A ring of a planet has an inner radius of approximately 51,400 km (measured from the center of the planet) and a radial width of 17 km. Use differentials to estimate the area of the ring. (Round your answer to the nearest thousand.)
A ring of a planet has an inner radius of approximately 52,000 km (measured from the center of the planet) and a radial width of 19 km. Use differentials to estimate the area of the ring. (Round your answer to the nearest thousand.)   I hate asking questions where I have nothing to contribute but I have absolutely no Idea on how to approach this question. A step by step solution to this problem which I could apply to similar problems would be greatly appreciated, thanks in advance.
Standard and/or common directories on Unix/Linux OSes Calculating the total number of surjective functions It is quite easy to calculate the total number of functions from a set $X$ with $m$ elements to a set $Y$ with $n$ elements ($n^{m}$), and also the total number of injective functions ($n^{\underline{m}}$, denoting the falling factorial). But I am thinking about how to calculate the total number of surjective functions $f\colon X \twoheadrightarrow Y $.  The way I thought of doing this is as follows: firstly, since all $n$ elements of the codomain $Y$ need to be mapped to, you choose any $n$ elements from the $m$ elements of the set $X$ to be mapped one-to-one with the $n$ elements of $Y$. This results in $n!$ possible pairings. But the number of ways of choosing $n$ elements from $m$ elements is $\frac{m!}{(m-n)!\,n!}$, so the total number of ways of matching $n$ elements in $X$ to be one-to-one with the $n$ elements of $Y$ is $\frac{m!}{(m-n)!\,n!} \times n! = \frac{m!}{(m-n)!}$.  Now we have 'covered' the codomain $Y$ with $n$ elements from $X$, the remaining unpaired $m-n$ elements from $X$ can be mapped to any of the elements of $Y$, so there are $n^{m-n}$ ways of doing this. Therefore I think that the total number of surjective functions should be $\frac{m!}{(m-n)!} \, n^{m-n}$.  Is this anything like correct or have I made a major mistake here? Indirectly access environment variable Given I have in a bash script  ev=USER   How can I get the environment variable value for $USER using ev?  Tried naively doing:  echo ${"$"$ev}   which results in bad substitution.  I'd expect to get back whatever the value of $USER is. How to select a value from a list with non-uniform probabilities? 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I mean in linear velocity the direction of velocity is in the direction of motion of body but what does it mean that body is moving in one direction while the direction of its angular velocity is in another direction? "Total number of votes for 'N' answers" is wrong in "Deleted Recent Answers" Below are the two screenshots. First one shows the number of votes          In above image a post which was deleted shown ) votes. Now in below image which is actual post deleted is having 1 vote. How to choose the number of hidden layers and nodes in a feedforward neural network? Is there a standard and accepted method for selecting the number of layers, and the number of nodes in each layer, in a feed-forward neural network? I'm interested in automated ways of building neural networks. 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