i want to wire two lights with the power coming in the first light go to the second light and then to a switch
How do I wire two lights with a switch?
Verify the identity: $\tan^{-1} x +\tan^{-1} (1/x) = \pi /2$ Verify the identity: $\tan^{-1} x + \tan^{-1} (1/x) = \frac\pi 2, x &gt; 0$  $$\alpha= \tan^{-1} x$$  $$\beta = \tan^{-1} (1/x)$$  $$\tan \alpha = x$$  $$\tan \beta = 1/x$$  $$\tan^{-1}[\tan(\alpha + \beta)]$$  $$\tan^{-1}\left [{\tan\alpha + \tan\beta\over 1 - \tan\alpha \tan\beta} \right]$$  $$\tan^{-1}\left[ {x + 1/x\over 1- x/x }\right]$$  $$\tan^{-1}\left[{x + (1/x)\over 0} \right]$$  I can't find out what I'm doing wrong.. I have to do proof of $(a+b)^n$ and $(a+b)^{n+1}$ with mathematical induction.  I finished the first one $(a+b)^n = a^n + na^{n-1}b+\dots+b^n$.  I however have trouble with the second one, I don't know what to start exactly. Any help/hints? Generic flatness on modules I am looking for a stronger notion of generic flatness. Let $A$ be a Noetherian ring, $M$ a finitely generated module over $A$. Suppose there exists a maximal ideal $m$ of $A$ such that $M_m$ (the localization of $M$ at $m$) is $A_m$-flat (here $A_m$ is the localization of $A$ at $m$). Does there exist an open neighbourhood $U$ of $\mathrm{Spec}(A)$ containing the point corresponding to $m$ such that for all point (not necessarily closed) $u \in U$, the localization of $\tilde{M}$ (the coherent sheaf corresponding to the module $M$) at $u$ is $\mathcal{O}_{U,u}$-flat i.e., $\tilde{M}|_U$ is $\mathcal{O}_U$-flat? Removing file / folder link after using "Save As..." then "Web Page, complete" When you right-click save-as a web page in FF, the page is saved along with a folder containing any associated media that page needs (images, js, etc).  My problem is that I want to reorganise the associated media folder, but wherever I move this folder, the saved .html file is moved as well. ARGH!   I can rename each folder, which breaks the "link" between html file and media folder, but there must be a cleaner way to do it. Does anyone else know? How to check iOS version? I have association bonus on superuser.com. After that I've started a bounty worst of 50 rep and earned more than 10 rep. Now I have 89 rep (38 of which is earned at superuser which is more than 10) but still not able to answer protected questions.  So, currently new user with 10 rep can answer protected question and I with 89 (38) rep can't.   How does it work now: after registration on new Stack Exchange site you get 101 rep Association Bonus and are able to answer protected questions only when you have 111+ rep on that site. How should it work: after registration on new stackexchange site you get 101 rep Association Bonus and are able to answer protected questions only when you have earned 10+ rep on that site. Windows Managers vs Login Managers Vs Display Managers Vs Desktop Environment I posted a  and noticed people weren't distinguishing correctly between many of these things: Windows Managers vs Login Managers Vs Display Managers Vs Desktop Environment.  Can someone please clear this up, i.e. tell us the difference between them and how they are related perhaps?  What category does Xorg fall under?  What about Gdm/Kdm/Xdm?  People also talk about X.  What is X? Firefox running with rare arguments I got this output from ps aux|grep firefox command:  $ ps aux|grep firefox auraham   5443 17.3 11.0 2600628 426484 ?      Sl   18:10   0:54 /usr/lib/firefox/firefox auraham   5496 24.0 17.9 2558108 691700 ?      Sl   18:10   1:15 /usr/lib/firefox/firefox -contentproc -childID 1 -isForBrowser -intPrefs 5:50|6:-1|18:0|28:1000|33:20|34:10|43:128|44:10000|49:0|51:400|52:1|53:0|54:0|59:0|60:120|61:120|91:2|92:1|106:5000|117:0|119:0|130:10000|155:24|156:32768|158:0|159:0|167:5|171:1048576|172:100|173:5000|175:600|176:4|177:1|186:2|200:60000| -boolPrefs 1:0|2:0|4:0|26:1|27:1|30:0|35:1|36:0|37:0|38:0|41:1|42:1|45:0|46:0|47:0|48:0|50:0|55:1|56:1|57:0|58:1|62:1|63:1|64:0|65:1|66:1|67:0|68:1|71:0|72:0|75:1|76:1|80:1|81:1|82:1|83:0|85:0|86:0|87:1|88:0|93:1|94:0|100:0|105:0|108:1|109:0|111:1|112:1|114:1|118:0|120:0|122:0|124:1|125:1|131:0|132:0|133:1|135:0|146:0|153:0|154:0|157:1|160:0|162:1|164:1|165:0|170:0|174:1|179:0|180:0|181:0|182:1|183:0|184:0|185:1|188:1|192:0|193:0|194:1|195:1|196:0|197:1|198:1|199:1|201:0|202:0|204:0|212:1|213:1|214:0|215:0|216:0| -stringPrefs 3:7;release|134:3;1.0|151:332;  ¼½¾ǃː??։֊׃״؉؊٪۔܁܂܃܄ᅟᅠ᜵           ???‐’․‧??????? ‹›⁁⁄⁒ ⅓⅔⅕⅖⅗⅘⅙⅚?⅜⅝⅞⅟∕∶⎮╱⧶⧸⫻⫽⿰⿱⿲⿳⿴⿵⿶⿷⿸⿹⿺⿻　。〔〕〳゠ㅤ㈝㈞㎮㎯㏆㏟꞉︔︕︿﹝﹞?．／｡ﾠ???￼�|152:8;moderate| -greomni /usr/lib/firefox/omni.ja -appomni /usr/lib/firefox/browser/omni.ja -appdir /usr/lib/firefox/browser 5443 true tab auraham   5694  0.0  0.0  15444  1092 pts/2    S+   18:15   0:00 grep --color=auto firefox   According to , this error occurs after firefox crashes. However, every time I run Firefox again, that large line of arguments appears too.  I already try these things:   Run Firefox with addons disabled Reinstall Firefox (sudo apt-get purge firefox; sudo apt-get install firefox)   However, it did not work.  Is it possible to remove such a line of arguments? Lie algebra of $\left(\begin{smallmatrix}a & b\\ & a^2\end{smallmatrix}\right )$ in $GL_2(\mathbb{R})$ I'm working on the question     Let $G$ be the group of invertible real matrices of the form $\left [\begin{array}{c c}a &amp; b\\ &amp; a^2\end{array}\right ]$. Determine the Lie algebra $L$ of $G$, and compute the bracket on $L$.   I'm familiar with how to derive the Lie algebra for a linear group like $U_n$, $SU_n$, etc. but I'm not sure what to do in a more explicit case like this. Strategies to denest nested radicals $\sqrt{a+b\sqrt{c}}$ I have recently read some passage about nested radicals, I'm deeply impressed by them. Simple nested radicals $\sqrt{2+\sqrt{2}}$,$\sqrt{3-2\sqrt{2}}$ which the later can be denested into $1-\sqrt{2}$. This may be able to see through easily, but how can we denest such a complicated one $\sqrt{61-24\sqrt{5}}(=4-3\sqrt{5})$? And Is there any ways to judge if a radical in $\sqrt{a+b\sqrt{c}}$ form can be denested?  Mr. Srinivasa Ramanujan even suggested some CRAZY nested radicals such as: $$\sqrt[3]{\sqrt{2}-1},\sqrt{\sqrt[3]{28}-\sqrt[3]{27}},\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}, \sqrt[3]{\cos{\frac{2\pi}{7}}}+\sqrt[3]{\cos{\frac{4\pi}{7}}}+\sqrt[3]{\cos{\frac{8\pi}{7}}},\sqrt[6]{7\sqrt[3]{20}-19},...$$ Amazing, these all can be denested. I believe there must be some strategies to denest them, but I don't know how.  I'm a just a beginner, can anyone give me some ideas? Thank you. I want to argue that argue that $\pi(\alpha)=\alpha^3+3\alpha+3$ is an irreducible polynomial over the finite field with 5 elements $\mathbb{F}_5$. My approach was just to check that $\pi$ has no roots in $\mathbb{F}_5$. Is this right? algebra - matrices and polynoms $T:\mathbb P_2[x]↦\mathbb P_2[x]$ s.t.:   $T(1)=3+2x+4x^2$, $T(x)=2+2x^2$, $T(x^2)=4+2x+3x^2$.   Is there base $B$ of $\mathbb P_2[x]$ that $[T]_B$= \begin{bmatrix}     2 &amp; 0 &amp; 0\\     -1 &amp; 1 &amp; 0\\     5 &amp; 0 &amp; 4\\  \end{bmatrix}  Please help. Thanks. Series $\frac{x^{3n}}{(3n)!} $ find sum using differentiation Find sum of the series $$\sum_{n=1}^{\infty}\frac{x^{3n}}{\left(3n\right)!}$$ using differentiation. So far I found that $$S(x)+1=S'''(x)$$ but it does not help. Then I tried different interesting ideas  like $$S(x)+S'(x)+S''(x)=e^x-1\,.$$Maybe if I get the third equation it will allow me to construct a kind of differential equation. Then, by solving it, obtain $S(x)$. I used to say "sharp sign" to refer to the # sign.   Today a friend told me that the correct term is number sign or hash sign or even just hash.  What is the difference between these options and what's the correct usage of the names for this sign? I only occasionally use the Fixed Zoom In/Out buttons on the Tools toolbar of ArcMap and had always assumed that they zoomed in/out by a set scale factor.  However, using ArcGIS for Desktop 10.2, I just set my scale to be 1:10,000,000 and then hit the Fixed Zoom In button 10 times while recording the subsequent scale each time and was surprised to see:  10,000,000 8,000,000 6,000,000 5,000,000 4,000,000 3,000,000 2,500,000 2,000,000 1,500,000 1,250,000 1,000,000   Dividing each scale denominator by its successor shows a sequence of: 1.25, 1.33, 1.2, 1.25, 1.33, 1.2, 1.25, 1.33, 1.2  Curious about what happened in between the scales above I experimented a little to discover that the first issuance of the Fixed Zoom In button simply takes the scale to the first of those listed above and then starts following the same pattern.  Try starting with 1:8,000,001 to see ...  8,000,001 8,000,000 6,000,000 5,000,000 4,000,000 3,000,000   This seems like quite a neat solution, but not one that I had realised was in place - does anyone know if it has been documented anywhere?    I've looked in the Online Help without success.  In answer to @DevdataTengshe, the scales currently in my available list (see below) seem to bear no relation to those used by Fixed Zoom In/Out.    However, when I add 1:7,500,000 into my available list it does seem to insert that as an additional scale step ...  10,000,000 8,000,000 7,500,000 6,000,000 5,000,000 4,000,000   This makes the algorithm being used even more mysterious to me. Is it possible to have several different views of one scene and set them as named "presets"? If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$ Let $1\leq p &lt; \infty$. Suppose that    $\{f_k\} \subset L^p$ (the domain here does not necessarily have to be finite),  $f_k \to f$ almost everywhere, and  $\|f_k\|_{L^p} \to \|f\|_{L^p}$.    Why is it the case that $$\|f_k - f\|_{L^p} \to 0?$$   A statement in the other direction (i.e. $\|f_k - f\|_{L^p} \to 0 \Rightarrow \|f_k\|_{L^p} \to \|f\|_{L^p}$ ) follows pretty easily and is the one that I've seen most of the time. I'm not how to show the result above though. Choosing coordinate system to use in South Africa? What are the principal datums and projections used in South Africa including the names of geodetic datums and their projections? What's the best way to develop old, exposed film? A friend of mine just found 3 rolls of exposed 135 (i.e. 35mm) film. They are at least 10 years old. He'd like to know if it is even worth taking them to the local hour photo lab but also if he should give them any special instructions. Is there a software in Ubuntu that can analyse the cross references (theorems, lemmas, equations, etc.) in a tex project? There are some software to analyse the cross references among codes (Java or C++). I used to use a software for code analysis under Windows many years before. But I can't remember the name. On linux, an example might be LXR Cross Referencer.   Is there a similar tool that can analyse the latex files to find out the cross references of theorems, lemmas, propositions and equations?