The speed of light is constant as long as you are measuring it from a reference frame moving at a constant velocity, such as earth  What do we have to measure it from a reference frame moving at a constant velocity ? Isn't the speed of light always constant?  I don't really understand..Please explain.  Also sorry if this question seems dumb, im a 10th grader..
The speed of light is the same in all inertial frames.  Does it change from a non-inertial frame to another? Can it be zero?  If it is not constant in non-inertial frames, is it still bounded from above?
$\sum (-1)^n/n$ fails the p-series test, but passes the alternating series test? Compiling a document with PGFplots processing only every x-th data point? Can a Ranger select two humanoid races as their favored enemies at 6th and 14th levels? In D&amp;D 5e, the Ranger can choose at first level to have a Favored Enemy of a single broad type (i.e. fiends, giants, aberrations, etc.) or of two different specific humanoids (such as orcs and gnolls). They gain additional Favored Enemies at 6th and 14th level.  At each of those levels, could they opt to pick two humanoid races? Or would the choice be between one type and one specific humanoid?  Relevant text:     Choose a type of favored enemy: aberrations, beasts, celestials,   constructs, dragons, elementals, fey, fiends, giants, monstrosities,   oozes, plants, or undead. Alternatively, you can select two races of   humanoid (such as gnolls and orcs) as favored enemies.   And:     You choose one additional favored enemy, as well as an associated   language, at 6th and 14th level.   (Both quotes from PHB, pg 91.)  Specifically, I'm wondering whether "one additional favored enemy" means one absolutely, or whether the "Alternatively..." sentence means that two humanoid races can be substituted for one type whenever you select a favored enemy. I have two related problems that are causing me big trouble:  Let $\;a_1,...,a_n\in\Bbb R\;,\;\;a_i\neq 0\;\;\forall\;i\;$ , and let $\;b_1,...,b_n\in\Bbb R\;,\;\;b_i\neq b_j\;\;\forall\,i\neq j\;$ .  (1) Prove that the equation  $$a_1x^{b_1}+\ldots+a_nx^{b_n}=0$$  has at most $\;n-1\;$ different zeros in $\;(0,\infty)\;$ (Hint: Use induction)  (2) Prove that the equation  $$a_1e^{b_1x}+\ldots+a_ne^{b_nx}=0$$  has at most $\;n-1\;$ different zeros in $\;\Bbb R\;$ .  Now, the following is what I've done so far: for a differentiable function $\;f\;$ ,  I can prove that if $\;f'(x)=0\;$ has $\;n-1\;$ different zeros, then $\;f(x)\;$ has at most $\;n\;$ different zeros, using the mean value theorem, say.  But I can't see how to use induction in this case: if I differentiate in the first problem, I get $$0=f'(x)=a_1b_1x^{b_1-1}+\ldots +a_nb_nx^{b_n-1}=\frac1x\sum_{i=1}^na_ib_ix^{b_i}$$  ...and now?! How does induction kick in here? I though perhap something like: if we suppose WLOG $\;b_1&lt;b_2&lt;...&lt;b_n\;$ , then perhaps inducting on $\;\lfloor b_n\rfloor\;$, but it gets messy and blurry if $\;b_n&lt;0\;$...  Any help, hints are very much appreciated. On several occasions, I was reading a question thinking "I know a guy that knows the answer to this" and that guy (or gal) also happens to be a registered user. How can I bring this to the attention of this user? Like most Python developers, I typically keep a console window open with the Python interpreter running to test commands, dir() stuff, help() stuff, etc.  Like any console, after a while the visible backlog of past commands and prints gets to be cluttered, and sometimes confusing when re-running the same command several times.  I'm wondering if, and how, to clear the Python interpreter console.  I've heard about doing a system call and either calling cls on Windows or clear on Linux, but I was hoping there was something I could command the interpreter itself to do.  Note: I'm running on Windows, so Ctrl+L doesn't work. Why does part of my model disappear when I zoom in on it in the 3D Viewport? I'm having an odd issue - When I try to zoom in on a detail using my MMB, the "camera" in the 3D view seems to be cutting off the exterior surface of my object and showing me the inside instead. I'd expect this behavior, but only when I was much more zoomed in.  If I zoom out a bit (one click on the scroll wheel) then I can see the exterior as I intend.  Is there any way to adjust this behavior?  Thanks! Noise in JPEG file after processing RAW file in photoshop Recently i started shooting in RAW after understanding its advantages over JPEG format.   While processing the RAW file there is an option to reduce noise in a captured picture. It works great when i am working on RAW file. But as soon as I save file in JPEG format, noise comes back.  I understand that while converting from RAW to JPEG compression techniques will be applied. But how can i handle this situation (while doing post processing)? Looking for a classic sci-fi short story about a boy who discovers pods growing in a field For years, I've been looking for a short story about a boy who discovers alien pods in a field that are growing replacement people. If I remember right, he sees the pod creature eat his mother and then become her, and no one believes him. The story ends with him going in to see his dad, one of the few real people left until that point, and seeing something (an empty pod maybe) that lets him know his dad has been taken and he's next. I'm thinking that the title was something like Father Figure, but I may be remembering wrong.  The story was part of several collections of classic science fiction stories that we had on our bookcase when I was growing up, so I'm guessing that the story could be from the 70's or any time earlier. Please explain this put option TRON: Game A.I algorithm? Square bracket notation for dimensions and units: usage and conventions Content replacement from external website (a) Solve the equation $yu_x+xu_y=0$  with the condition $u(0,y) = e^{-y^2}$. (b) In which region of the xy plane is the solution uniquely determined?     I did the first part but I don't understand how to do part b.  I read   But I don't understand how the argument is based. A more clear explanation is appreciated Want to delay startup of program but can't find it in Task Scheduler I'm trying to delay the startup of a specific program that loads at login. As per an answer in , I should be able to do it using Task Scheduler. The problem is, I can't find the program listed anywhere. Is there a particular pane I should be looking in? The program is Razer Synapse so I don't think it would be in the Microsoft or Western Digital folders.    If it's not in Task Scheduler, is there another way I can delay it at startup?  Out of curiosity how many ways are there for a program to be run at Startup in Windows? When I import text file into R, I get a special character appended to the first value of the first column If $ a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}<1$ If $\displaystyle a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\displaystyle \frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}&lt;1$   $\bf{My\; Try::}$ Using $$\sin(a+\underbrace{b+c}) = \sin a\cdot \cos (b+c)+\cos a\cdot \sin (b+c)$$  $$ = \sin a\cdot (\cos b\cos c-\sin b\sin c)+\cos a(\sin b\cos c+\cos b\sin c)$$  $$ = \sin a\cos b\cos c-\sin a\sin b\sin c+\cos a \sin b\cos c+\cos a\cos b\sin c$$  Now how can i solve it after  that , Help required, Thanks How to animate morphing a rectangular plane into a sphere Control cannot fall through from one case label Horn and spindle tori