sorry, I should have been clearer the first time. I recently re-watched Contact for the first time since my childhood, and while I thoroughly enjoyed it, I realized that there was something I'd never understood: why couldn't they corroborate Ellie's account of her journey?  As far as I could tell, the pod fell harmlessly through the machine.  That is, it didn't break anything, and the machine wasn't destroyed.  I don't recall any dialogue about circuits being fried or the system shutting down, so presumably it wouldn't be hard to simply hoist the pod up and go again.  I imagine the energy draw was substantial on the local Japanese power grid, but given the amount of effort and money already invested in the machine, surely "Round 2" wasn't out of the question?  I mean, they almost certainly expected that this machine would get more than one good use out of it, anyway!  So given Ellie's vehement insistence that the machine had worked, the public nature of the controversy surrounding her testimony, and the government's (secret) findings that her device had recorded 18 hours of static, why wasn't it the obvious choice to have someone else suiting up the next day, ready to drop through the machine and corroborate her story? I don't really remember the plot but I think the a couple of alien girls (look human) crash land on Earth and are helped by human boy (18-19 ish). They get back to their ship but the older girl, with white hair, decides to stay on Earth to be with the boy.  At the beginning of the TV movie the boy wakes up and uses a ham radio and then goes to work on a ranch/farm(?).  I think it might have been one of these old Disney Sunday night movies. startsWith() and endsWith() functions in PHP Why is my Canon 300D not switching on despite changing both batteries and the CF card? Reflection of a line in a plane The line $l_1$ has the equation $r=(6i+2-2k)+\lambda(4i+5j-k)$ and the plane $\pi_1$: $2x-y+4z=4$, the line $l_2$ is the reflection of $l_1$ in the plane $\pi_1$. Find the exact vector equation of line $l_2$   So the line intersects the plane when $\lambda=-2$, giving the point $(-2,-8,0)$ which will be common on $l_1$ and $l_2$. But I am unsure on how to find the direction vector for $l_2$. Any help would be appreciated. How to find the kth largest element in an unsorted array of length n in O(n)? I believe there's a way to find the kth largest element in an unsorted array of length n in O(n).  Or perhaps it's "expected" O(n) or something.  How can we do this? What characters do I need to escape when using sed in a sh script? Take the following script:  #!/bin/sh sed 's/(127\.0\.1\.1)\s/\1/' [some file]   If I try to run this in sh (dash here), it'll fail because of the parentheses, which need to be escaped. But I don't need to escape the backslashes themselves (between the octets, or in the \s or \1). What's the rule here? What about when I need to use {...} or [...]? Is there a list of what I do and don't need to escape? Unable to see anything after importing .obj file I try to import .obj files from this project:  - the files contain Polygon Mesh Data.  When I import the obj file into blender, the outliner shows a new mesh added, but nothing is visible in the 3D viewport:      Any help will be appreciated. How can I install Gimp 2.8's help documentation on Ubuntu 12.04?