I stumbled upon the fact that I had about 8 different versions (I started uninstalling them) of Windows Visual C++ Redistributable installed.  I wonder, can I remove all except the latest one? Why isn't Windows itself taking care of this? I work a lot with Python. Is there a specific reason I'd need an older version?  Thanks! Ronny
I am using Windows 10. I am trying to install 1 open source software.  In the readme.txt of that software, it says it requires Visual C++ 2008 Redistributable. I found that my Windows already has Visual Studio 2012 Redistributable installed.  After I install the open source software, it seems that it is working, even though I haven't installed Visual C++ 2008 Redistributable.  Do I need to install Visual C++ 2008 Redistributable if my Windows already has Visual Studio 2012 Redistributable?
Finding roots/zeros for collision detection? For the most simple of 2D games, I have implemented a posteriori collision detection (overlapping rectangles) on the x/y Cartesian plane, but am now interested in understanding the basics of a priori collision detection...  In the link , I noticed the reference to Newton’s Method.  So, I want to better understand the link b/w finding zeros of an equation and detecting a posteriori collision.    Let's start with the most obvious case of finding roots of an equation:  If you have a projectile's trajectory modeled as a quadratic function, you can find the roots to predict at what time the height will equal zero (or any other constant height, actually, by just solving f(x)=C to be f(x)-C=0 and then finding roots of that expression).    So, as I understand, finding the root can tell me the time at which the object will be at any chosen height.  More broadly, we basically know the (x,y) location of the object for any given time.  But how does root finding, in particular, translate to detecting collisions with another object?  (The other object may be stationary, or be moving.  If the latter, do you also determine roots/location of this moving object as well? Calculate the (x,y) trajectory of both objects and determine where they will intersect?)  Again, the basic question is where does root finding come into play?  Any links to a basic primer on this topic, with a simple example would also be greatly appreciated. Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$ The following identity is true for any given $x \in [-1,1]$: $$\arcsin(x) + \arccos(x) = \frac{\pi}{2}$$  But I don't know how to explain it. I understand that the derivative of the equation is a truth clause, but why would the following be true, intuitively?  $$\int^{x}_{C1}\frac{1\cdot dx}{\sqrt{1-x^{2}}} + \int^{x}_{C2}\frac{-1 \cdot dx}{\sqrt{1-x^{2}}} =\\  \arcsin(x) - \arcsin(C1) + \arccos(x) - \arccos(C2) = 0 \\  \text{while } \arcsin(C1) + \arccos(C2) = \frac{\pi}{2}$$  I can't find the right words to explain why this is true?    Edit #1 (25 Jan, 20:10 UTC): The following is a truth clause: $$ \begin{array}{ll} \frac{d}{dx}(\arcsin(x) + \arccos(x)) = \frac{d}{dx}\frac{\pi}{2} \\ \\ \frac{1}{\sqrt{1-x^{2}}} + \frac{-1}{\sqrt{1-x^{2}}} = 0 \end{array} $$  By integrating the last equation, using the limits $k$ (a constant) and $x$ (variable), I get the following:  $$ \begin{array}{ll} \int^x_k\frac{1}{\sqrt{1-x^{2}}}dx + \int^x_k\frac{-1}{\sqrt{1-x^{2}}}dx = \int^x_k0 \\ \\ \arcsin(x) - \arcsin(k) + \arccos(x) - \arccos(k) = m  \text{ (m is a constant)}\\ \\ \arcsin(x) + \arccos(x) = m + \arcsin(k) + \arccos(k) \\ \\ \text{Assuming that } A = m + \arcsin(k) + \arccos(k) = \frac{\pi}{2} \text{ ,for } x \in [-1,1] \end{array} $$ Using Calculus, why is that true for every $x \in [-1,1]$?    Edit #2:  A big mistake of mine was to think that $\int^x_k0 = m \text{ (m is const.)}$, but that isn't true for definite integrals.  Thus the equations from "Edit #1" should be as follows: $$ \begin{array}{ll} \int^x_k\frac{1}{\sqrt{1-x^{2}}}dx + \int^x_k\frac{-1}{\sqrt{1-x^{2}}}dx = \int^x_k0 \\ \\ \arcsin(x) - \arcsin(k) + \arccos(x) - \arccos(k) = 0\\ \\ \arcsin(x) + \arccos(x) = \arcsin(k) + \arccos(k) \\ \\ A = \arcsin(k) + \arccos(k) = \frac{\pi}{2} \text{ ,for } x \in [-1,1] \end{array} $$ What do the E and R prefixes stand for in the names of Intel 32-bit and 64-bit registers? I am a little at a loss.  A couple years before my mother-in-law passed away she signed her house over to my wife and her sister via a quitclaim deed.    After she passed we sold the house for $80,000. The money was used to pay off the mortgage, some other funeral expenses, and sent $15,000 to other family members.  All the money was dispersed at the closing of the house.  My wife and her sister each ended up with about $20,000.  How do we go about claiming this income?  Since there was a quitclaim deed I guess we technically owned the house for a few years prior to its sale.  How does that affect our tax and what is the basis?  Is the basis the selling price(fair market value) or something else?  How much does each sister claim for gains?  Sorry it this is a jumble of questions I am just trying to get this straightened out before tax is due. Securely erasing all data from a hard drive Let $X_1,...,X_n$ be mutually independent RVs. Suppose $X_i \perp \mathcal F $ for $1\ \leq \forall i \leq n$.    How can I show that:  $$\sigma (X_1,...,X_n) \perp \mathcal F$$ ?  What I have tried:  $\sigma (X_1...X_n) = \sigma(\cup_{i=1} ^n \sigma(X_i))$ holds. I think I need some Dynkin's lemma-ish argument but can't see how. Let $ f $ be a continuous function defined on $ [0,\pi] $. Suppose that      $$ \int_{0}^{\pi}f(x)\sin {x} dx=0,   \int_{0}^{\pi}f(x)\cos {x} dx=0 $$   Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $ Solution for PHP / MySQL website loading fast in multiple regions There are many visa applicants who are working as an unregistered freelancer (photographer, construction contractor, fashion designer, journalist etc ). Some of these freelancers make really handsome monthly income and don't really need to work as a full time employee. Most of them receive variable amount of payments (cash, cheques, demand drafts etc) When it comes to filling a visa application form (USA, UK, Schengen etc), there is always an employment section in all visa form, eg for Schengen visa employment form :    This is a very important factor to make an application really strong.  Questions:   1 Unregistered freelancers can just simply write their profession? what documents to produce along with the application?  2 Bank statements with variable methods of payments could convince the visa officer that these are all legitimate payments? Best way to restrict access by IP address? For an ASP.NET C# application, we will need to restrict access based on IP address. What is the best way to accomplish this? I changed permissions of a file (chmod g+w testfile) and running ls -l testfile gives:  -rwxrwxr-x 1 user1 user1 0 2011-01-24 20:36 testfile   I then added a user to that group ("/etc/group" has user1:x:1000:user2 line), but am failing to edit that file as user2. Why is this so? What is the command to open the shutdown dialog? What is object slicing? Are bicategories and lax 2-categories the same? Some websites have code to "break out" of IFRAME enclosures, meaning that if a page A is loaded as an IFRAME inside an parent page P some Javascript in A redirects the outer window to A.  Typically this Javascript looks something like this:  &lt;script type="text/javascript"&gt;   if (top.location.href != self.location.href)      top.location.href = self.location.href; &lt;/script&gt;   My question is: As the author of the parent page P and not being the author of the inner page A, how can I prevent A from doing this break-out?  P.S. It seems to me like it ought to be a cross-site security violation, but it isn't. I'm using Java, and need to generate a simple, standards-compliant RSS feed. How can I go about this? Suppose we view fluids classically, i.e., as a collection of molecules (with some finite size) interacting via e&amp;m and gravitational forces. Presumably we model fluids as continuous objects that satisfy some differential equation. What mathematical result says that modeling fluids as continuous objects can accurately predict the discrete behavior of the particles? I don't know anything about fluid mechanics, so my initial assumption may in itself be wrong. 35km commute possible? Currently, on every other day I commute to work which is a distance of 18km each way. I enjoy this ride but next year I may be moving to a place which will be about 35km from work. Questions:  1) Would it still be reasonable to commute this kind of distance each way once I have moved?  2) Google maps estimates that this distance would take 2 hours to complete. Would it be possible (depending on the bike and fitness) to do this distance in about an hour? OK we are all adults here, so really, how on earth should I live without bidet? This is the part four in the interesting series: "OK we are all X here, so really". You can find the past episodes here:        Travelling always requires a bit of adjustment. While doing our favorite activity we always leave home our comfort, our routines and, unfortunately, Italians (and others) leave home their beloved .  The question is simple: what are the substitutes / tips&amp;tricks for bidet while travelling in bidet-unfriendly countries so that we can do our business without end up feeling, let's say, uncomfortable? I've been reading a lot about closures and I think I understand them, but without clouding the picture for myself and others, I am hoping someone can explain closures as succinctly and clearly as possible.  I'm looking for a simple explanation that might help me understand where and why I would want to use them.