Why boil sugar for lemonade? I've started making home lemonade recently and all the recipes boil about one cup of sugar in one cup of water. I never questioned that until my father saw the process and asked why don't I just add water and sugar to lemon juice or add boiling water to the pitcher with lemon juice and sugar and I couldn't really tell, I just knew the sweetness was greater in my experience.
Is lemonade better when made with simple syrup? On a hot summer day and with a basketful of lemons I often want a nice cold glass of lemonade. A lot of recipes suggest making lemonade with simple syrup, which requires cooking, whereas other recipes just have stirred-in sugar.  What exactly are the benefits of making lemonade (or limeade) with simple syrup versus just stirring in sugar?
Making hats (and other accents) bold I've been typesetting some equations, and I've found that the default behavior accents like \hat, \bar, \tilde, etc. makes a rather small and easily-missed mark. Is there some way to make the accents stand out more? In particular, is there any way to make them appear in bold (without affecting the letter they are over)? Search and replace multiple values with multiple/different values in PHP5? How can native English speakers read an unknown word correctly? Are there either examples, or a mention of this having happened, of students permanently transferring from one magical school to another in Potterverse?  Canon only please (books/JKR/Pottermore).  Please note that I am only asking about transfers, e.g. you must already be studying in one school. Therefore an example of Malfoys considering sending Draco to Durmstrang is not in scope, since that happened before he attended Hogwarts. Also, guest-studying during Tri-Wizard doesn't count as it wasn't permanent.  Also, if the answer is a "no", please provide evidence (other than "well I read the books before and I don't remember a single case like that", unless you have eidetic memory) from entire canon. Is it possible to use a laptop as an external monitor? I need to create a multi-monitor setup for my desktop computer but I have no additional monitors with me right now, aside from my laptop. Is it possible to use my laptop screen as an external monitor?  Note that I am not trying to connect a monitor to my laptop, rather, I am trying to connect my laptop screen to a desktop video card (if this is possible). Lightning Web Component embedded in Visualforce Page via Aura Component and App not displaying I am writing a lightning web component that is going to be used in Salesforce Classic, Lightning Experience and an Employee Community. It does not HAVE to be a lightning web component - I could use a traditional Aura Lightning Component if I must.   However, what I am finding is that the visualforce page does not work, even when the lwc component is embedded in a aura component that is then used with Lightning Components for Visualforce. I can see from the documentation  that using a lwc directly from within visualforce is not supported, but I was under the impression that it may work if wrapped in an aura component.   My question then is this:  Has anyone had success having a lwc wrapped in an aura component display successfully within Visualforce? Or is this completely unsupported behaviour? Retrieving the last record in each group - MySQL Proof of triangle inequality I understand intuitively that this is true, but I'm embarrassed to say I'm having a hard time constructing a rigorous proof that $|a+b| \leq |a|+|b|$. Any help would be appreciated :) What is the purpose of the bin directory? What are some examples? How do you kill a java.lang.Thread in Java? barchart with pgfplot - missing bar I am using PGFplot to make a barchart. There are 4 entries in my csv file and unfortunately I have only 3 bars in my figure.   my LaTeX code:  \begin{figure}     \centering     \begin{tikzpicture}          \begin{axis}[             x tick label style={/pgf/number format/1000 sep=},                 xlabel=Sequence,             ylabel=Heigth,                 ymin=0.7,             enlargelimits=0.05,             legend style={at={(0.5,-0.15)},                 anchor=north,legend columns=-1},             ybar interval=0.7,             width=\textwidth,             ]             \addplot table [col sep=comma,trim cells=true,y=height] {numericaltests/data/test.csv};              \addplot[red,sharp plot,update limits=false]                 coordinates {(-1,1.00) (34,1.00)}                 node[above] at (axis cs:15,1.00) {};             \legend{Ca2Fe2As2}         \end{axis}     \end{tikzpicture}     \caption{Sequence}     \label{fig:sequenceHeight} \end{figure}   my test.csv file:  sequence,height 1,2.0 2,1.5 3,1.8 4,2.4   Barchart: Changing affiliation on publication I am moving from one job to another (postdoc to tenure track) this summer and I have papers in several stages of being written, these go from handwritten notes with all the necessary arguments to under revision at a journal. All the papers will have my new contact information put on them but where is the line for changing affiliation? It seems obvious to me that the one that is still in the handwritten notes stage will get the new affiliation and that the ones under revision won't. So somewhere in between is a line.   Where is it?  There are some similar questions so far (see  and  but they do not seem to be quite the same situation since I am not changing fields and the appointments are not concurrent. Is there any way I can 'undo' the factorial operation? JUst like you can do squares and square roots, can you do factorials and factorial roots (for lack of a better term)?   Here is an example: 5! = 120.  Is there a way I can work out the number that must be factorialed (??) to give the answer 120? Divergent infinite series $n!e^n/n^n$ - simpler proof of divergence? $$ \sum_{n=1}^\infty \frac{n!e^n}{n^n} $$ Where $e$ is Euler's number.  Recently on calculus class we were covering convergence tests and my group got stuck with this infinite series. Our calculus teacher told us that it diverges but he doesn't see any elementary way or simple test to prove it. He told us something about Euler's Gamma function and said that he knows it diverges because of Stirling's formula but this is not quite our level yet.  I tried to think about it myself but I established only that this  is some kind of an edge case. We could generalize the problem to series of $\frac{n!a^n}{n^n}$. Then, from the ratio test we know that it converges for $a &lt;e$ and diverges for $a&gt;e$. For $a=e$ the test is inconclusive. I've also tried to compare it with various divergent series, but nothing worked...  Does anybody have any idea for a simple solution? Not sure if the title is specific enough, so here we go:  I crashed my Windows pc, and now I want to install Ubuntu on that computer. I'm currently using my Mac, as it is the only operable computer I have left. I have downloaded the .iso. I guess my question is; How do I go about installing Ubuntu on my crashed computer from the external harddrive? I've used Ubuntu before, but I used to install it from a CD-rom. I tried reading the instructions, but couldn't really understand them. Please help  Edit: As Tom mentioned, I only want to install Ubuntu on the (formerly) Windows machine.  Anyways, thanks for the quick responses, I think I've got it from here. Cheers What would be an appropriate opposite of "exceed"? Rotate only one screen If I have only the internal monitor (LVDS1) with an xrandr -o left command. Now I want to attach a second monitor, say to HDMI1. Then I'd like to rotate only the internal monitor, but not the external one. I tried the following (with no external attached though, since I am mobile currently), but that does not do anything:  xrandr --output LVDS1 -o left   How can I rotate only one monitor?  I do need some command line, since I want to put this into a script. I decided to make sure that I know this important difference between American and British English, so I wrote what I have found out so far and I would be grateful to anyone who reads this and tells me whether I am wrong, or not.  In British English when people say  to hospital or in hospital when  talking  about somebody being there as a patient they don't use the definite article : "I had to go to hospital", "She spent two weeks in hospital". And the meaning is that somebody was there as a patient.   If then for some other reasons British English speakers  will use the definite article which will change the meaning itself, I noticed that, in American English, native speakers often use the  the and if they need to show that somebody is in church to pray,  in school as a student, in hospital as a patient, in prison as a prisoner, they use 'in' and not 'at'. Do American English speakers use 'at' like British English speakers use 'the' to give the sentences a different meaning?    Are my sentences correct? Do they show American English usage?   He is in the school. (enrolled as a student) He is at the school. (for some different reasons) He is in the hospital. (as a patient) He is at the hospital. (visiting somebody) He is in the church. (to pray) He is at the church. (for some different reasons) He is in the university. (as a student) He is at the university. (not as a student) He is in the college. (as a student) He is at the college. (Not as a student) He is in the prison. (as a prisoner) He is at the prison. (not as a prisoner) Hot and Week tabs not shown to non-logged in users (except on SO) Visiting a SE site without logging in, one can no longer access the tabs Hot and Week (except on StackOverflow). I believe this change hides the feature from those most likely to use it: casual, but repeated, visitors. A number of people visit SE sites such as Travel or Mathematics just to read the content. They have no intention to post, and consequently, no reason to register. It makes little sense to hide the Hot and Week lists from them.   I propose that the tabs  ... Hot | Week | Month should again be made visible to anonymous visitors on SE sites, as they are on StackOverflow. extracting energy from cosmological expansion This question is a more concrete reincarnation of an .  Are there mechanisms to extract energy from the cosmic rate of expansion? putting some extremely long ropes across the universe and extract work from their increase of separation?  assuming this is possible ( i don't see why it would not ), what form would take the back-reaction force? in all physics, every time you extract work from some system by some force, this system will exert a force back. Can we slow down cosmic expansion by variations of these mechanisms?