How to calculate the geographic position of an object in sky (Point B)(like an aircraft) from Home Point (Point A) based on only four variables:  Lattitude and Longitude at Home Point, Azimuth at point B, Distance from home point to point B and height of point B?
I would like to know how to find a set of coordinates on a small circle some distance from another point.   For example, lets say A = (39.73, -104.98) #Denver  B = (39.83, -106.06) #point approximately 50 nautical miles away from A along the great circle track to C  C = (40.75, -111.88) #Salt Lake City, approximately 323 nautical miles away from A  How do I get the set of orange coordinates when I don't know the angle but I do know the cross track distance?  For concreteness, lets say the outer points near B have a cross track distance of +- 30 nautical miles and the inner points have a cross track of +- 15nm.  And the points near C have a cross track of +- 25 nm.  Also I have an initial bearing from A to C of -1.34 #radians
As my question says,   $$\frac 1{1.2.3}+\frac 1{2.3.4}+\frac 1{3.4.5}+...$$  As far as $\frac 1{1.2}+\frac 1{2.3}+\frac 1{3.4}+...$ is concerned, we can write it as $\frac 1{n-1} - \frac 1{n}$ What can we do here? In hearthstone, you receive one quest per day, barring unique quests. What I'm wondering is when exactly does a new day start? I assume it's at a specific global time, so I'm looking for a time in GMT or UTC.  I did find out you need to exit the game and come back to receive new quests, but I'm hoping someone actually knows when i have to do that. How and why do normalization and feature scaling work? I see that lots of machine learning algorithms work better with mean cancellation and covariance equalization. For example, Neural Networks tend to converge faster, and K-Means generally gives better clustering with pre-processed features. I do not see the intuition behind these pre-processing steps lead to improved performance. Can someone explain this me? What is the correct name to use with /give for Lapis Lazuli? In Minecraft, when cheats are enabled you can give yourself items using the command /give [user] [item] [count], e.g. /give user45623 dirt 32. What is the item name to use for Lapis Lazuli? I've tried lapis_lazuli, lapis, lazuli, dye4, and dye_4, but it's none of those. Choosing between $z$-test and $t$-test Background: I'm giving a presentation to colleagues at work on hypothesis testing, and understand most of it fine but there's one aspect that I'm tying myself up in knots trying to understand as well as explain it to others.  This is what I think I know (please correct if wrong!)   Statistics that would be normal if variance was known, follow a $t$-distribution if the variance is unknown CLT (Central Limit Theorem): The sampling distribution of the sample mean is approximately normal for sufficiently large $n$ (could be $30$, could be up to $300$ for highly skewed distributions) The $t$-distribution can be considered Normal for degrees of freedom $&gt; 30$   You use the $z$-test if:   Population normal and variance known (for any sample size) Population normal, variance unknown and $n&gt;30$ (due to CLT) Population binomial, $np&gt;10$, $nq&gt;10$   You use the $t$-test if:   Population normal, variance unknown and $n&lt;30$ No knowledge about population or variance and $n&lt;30$, but sample data looks normal / passes tests etc so population can be assumed normal   So I'm left with:    For samples $&gt;30$ and $&lt;\approx 300$(?), no knowledge about population and variance known / unknown.   So my questions are:   At what sample size can you assume (where no knowledge about population distribution or variance) that the sampling distribution of the mean is normal (i.e. CLT has kicked in) when the sampling distribution looks non-normal? I know that some distributions need $n&gt;300$, but some resources seem to say use the $z$-test whenever $n&gt;30$... For the cases I'm unsure about, I presume I look at the data for normality. Now, if the sample data does looks normal do I use the $z$-test (since assume population normal, and since $n&gt;30$)? What about where the sample data for cases I'm uncertain about don't look normal? Are there any circumstances where you'd still use a $t$-test or $z$-test or do you always look to transform / use non-parametric tests? I know that, due to CLT, at some value of $n$ the sampling distribution of the mean will approximate to normal but the sample data won't tell me what that value of $n$ is; the sample data could be non-normal whilst the sample mean follows a normal / $t$.  Are there cases where you'd be transforming / using a non-parametric test when in fact the sampling distribution of the mean was normal / $t$ but you couldn't tell? Steam Bollywood Achievement:     As Gandhi, win a cultural victory with   3 or fewer cities in your empire.   I wish to do this achievement on a Pangaea Standard map size or larger and on Prince difficulty or higher,  What tactics do people recommend to achieve this. Any tips on the use of, Social Policies, Wonders, Diplomacy, City States and Military. Excel VBA code to turn a row with a variable number of columns into fixed-length rows I would like to change this:  Filer   ShareName       IPAddress1    IPpaddres2    IPAddress2    ... ... .... ServerA /share1/tools   192.168.1.52  192.168.1.65  192.168.1.158 ServerA /share/library  192.168.1.65  192.168.1.61  192.168.1.155 ServerB /share/tools    192.168.1.158 192.168.1.159 ServerD /share/misc     192.168.1.7 .. ... ..... .......   To this, in a new worksheet:  Filer   ShareName       IPAddress ServerA /share1/tools   192.168.1.52 ServerA /share1/tools   192.168.1.65 ServerA /share1/tools   192.168.1.158 ServerA /share/library  192.168.1.65  ServerA /share/library  192.168.1.61  ServerA /share/library  192.168.1.155 ServerB ... ... ServerD ... ... .. ... ..... ....... One frequent aspect of pdflatex output that could be improved is to what extent one can select text output from the generated pdf-file and copy-and-paste it. This is essentially an issue of having the right output encoding. There are at least two important aspects to this:   In the ideal case, Unicode would be the output encoding. Ligature glyphs (such as ﬁ) are ideally de-ligated in the output (here: "fi").   It seems that output encodings are specified through the fontenc package. What is the range of possible output encodings, and most importantly: Is there a way to specify a Unicode output encoding and one that deals with ligatures in the intended way?  (Note: It is important to distinguish output from input encodings. How to use different input encodings in LaTeX has been documented widely. My understanding is that this is best handled by the inputenx package, as it supersedes the inputenc package.)    Quick guide to the solutions: The information in the answers and answer threads is a bit distributed, so here the short summary: one approach is to use \input glyphtounicode together with \pdfgentounicode=1; the other approach is to use cmap/mmap.  Addendum: Sometimes one will need to load the package accsupp and enclose one's macro definition in \BeginAccSupp{method=hex,unicode,ActualText=&lt;codepoint&gt;}[...]\EndAccSupp{} to generate a specific code point. See the caveat about non-BMP code points  and the fix (starting from accsupp version v0.4, 2012/11/18) , which provides the new unichar package option. Proving $\sum_{k=0}^n(-1)^k\binom nk=0$ I've seen a couple other questions with this error message but it seemed that the host and ip in question were ones the OP knew. These two are unrelated to my server.  Where and why is postfix generating this error?     Jul 24 17:42:14 email postfix/smtpd[32277]: warning: hostname kimtake.respectedopinion.com does not resolve to address 62.210.28.114   Jul 24 17:42:14 email postfix/smtpd[32277]: connect from unknown[62.210.28.114]   Jul 24 17:42:14 email postfix/smtpd[32277]: disconnect from unknown[62.210.28.114] I am trying to do a clean install of the octave3.2 package.   To do this, I removed it, then tried to reinstall it.   When I reinstalled, an error occurred. It could be a bug in the package, but I want to make sure I have everything removed so that I can do a clean install.  Is it enough to do this?  sudo apt-get --purge remove octave3.2 Trailing Sum Query Detail in bijection between Inn(G) and G/Z(G)? Print escaped representation of a str What do *args and **kwargs mean? What exactly do *args and **kwargs mean?  According to the Python documentation, from what it seems, it passes in a tuple of arguments.  def foo(hello, *args):     print hello      for each in args:         print each  if __name__ == '__main__':     foo("LOVE", ["lol", "lololol"])   This prints out:  LOVE ['lol', 'lololol']   How do you effectively use them? Why a subspace of a vector space is useful $ a+b+c+d=6 , a^2+b^2+c^2+d^2=12$ $\implies$ $ 36 \leq 4(a^3+b^3+c^3+d^3)-(a^4+b^4+c^4+d^4) \leq48 $ Let $a , b, c, d$ be real numbers such that $$ a+b+c+d=6 \\ a^2+b^2+c^2+d^2=12$$  How do we prove that $$ 36 \space \leq\space 4(a^3+b^3+c^3+d^3)-(a^4+b^4+c^4+d^4) \space\leq48\space$$ ? How to insert text into a root-owned file using sudo? Can I have multiple background images using CSS? Thunderbolt 2 docks have been quite expensive and they will be obsolete once I purchase the new Macbooks with USB-C ports. I currently use a 2014 MacBook Pro with Thunderbolt 2 ports, and I want to futureproof my purchase by acquiring a cheaper USB-C dock now.  The cheapest Thunderbolt 2 dock costs around $200 while USB-C docks cost around $30. Being able to use a USB-C dock with older Thunderbolt 2 Macbook Pros would not only be cheaper but also allows me to use the same USB-C dock if I decided to upgrade to a future Macbook.  For that to work I need a Thunderbolt 2 (male) to USB-C female adaptor, after some searching it doesn't seem to exist. Is there a reason why something like this hasn't been made? Or is the USB-C specification designed such that it is impossible? (hence businesses can still continue to sell expensive Thunderbolt 2 docks...)  I will accept an answer that meets the following requirements:   If there is such an adapter please give a link and some form of evidence that these would have 100% compatibility with USB-C docks. If there is no such adapter please explain:   Is it impossible to produce? If not, why hasn't a vendor created one yet? I've explained that its a better financial investment than buying a TB2 dock... surely there's a market for those still using TB2 MBPs wanting to upgrade in the next couple of years. Not only docks but it would open a gateway to cheaper alternatives to those hideously expensive TB2 peripherals.