If, for example, a crystal oscillator is specified as +/- 100ppm what does that mean? That the exact frequency is uncertain to that degree, or that the frequency varies by that degree over normal operation? Also, does that automatically imply that any timing based on it is inaccurate to the same degree?
I'm a student and I'm working on a low power communication project. I am trying to design a PCB using the . There is a MC-306 (32.768kHz, 12.5pf, and 20/50ppm).   I don't know what the 20/50ppm rating is. For me, the size is very important, so I decided to replace it with the , but its ppm is -20/+20. Will it cause a problem if I use this one instead?  What is the ppm rating in the crystal oscillator?
Why does the experience-to-next-level not change between some levels? At every level from 1st to 11th, the experience needed to reach the next level (from the current level) increases every level. However, this pattern gets broken for most of the later levels:   Going from 10th to 11th takes 21,000xp (= 85k - 64k), but 11th to 12th takes only 15,000xp! (= 100k - 85k). Both 13th and 14th level only take extra 20k experience each, i.e. the amount needed doesn't increase between those two levels. Levels 16 and 17 similarly only need 30k experience each, and 18 and 19 only need 40k experience each.   Why does the last half of the experience chart have some of these levels maintain the same experience costs, and even briefly decrease the experience cost for 12th level? Is soaking beans 24 hours unrefrigerated safe? It strikes me as an unsafe food practice to follow Cook's Illustrated's advice for soaking dried beans for 24 hours unrefrigerated.  I've also seen them suggest you soak steel-cut oats unrefrigerated overnight.    Is there some reason why these practices are okay?  Would there be any harm in refrigerating them, particularly the beans, while soaking?  From Cook's Illustrated:     Dissolve 3 tablespoons salt in 4 quarts cold water in large bowl or   container. Add [one pound] beans and soak at room temperature for at least 8 hours   and up to 24 hours. Drain and rinse well. Disabling IPv6 on Mint and Debian How does one disable IPv6 completely (for all interfaces, resp. for the whole machine?  Keep in mind, I don't want any kind of GUI solution.    OS in question:   Linux Mint 18.x Cinnamon 64-bit GNU/Linux Debian 9.x Cinnamon 64-bit Show that there's no continuous function that takes each of its values $f(x)$ exactly twice. I need to prove the following:  There's no continuous function $f:[a,b]\to \mathbb{R}$ that takes each of its values $f(x)$, $x\in [a,b]$  exactly twice.  First of all, I didn't understand the question. For example $x^2$ takes $1$ twice, in the interval $[-1,1]$. Is it saying that it does not occur for all $x$ in the interval? But what about $f(x) = c$? Is it saying that it does not occur only exactly $2$ times, then? I have no idea about how to prove it. I know that for $f(x)$ such that $f(a)&lt;f(x)&lt;f(b)$, if $f$ is continuous then there is a $c\in [a,b]$ such that $f(c) = f(x)$.  Now, there's the following proof in my book and I really wanted to understand it, instead of just getting a new proof  Since the interval $[a,b]$ has only $2$ extreme points, then the maximum or minimum of $f$ must be in a point $c\in int([a,b])$ and and in another point $d\in [a,b]$. Then, there exists $\delta&gt;0$ such that in the intervals $[c-\delta, c), (c,c+\delta)$ (and if $d$ is not extreme of $[a,b]$, $[d-\delta, d]$) the function takes values that are less than $f(c) = f(d)$. Let $A$ be the greatest of the numbers $f(c-\delta), f(c+\delta), f(d-\delta)$. By the intermediate value theorem, there are $x\in [c-\delta, c), y\in (c, c+\delta]$ and $z\in [d-\delta, d)$ such that $f(x)=f(y)=f(z)=A$. Contradiction.   Well, why the last part? Why is it that I can apply the intermediate value theorem to these values? For example, $&lt;f(c-\delta)&lt;p&lt;f(c)$, then by the theorem I know that there exists $m\in [c-\delta, c)$ such that $f(m) = p$. Same for the other intervals. But what guarantees thhat the greatest of the values between  $x\in [c-\delta, c), y\in (c, c+\delta]$ will be inside the intervals $[c-\delta), c), (c,c+\delta), [d-\delta, d)$? I'm a physics teacher and I would like to find a simulation software that could be used to give exact numerical answers to high school level problems in Newtonian mechanics.  I want the students to first calcultate a numerical answer to a physics problem and then use the simulator to visualize the problem in order to understand it better and verify that the simlator gives the same answer that they got when doing the calculation themselves.  Here are some examples of what kind of problems I want the students to be able to solve with the simulator:   A slope with a specific angle of inclination and a ball starts rolling at a certain point. Determine the speed, angular momentum and total mechanical energy of the ball after a specific time t. A ladder of known mass and length is leaning against the wall at a specific angle. The contact between the ladder and the wall is frictionless. Calcultate the x and y components of the force between the floor and the ladder.   I would like the software to have the following features:  - Simulation in 2D. No 3D simulations are necessary and the software should at least have the option of doing simulations only in 2D.  - Position all objects exactly by writing numbers (just positioning the objects using the mouse is not precise enough).  - Show animations of the time evolution of the system.  - Show forces, velocities and accelerations as arrows.  - Give exact numerical results so that the students can use the software to verify their calculation.  Ideally the software would have a graphical user interface, but if no suitable software with graphical interface exixts, I could also consider a software with text-based inputs. I would consider both free and commercial software.  My question is: Is there any software that would meet these requirements and if there is, where could I get it? There is a socket related function call in my code, that function is from another module thus out of my control, the problem is that it blocks for hours occasionally, which is totally unacceptable, How can I limit the function execution time from my code? I guess the solution must utilize another thread. I just realized I can't unrar .rar files on my Ubuntu machine!  What's the easiest way to accomplish this fundamental task? If possible I'd love something like 7Zip that I can just right Click, and extract and have the program worry about how to do it regardless if it's a .zip, a .rar or a .foo compressed file. I am trying to find the correct opposite of a delegate in the context of a person being a representative of someone else that have allowed or chosen them to be their delegate. What would you call that "someone else?" The only word I could find is a delegator (which isn't a real word in English) or assigner, but they are technical words rather than descriptive.    Any other word I could use?    Think of it in a sentence like this:       Here is a list of all the delegates in the company.   But that is the list of their _ _ _ _ _ (what can go here?).   I am trying to avoid fillers such as:  bosses, agents, managers, etc. How can I say this? can I put a double 50 amp pole in a 100 amp box I'm new to linux and the terminal. As I learn how to use the terminal to navigate through directories, I like to use the gui file explorer to mirror my terminal navigation. The icons and file extension info in the gui file explorer help me figure out what everything is. However, I can't access the root folder via the gui, I can only access it via the terminal. Is there a way to enable access to the root folder outside of the terminal? Elements of $\mathbb Q(2^{1/3})$ Why can't I launch eclipse from a terminal ? change $PATH environment variable Bake Simple Deform animation into mesh for Unity3D export? I'm trying to use a .blend file with a keyframe animation on the angle of a Simple Deform modifier in Unity3D. Unity3D however does not know how to handle modifiers and hence cannot play the animation.  How can I bake/save the animation to the .blend file so that Unity3D can play it? Automatically growing lists as in MATLAB? Avoid trailing zeroes in printf() I keep stumbling on the format specifiers for the printf() family of functions.  What I want is to be able to print a double (or float) with a maximum given number of digits after the decimal point.  If I use:  printf("%1.3f", 359.01335); printf("%1.3f", 359.00999);   I get  359.013 359.010   Instead of the desired  359.013 359.01   Can anybody help me? Why do we need to be root in terminal for shutdown and restart? Determine the set of points $z$ that satisfy the condition $|2z|>|1+z^2|$ Determine the set of points $z$ that satisfy the condition $|2z|&gt;|1+z^2|$  I tried to redo this problem and got to this point  $|2z|&gt;|1+z^2|$ $\Rightarrow$ $2|z|&gt;1+|z^2|$ $\Rightarrow$ $2|z|&gt;1+z\overline z$  Let $z=x+iy$ then   $$2\sqrt{x^2+y^2}&gt;1+(x+iy)(x-iy)$$  $$2\sqrt{x^2+y^2}&gt;1+(x^2+y^2)$$  $$0&gt;1-2\sqrt{x^2+y^2}+(x^2+y^2)$$  $$0&gt;(1-\sqrt{x^2+y^2})^2$$  since $x,y$ are real number , so there is no solution for this inequality? Getting nauseated from air travel, but it's not motion sickness... what to do? What is an idiom/slang for "someone who pretends to be good when they're not"? This is not from real life, but from a movie on my local TV. A character in the movie is really bad, but when she talks with others, she pretends to be an innocent/ good woman. I want to know how to describe this kind of person.