How to derive the formula for the uncertainty of opposite in TOA? (let the opposite be h and the adjacent be x)
As a lab assignment I have to replicate experiment with spring oscillations, and eventually calculate spring constant. The measurements I took are: spring displacement from equilibrium $x$, mass of weights $m$, and period $T$. And presumed uncertainties: $\Delta_\alpha(x)=1[mm]$, $\Delta_e(x)=2[mm]$,  $\Delta_\alpha(t)=0.1[s]$,  $\Delta_e(t)=1[s]$. Where $\alpha$ stands for uncertainty of used equipment, and $e$ is readings uncertainty made by me.  I calculated the standard uncertainty using this formula: $$\sqrt\frac{\Delta_\alpha(x)^2+\Delta_e(x)^2}{3}$$ Which produced $u(x)=1.29[mm]$. Then using the following substitutions:  $$F=kx$$ $$mg=kx$$ $$x=\frac{g}{k}m$$ I assert that:  $$tan(a)=\frac{g}{k}$$  Because in this part of experiment I plotted $x=f(m)$, using excel's linest, I get the slope $s$  $$tan(a)=\frac{g}{k}=s$$  Now, my question is, since I had uncertainty for $x$ introduced, and it is used to compute $tan(a)$, then the latter is affected and should have uncertainty of itself? How in this case should I go about propagating uncertainty to $tan(a)$?
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 ? In SQL Server, how do I generate a CREATE TABLE statement for a given table? I've spent a good amount of time coming up with solution to this problem, so in the spirit of , I'm posting it here, since I think it might be useful to others.   If anyone has a better script, or anything to add, please post it.  Edit: Yes guys, I know how to do it in Management Studio - but I needed to be able to do it from within another application. How can I determine the height and the least number of generators of the ideal $ I=(xz-y^2,x^3-yz,z^2-x^2y) \subset K[x,y,z] $?      I tried to calculate the dimension of the vector space $I/I\mathfrak m$ with $\mathfrak m=(x,y,z)$, but I'm not able to find it.  I think the height is $2$, because the affine variety should be a curve, and also I know that the ideal is prime, so I need a chain $0\subset \mathfrak p \subset I$. Maybe $(xz-y^2)?$ Is it prime? Super+D key shortcut does not show desktop I recently installed Saucy Salamander on my computer. Previously in Ringtail, Super+D used to show the desktop. However for this release, the Super+D does not seem to work properly... Is it a bug? Drawing on an image with TikZ Recently I have learned how to draw simple stuff with TikZ. I really like it. Now I wonder if it is possible to draw with TikZ on a image. Instead of pasting a image in Illustrator and adding some vectors to point something in the picture I would like to do it using TikZ. Is it possible?   For example, on a picture of a computer (PNG,etc) I would like to draw some arrows and labels saying "Keyboard", "Monitor", etc. As you can see, the off-topic page isn&#39;t quite right...    Could this (minor) issue be fixed? $(p\!-\!1\!-\!h)!\,h! \equiv (-1)^{h+1}\!\!\pmod{\! p}\,$ [Wilson Reflection Formula] How many roots have a complex number with irrational exponent? If a rational exponent on a complex number $z^q$ is the representation of a finite number of roots, then if the exponent is irrational this mean that there is infinite countable roots?  If this is the case... the cardinality of the number of roots is the same for any irrational exponent? Thanks in advance.  NOTE: there are different questions about irrational exponents but no one answer what Im searching so please dont mark this as repeated. I have created a fishnet grid (3km x 3km) over a vector polygon.   I now want to clip the fishnet over the vector polygon retaining all grid squares within the boundary of the polygon.   Therefore I want all squares that would typically be clipped into partial squares to remain as whole squares.   Does anybody know how to do this? Is there any physical or mental cost to casting spells? How do function pointers in C work? If I wrote something in plperlu, when would that module be reloaded?  Every time the function ran?  The first time it ran?  Does the Perl DLL get unloaded if it hasn't been used in a while, and then after that it'd be another module reload? Is there an official rule that the minimum damage can't be negative? Reducing size of KML file (after converting from Shapefile) Light is clearly affected by gravity, just think about a black hole, but light supposedly has no mass and gravity only affects objects with mass.  On the other hand, if light does have mass then doesn't mass become infinitely larger the closer to the speed of light an object travels. So this would result in light have an infinite mass which is impossible.  Any explanations? Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable Recall that a countable set $S$ implies that there exists a bijection $\mathbb{N}\to S$. Now, I consider (0,1). I want to prove by contradiction that $(0,1)$ is not countable.  First, I assume the contrary that there exists a bijection $f$, and I can find an element in $S$, but not in the range of $f$. But I can't find such element. How can you construct such $f$? Is it possible to increase Output Field Name length beyond 10 characters? When creating a new Column, the default value for the length of the name is 10. Using the Field Calculator via the Model Builder, I want to include the names of regional areas into the columns which has more than 10 characters.  Can the length of the Output Field Name be increased? Get polynomial interpolation formula Why are there no animals in "The Matrix"? Number of total possibilities for an equation I need to find the number of possibilities for which the following equation exists:  $$x_1 + x_2 + x_3 + \cdots + x_{10} \leq 70$$  Each variable is a non-negative integer.  I tried simplifying the question to the point of finding the number of possible solutions to each equation seperatly:  $$x_1 + x_2 + x_3 + \cdots + x_{10} = 70,$$ which is ${79}\choose{10}$.  $$x_1 + x_2 + x_3 \cdots + x_{10} = 69,$$ which is ${78}\choose{10}$.  $$x_1 + x_2 + x_3 + \cdots + x_{10} = 68,$$ which is ${77}\choose{10}$, and so forth.  Then I thought about adding all of these together. This seems a bit too much work considering that the textbook solution is: ${80}\choose{10}$, and I can't seem to figure out the idiomatic way of approaching these kind of questions.   Any help is greatly appreciated.