tan additions formula expressions only representing with tan This is expression for $\tan(a+b+y)$  $$\frac{\tan(a)+\tan(b)+\tan(y)−\tan(a)\tan(b)\tan(y)}{1− \tan(a)\tan(b)−\tan(a)\tan(y)−\tan(b)\tan(y)}$$  I want to represent this with only $\tan(a)$, $\tan(b)$ and $\tan(y)$.  Clearly,I want to replace $1$ with tan functions of these three variables.  I need this answer because thie is from GelfAndSaul Trigonometry Book questions.Pg-145
Finding an expression for $\tan (a+ b + y)$ which involves only $\tan a, \tan b,$ and $\tan y$. How to find this ?   I'm stuck at $1$ and how to $1$ to change the tangent associated with a,b or c.  I meant this ,everybody.  $\frac{tan(a)+tan(b)+tan(y)−tan(a)tan(b)tan(y)}{1−tan(a)tan(b)−tan(a)tan(y)−tan(b)tan(y)}$
How did they dispose old Joe's wife's body in the movie Looper (2012)? The reason given in the movie Looper for sending targets to the past is that it is difficult to dispose bodies.  From ,     Thirty years into the future in 2074, time travel is invented, but is   immediately outlawed. However, because by that point tracking   technology has rendered it nearly impossible to dispose of bodies   secretly, crime bosses turn to time travel to send their targets to   the past to be killed using "loopers": hired guns paid in silver to   kill whoever is sent to them.   When trying to capture old Joe, they kill his wife. So how did they dispose the body of his wife? Or is it difficult to dispose bodies only in US and not in China? And they came for old Joe only because the Rainmaker wanted to close the loops?  Could someone explain? What am I missing? Granted there are already quite a few badges for community service on this site, I thought, how about some more!  The theme is merging enthusiast/fanatic with suffrage/vox populi. Something like this (names and numbers open to suggestions)  Enthusiastic Voter - Voted 20 times per day consecutively for 30 days ????? - Voted 30 times per day consecutively for 50 days Fanatic Vox - Use the maximum number of 40 votes consecutively for 100 days Use (or non-use) of articles before abstract nouns Array of Matrices in MATLAB I am looking for a way to store a large variable number of matrixes in an array in MATLAB.  Are there any ways to achieve this?  Example:  for i: 1:unknown   myArray(i) = zeros(500,800); end   Where unknown is the varied length of the array, I can revise with additional info if needed.  Update: Performance is the main reason I am trying to accomplish this.  I had it before where it would grab the data as a single matrix, show it in real time and then proceed to process the next set of data.  I attempted it using multidimensional arrays as suggested below by Rocco, however my data is so large that I ran out of Memory, I might have to look into another alternative for my case.  Will update as I attempt other suggestions.  Update 2:  Thank you all for suggestions, however I should have specified beforehand, precision AND speed are both an integral factor here, I may have to look into going back to my original method before trying 3-d arrays and re-evaluate the method for importing the data. Expand a random range from 1–5 to 1–7 Given a function which produces a random integer in the range 1 to 5, write a function which produces a random integer in the range 1 to 7.   What is a simple solution? What is an effective solution to reduce memory usage or run on a slower CPU? Legend in tikzpicture Photoelectric effect intensity I understand the PE effect quite well but I'm failing to understand one thing. Intensity is the amount of energy per second incident to a given area.   So can you can increase the intensity by either increasing the electrical energy or making the area smaller? By increasing the electrical energy, what exactly is happening?  I assume that by increasing intensity you are increasing the number of photons incident to an area of the metal thus increasing the rate of photoelectric emission. But why doesn't increasing intensity via more electrical power lead to greater energy of the electrons, if by increasing intensity you are increasing the energy of the incident waves?  I understand the results but I'm trying to understand why the intensity works the way it is thanks Question:   Answer:   The question was closed at 11:57:57 (according to the hover-over-"x-mins-ago" bar) and the answer was posted at 12:16:35. It's a fairly lengthy answer, so it's possible that it was started to be written before it was closed but I swear I've started to answer a question then I got a banner along the top saying "this question has been closed" and the answer was no longer post-able. I have to find an easy ring which this ring is isomorphic with.  I can prove that $5 = (2+i)(2-i) \in (2+i)$ but this doesn't help me further.  My book says the answer is $\mathbb {Z_5} $ NSdate Assuming wrong time zone Strange problem with BibTeX sorting I want to be able to calculate the confidence interval from the estimated coefficient and respective standard errors.  I have a linear regression model which can be summarized (in R):  summary(fit1)  Call: lm(formula = bwt ~ height + weight + parity, data = data)  Residuals:     Min      1Q  Median      3Q     Max  -66.913 -10.624   0.991  10.979  55.621   Coefficients:             Estimate Std. Error t value Pr(&gt;|t|)     (Intercept) 31.19217   13.56879   2.299   0.0217 *   height       1.24964    0.23083   5.414 7.48e-08 *** weight       0.06781    0.02823   2.402   0.0164 *   parity1     -1.83309    1.19838  -1.530   0.1264     --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Residual standard error: 17.9 on 1170 degrees of freedom Multiple R-squared:  0.04898,   Adjusted R-squared:  0.04654  F-statistic: 20.08 on 3 and 1170 DF,  p-value: 1.071e-12   With this model I can calculate the respective confidence intervals:  &gt; confint(fit1)                   2.5 %     97.5 % (Intercept)  4.57029503 57.8140351 height       0.79676227  1.7025207 weight       0.01243198  0.1231932 parity1     -4.18429933  0.5181151   I would expect the intervals of the predictor height to be given by  $$ 1.24964 \pm (1.96*0.23083) = [0.7972132,1.702067] $$  where 1.24964 is the estimated value for the coefficient and 0.23083 is the standard error for this coefficient. The numbers are close but not quite the same.  What am I doing wrong? Shell programming temp=$1 vs temp=1 What's the difference between temp=$1 and temp=1? Why do I need the dollar sign?  For example:   #!/bin/bash  temp=$1 cell=$((($temp-32)*5/9))  echo $cell Why does my item name not show up in 1.13? Does Airplane Mode allow GPS location to pass through? This is what I saw when my plane was taxing to the runway at CDG:     Airplane mode was on and all other transmissions (except Location), including WiFi, mobile data, NFC and Bluetooth were off.  Location was not manually turned on by me, after I enabled Airplane Mode. It remained turned on.  What am I missing? Is GPS now so widely accepted on-board planes that Android changed its configuration to let this kind of signal/communication to pass through Airplane mode "block"?  I believe that  isn't a duplicate, because at that time (2016) Location was generally "included" in Airplane mode and was turned off by enabling it. Meaning of backtick in floating-point literal The following example must be compiled with XeLaTeX to reproduce the issue.  % arara: xelatex \documentclass{article} \usepackage{fontawesome} \begin{document} Text Text \faMobilePhone\ Text Text \end{document}   Normally I am using TeXworks to compile and view the output. With the internal viewer I am getting the desired result. The following image demonstrates it:    However if I open the pdf with Preview (viewer of Mac) the scaling of the icon fails.     If I open the pdf file with Adobe Acrobat Reader the icon is still scaled correctly. If I print the page my printer is also not able to scale the icons correctly.   If I use LuaLaTeX everything seems to work correctly.   Can you reproduce the issue and do you know a solution? How can I simulate a slow machine in a VM? Modified files in a git branch are spilling over into another branch How to run Ubuntu without GUI in Virtual Box?