I have some golden syrup in a plastic bottle, all looks normal. It has a best before date Feb 2010. Is it still ok to feed to kids on pancake day February 2015??
I had a tin of golden syrup for a long time - longer than I care to admit. When I opened it up yesterday (to sweeten up some mulled wine), it was granular (a bit like honey can be), and black around the edges.   Is this 'bad', or just different?   Is the blackness the result of some chemical reaction with the tin?  And in general, does it eventually go off, or does it last indefinitely?
ascending/descending in LINQ - can one change the order via parameter? How do you collect valuable information from regular "User Group" meetings? The scenario:   You work on a SaAS application.  Some of your users use your application heavily each day. Every 2 weeks (or month or whatever), a "User Group" of your most avid users gets together to talk shop and see how their progress is going in the context of a larger project they are working on. You can participate and potentially direct some group activities aimed at improving the application.   How do you gather valuable user information in this group setting? What is the gradient of $f(x, y, z) = \sqrt{x^2+y^2+z^2}$? What is the gradient of $f(x, y, z) = \sqrt{x^2+y^2+z^2}$?  I know that $\nabla f = \left\langle\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right\rangle$ or equivalently $\nabla f = \frac{\partial f}{\partial x}\mathbf{i} + \frac{\partial f}{\partial y}\mathbf{j} + \frac{\partial f}{\partial z}\mathbf{k}$.  Eventually, I am going to evaluate this gradient at a point and then dot it with some given unit vector to find a directional derivative. I think maybe what is troubling me is the radical in $f$. Will I have to use the chain rule in order to find the three partial derivatives?  I tried this:  $$\frac{\partial f}{\partial x} = \frac{1}{2}(x^2 + y^2 + z^2)^{-\frac{1}{2}}2x$$ $$= \frac{x}{\sqrt{x^2 + y^2 + z^2}}$$  That result looks ugly to me. However, if I did that partial derivative correctly, then I think I know what I am doing. What happens to the energy when waves perfectly cancel each other (destructive interference)? It appears that the energy "disappear" but the law of conservation of energy states that it can't be destructed. My guess is that the kinetic energy is transformed into potential energy. Or maybe it depends on the context of the waves where do the energy goes? Can someone elaborate on that or correct me if I'm wrong? Possible Duplicate:          Both words seem to be used interchangeably. I generally don't differentiate between them and intuitively pick one over the other. Is there a standardized way to distinguish between the two? Prima facie this is impossible but perhaps someone has some kind of hack to do it. This is one of the last things holding me back from switching to Gmail from Pine.  To be clear, bouncing a message is like forwarding but leaving all the headers intact. It sort of amounts to spoofing the email, which perhaps is why Gmail doesn't support it. To the recipient of a bounced email, it seems as if they were just BCC'd. How do you run as a different user from the Start Menu in Windows 10? Running an application as a different user (e.g. domain admin account) from the start menu (by shift + right-clicking the application) used to be an option in Windows 7 &amp; XP.  However, I can't find that option in Windows 10. The workaround seems to be either 1) to find the application in Windows Explorer (shift + right-click) or 2) use runas.exe from the command line.  However, in order to use those workarounds, I have look up the executable name first. It's a bit difficult because I don't have the name of every RSAT tool or executable name memorized.  (e.g. "Active Directory Users and Computers" is dsa.msc, "Routing and Remote Acces" is rrasmgmt.msc)  Is there a simpler way to do this? Domain Controller etiquette after a crash between Server 2003 & Server 2008 I have 2 domain controllers on a non-Internet connected network running Windows Server 2008 R2. They running RAID 5 on a 8 Hard Drive server. Sometime last week the Boot Sector became corrupt on DC1 and I was unable to recover the server. I am not going to have to rebuild the server. I have been reading about the changes from Server 2003 to Server 2008. DC1 was the main domain controller and now that it won't but it is all falling to DC2. I know that in previous versions of Windows Server you had to make on the primary and one the secondary. Since DC2 does not see DC1 anymore is there anything I need to do to DC2 as it is now the one in control? I am thinking some kind of meta data clean up but I can't find any hard information on what procedure to do. I understand as of Server 2008 domain controllers are on an equal footing and provide replication to each other so they should be the same correct? Another phrase for "a chicken and egg situation" Is there any other phrase that conveys the same meaning as  the phrase "a chicken and egg situation" especially if one has to use this phrase in an official/corporate set up? Is there a way to make rigid body interact with softbody physics? Can I embed a custom font in an iPhone application? I would like to have an app include a custom font for rendering text, load it, and then use it with standard UIKit elements like UILabel. Is this possible? Terminal flashes on empty backspace with Yosemite Since using Yosemite, I've had the annoying problem of my current Terminal window flashing when backspacing on an empty line. I know on previous versions of OS X this flashing was not default, and could be toggled in accessibility settings, but I cannot find the same setting and I'm dying to get this turned off. Any known ways to get rid of it? $(K[x,y,z]/(x^2+y^3+z^7))_{(x,y,z)}$ is a UFD. Justifying the Normal Approx to the Binomial Distribution through MGFs Would absolutely love if someone could help me with this question, in a step by step way to help those who are uninitiated to Statistics and Mathematics.   So, I am trying to "prove/justify" through MGFs how as n(the sample size) increases and goes to infinity, a standardized binomial distribution converges to the Standard Normal Distribution. So in the beginning we have $X_n $~$ Bin(n,p)$ then we standardize this $R.V.$ by subtracting the mean $E(X_n)=np$ and dividing by the $SD$ which is $np(1-p)$. After doing this, we get a new $R.V.$ with $mean=1$ and $variance=SD=1$. It is the distribution of this standardized quantity that converges to a fixed distribution, correct? Namely the Standard Normal Distribution. Let's call the standardized version of $X_n$, $Z_n$.   I think what we need to do is to find the MGF of $Z_n$ and show that this MGF becomes the Standard Normal Distribution's MGF as the sample size $(n)$ heads toward infinity. Now $Z_n$ is a function of $X_n$ which we know the MGF of which is $(1-p+pe^t)^n$.   Now I know that $Z_n$ is a linear transform and that we should be able to use this to simply the MGF but I don't understand how the course notes do it, mostly because they skip a lot of steps and it is difficult to follow. There is also a Taylor Series Expansion for the exponential that I am confused about although I do understand the concept of the series expansion.  Help would be greatly appreciated! I would love assistant in exactly how we can prove this via MGF.   Thanks so much in advance :) Drawbacks of making public which journal a manuscript is submitted to, while it is under review? Many researchers list out their submitted manuscripts on their website. Some specify the journal name, like     Smith J, Oliver J (under review) My awesome paper. Nature.   while others don't, like     Smith J, Oliver J (under review) My awesome paper.   One reason I can think of as to why some don't mention the journal name is that they may get embarrassed in the case where the current journal rejects the paper. Then, the "circle" will know this paper gets rejected from Nature first and then ends up in an inferior journal.  Besides this, are there any other considerations preventing people from mentioning to which journal they submit a paper to?  P.S.: I am asking because my advisor is a researcher who only mentions accepted  papers on his webpage. As a student hunting jobs, I feel it is advantageous for me to mention my submitted papers on my webpage. I hesitate to do so, as I worry I may make my advisor unhappy by announcing in which journal our papers are currently under review. Motivated by , can one prove that the order of an element in a finite group divides the order of the group without using Lagrange's theorem? (Or, equivalently, that the order of the group is an exponent for every element in the group?)  The simplest proof I can think of uses the coset proof of Lagrange's theorem in disguise and goes like this: take $a \in G$ and consider the map $f\colon G \to G$ given by $f(x)=ax$. Consider now the orbits of $f$, that is, the sets $\mathcal{O}(x)=\{ x, f(x), f(f(x)), \dots \}$. Now all orbits have the same number of elements and $|\mathcal{O}(e)| = o(a)$. Hence $o(a)$ divides $|G|$.  This proof has perhaps some pedagogical value in introductory courses because it can be generalized in a natural way to non-cyclic subgroups by introducing cosets, leading to the canonical proof of Lagrange's theorem.   Has anyone seen a different approach to this result that avoids using Lagrange's theorem? Or is Lagrange's theorem really the most basic result in finite group theory? How to make read-only file system writable? At some point, the filesystem on my digital audio player has become read-only. I cannot copy files into it or remove files on it.  Are there some possible reasons for the player's file system to change permissions in this way?  I tried using chmod:  $ sudo chmod a+rw SGTL\ MSCN/  chmod: changing permissions of `SGTL MSCN/': Read-only file system   SGTL MSCN is the mount point of the digital audio player.  What else can I try to make it writeable? My directory (in Linux) looks like com/com/{various,files} where com and com are folders of the same name and the second com holds the various files. I want the first com removed, but the second and files in the second kept. Why are my textures pink? Basically, I applied my textures by taking each individual object, unwrapping it in the uv editor, then opening up an image in the uv editor and it would apply the texture in the 3D editor. However, when I render my project none of the textures appear and everything looks odd. I don't know how to set up the images properly with the bee.  For example, here's the uv layout image for the bee's Cube.001:     How do I get that applied properly to the Cube.001 in my project?  Here is   Everything appears purple if the images aren't there and I don't know how to fix that either. When I'm connected to two networks with separate routers using Wifi and Ethernet, how does my Mac know what connection to use when I visit a website?