How can I derive Newton's gravitational law?  $$F=G\frac{m_1 m_2}{r^2}$$  Is it impossible to derive?  Did Newton get this just by obervations?
I am having trouble comprehending how anyone could come up with this formula:  $$F = \frac{GMm}{d^2}.$$   Could someone walk me through this?
We work heavily with serialization and having to specify Serializable tag on every object we use is kind of a burden. Especially when it's a 3rd-party class that we can't really change.  The question is: since Serializable is an empty interface and Java provides robust serialization once you add  implements Serializable - why didn't they make everything serializable and that's it?    What am I missing? How many Java string objects created in the code String s="abc"+"xyz";? What is dependency injection? Unwanted Lines when rendering using GPU and OpenCL (RX 580) I'm unable to access the following website from my Internet Explorer 8 under Windows XP with Internet Explorer unable to display web page error. By the other hand the FireFox browser at the same Windows XP can access this website.  How to solve the issue with IE8 ? How will multiple GPUs improve Cycles' rendering performance? I have an NVIDIA Titan GPU and I'm able to add another card, but I wonder whether  Blender will benefit from more than one GPUs?  Should I do it as SLI or should I just do it as an added card? I just need some help in understanding how Blender will use either SLI or a second GPU.  Note that I only use Cycles. Showing that a function is not differentiable Multiple Bluetooth speakers simultaneously I would like to pair two sticky dude Bluetooth speakers, at one time with my iPhone. With two of them at once it would be like stereo sound. Is there an app or something maybe? Prove $p_n(x) \rightarrow \sqrt{x}$ uniformly as $n \rightarrow \infty$ Define $(p_n)_n$ recursively by $p_0(x) = 0$ and $p_{n+1}(x) = p_n(x) + \frac{1}{2}(x - p_n(x)^2)$.  Prove that $p_n(x) \rightarrow \sqrt{x}$ uniformly for $0 \leq x \leq 1$ as $n \rightarrow \infty$.  I'm not sure where to go with this.  I can show inductively that $\forall n,\  0 \leq p_n(x) \leq 1$ for $0 \leq x \leq 1$, and I think that $p_n(x)$ is increasing with $n$, but I have no idea whether this helps me.  I know that I need to show that $\forall \epsilon&gt;0: \exists N \in \mathbb{N}: \forall n \geq N: \forall x\in [0,1]: \big|p_n(x) - \sqrt{x}\big| &lt; \epsilon$ Edit:  I just had a thought.  I'm given a version of Dini's theorem that reads  Let $X$ be a compact metric space, $(f_n)_n$ a sequence of real-valued continuous functions on $X$, $f$ a continuous function on $X$ such that: (i) $f_n \rightarrow f$ pointwise on $X$, and (ii) $f_n(x) \geq f_{n+1}(x) $ for all $x \in X, n \in \mathbb{N}$. Then: $f_n \rightarrow f$ uniformly on $X$.  Obviously, (ii) is not true for my sequence, but what if I took $f_n(x) = -p_n(x)$ and $f(x) = - \sqrt{x}$?  Then I could prove (ii) to be true, I know that $[0,1]$ is compact, and $f_n(x)$ is real-valued.  The only part I would need to prove is (i), which is where I get confused.  Correct me if I'm wrong, but after that I could say that since $(-p_n)_n \rightarrow -\sqrt{x}$, then $(p_n)_n \rightarrow \sqrt{x}$.  Any advice? How handicapped am I in graduate admissions if I graduated from a lower tier university? Due to a combination of factors, I ended up going for my undergraduate studies to a relatively unknown university that was close to me geographically.  Let's say that I have a relatively standard background for someone trying to apply to top tier schools for graduate studies (some research experience, some low to medium quality publications, very strong grades, good recommendation letters). Then how much does the alma mater have an impact for someone like me? I obviously know that it is still possible to be accepted, but how much of a disadvantage am I looking at exactly? Can you give a simple intuitive explanation of IRLS method to find the MLE of a GLM? Background:   I'm trying to follow .  I understand the basics of MLE estimation: likelihood, score, observed and expected Fisher information and the Fisher scoring technique. And I know how to justify .    The question:   I can't understand even the first line of this method :(   What's the intuition behind the $z_i$ working variables defined as:  $$ z_i = \hat\eta_i + (y_i -\hat\mu_i)\frac{d\eta_i}{d\mu_i}$$  Why are they used instead of $y_i$ to estimate $\beta$?   And what's their relation with the response/link function which is the connection between $\eta$ and $\mu$  If anyone has a simple explanation or can direct me to a more basic-level text about this I would be grateful. Can I travel to France with Fiktionsbescheinigung (Fiction Certificate) of Germany Can't use method return value in write context My laptop which had Windows 7 on it crashed today. Being unable to access any file kept within, I found about the LiveCD. So I created a LiveUSB with Ubuntu in it, and managed to access my Windows desktop. I'm now backing up files important to me, but I have a question:  Now I'm cutting and pasting the files I want to save, using Ubuntu. Are these files being moved in Windows as well, or do the alterations I make through Ubuntu not affect the Windows state?   So let's say,if I cut and paste all of the D drive, and then format C and reboot with Windows, would the files in D have been gone (since they were cut and not copied) or still be there?  Thanks. While browsing Stack Overflow, I noticed that I lost a lot of reputation:        Is this serial downvoting? Will it be corrected by a rep-recalculation? How often are those done?    Here's a second instance: Has the Doctor’s memory been reset? At the end of The Time of the Doctor, it is shown that Matt Smith has received an entire new regeneration cycle and using it he regenerates into Peter Capaldi. Capaldi's first question to Clara is about how to fly the TARDIS. Does this mean there has been a memory reset for the Doctor?  If so, has he forgotten his true name?  If he has forgotten his true name, then he can't bring back the Time Lords now can he? How do I get the icon associated with a file type? I have a form that displays file information in a TabControl, and I'd like the pages to have the file's icon in their tab.  How do I get the icon associated with a file type?  I'd prefer solutions that don't involve looking things up in the registry, but if that's the only way then so be it. On iOS, while watching a video in YouTube app, when I go to the Home Screen, the video stops playing. I found no setting to enable it.  I know it is available for Android, but is there a way to do so in iOS? Is there any setting, or a 3rd party app that I can use? How can I make a view that seems like orthographic, but not exactly? For the start, I thought was orthographic, but when I used the orthographic camera, it didn't match up. Client say they want a so-called &quot;industry schematic&quot;, talking about a 135 degree look.  I found a trick to do this, which is using lattice. I align the lattice with the cube, and move the upper four points a little bit along the axis showing on the following image. But I want to achieve this by just using the camera. I've used git clone to make a local copy of a GitHub repository containing a  I'd like to use. The local copy contains all of the source for the program; but as a newbie to Ubuntu, I've no idea of what tools or steps are involved in compiling and installing the driver.   I'd really appreciate if anyone could provide a step-by-step guide?