I bought some lights off of Amazon in both the &quot;White&quot; and &quot;Warm white&quot; options (). I think they are 3 V and operate at 15 mA, whatever that means. I want to wire the lights in a series/parallel circuit. Key:  Red: Positive Yellow: Negative / Ground Blue: Resistor (Green numbers are for ohms - See below) Green: Switch Grey: Lights with back numbers (Lights #3&amp;4 are &quot;White&quot; and Lights 1,2,5,6,7 are &quot;Warm White&quot;). Purple: 9 V battery   The problem: Only some lights will light up. Some only partially light up, etc. (Note: this is when I had fewer resistors in weird spots, not relevant anymore) The solution: Add a resistor (Blue in diagram) Where I get stuck: What resistors do I need? The resistors that come with the lights (Labeled &quot;5.1V-9V use&quot;) power one just fine (Like #5), but don't power the pairs well (Every light but #5). I think I need a 200 Ω (or maybe 180 Ω) resistor on the dual pair. And 390 Ω or 100 Ω on the single one. But I honestly have no clue, and each person I ask says something different. The ones I'm using now for the lights that work are, I believe, 100 MΩ, but that makes no sense.  Also, I have no clue what side goes first...   Can anyone help me figure out what resistor (and 5-band color) would be needed for both the 1 and 2 light combinations? I am not sure if the ones that came with the lights are the best or not. Thanks! I'm also brand new at this, so sorry if the answer is obvious.
So I'm trying to power 2 of these  together in series. I know that I have to add the voltage of the two lights together and get a resistor that restricts the power to that level. I have a 9V battery and the lights are 3V each. I brand new to all of this, and understand almost nothing, so any help would be appreciated. Can someone help me choose the correct resistor (And how to identify that resistor with the color branding thing) so two of those lights listed above can be wired in series? Thanks!
Dial PPPoE connection on Windows startup Is there a way to automatically dial a PPPoE connection on startup? In Mac OS X, this is done automatically after login. It was also possible in Windows XP: when creating a new connection, it also created a shortcut to it on the desktop. Adding it to the startup folder and setting it to not prompt for credentials solved the problem.  But in Vista and Windows 7, there are no shortcuts to the newly created connections, so I can't do the same thing here. Is there any other way to do this? Could anyone provide an example of a nonempty subset $U$ of $R^2$ such that $U$ is closed under scalar multiplication, but $U$ is not a subspace of $R^2$ Prove that for $ 0&lt;x&lt; \pi $, $$ \quad S_n(x) = \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} &gt;0 \quad \forall n = 1,2,... $$  Having trouble with this problem. This is an olympiad-style question, so an answer that doesn't use calculus or analysis would be preferred. A possible approach is induction, but for this we need to find a function in terms of $n$ and $x$ so that we can actually use the inductive step. If anyone has any ideas they would be appreciated.  If you really want to go down the calculus route (at this point I don't mind), then $ S_n' (x) = \cos x + \cos 3x + ... +\cos((2n-1)x) $ , which you can find a closed form for, but I don't know how useful that is. What is the standard solution in JavaScript for handling big numbers (BigNum)? Using sObject.get() to fetch a field value from a related parent object I have a contact in a generic sObject in apex and while I'm able to easily get detail field values using   sObject.get('MyContactField__c')  I'm not able to get fields off the related parent object, and I'm sure the related field is in memory, based on the debug logs. 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Just trying to  figure out something basic.   How can you tell where you are installing a program. For example I just installed Sphinx search engine by placing the tarball that I downloaded from their site to my:  /home/sphinx   directory. I created the sphinx directory to place that tarball in. Then I ran these commands:  tar xvzf sphinx-0.9.8.1.tar.gz cd sphinx-0.9.8.1/ ./configure --with-mysql-includes=/usr/include/mysql --with-mysql-libs=/usr/lib/mysql   and then these:  make sudo make install   Now I have a lot of files sitting in the directory where I ran these commands. Is this my Spynx installation or did it install somewhere else?  In windows if you run an installer (.exe file) anywhere the program will still install in your C:\Program Files directory. Does something similar apply to linux where all programs are installed in a central place, or can you install programs anywhere on the system.  Questions   I would prefer to keep all my installed programs in one place so what is the right place for this in terms of best practice. In other words what is the Linux equivalent of C:\Program Files? And how does one always install at this location, is it just a matter of placing the tarball and running the install commands from this location? What about if I use sudo apt-get to install a package. How can I point to this location to tell apt-get to always install there? How to work with iAds using xcode 3.1.3 I do as follows  $(1+x)^n= \binom{n}{0}+\binom{n}{1}x+\binom{n}{2}x^2+...+\binom{n}{n}x^n$   differentiating in both sides  $n(1+x)^{n-1}= \binom{n}{1}+2\binom{n}{2}x+3\binom{n}{3}x^2...+n\binom{n}{n}x^{n-1}$  then, for $x=1$  $n \cdot2^{n-1} = \sum_{k=1}^{n}k\binom{n}{k}$  From here, I don't know how to proceed, I have tried to multiply both sides for $(1+x)$ to make $n \cdot2^{n}$ but then the summatory changes, I don't know how to prove the equality. Some time ago, I baked a cake (Sachertorte to be exact). The taste and texture was fine, so my recipe is okay.  My biggest issue was the shape. In the middle it was really a lot higher than on the sides. I would like to redo it in the near future, but preferably with a flat(ter) surface. (Especially since I put icing on top and I don't want it to drip off this time.)  Anyone knows the cause of my problem, or even better a solution? I think I put enough butter on the side of my springform pan, in case this is an option. Is there a way to display a player name in /tellraw command? like the title says, I'm looking for a way to display a player name in a /tellraw command which is run by a command block. Example:  /tellraw @a {"text":"","extra":[{"text":"A player has won the game!","color":"blue"}]}   And the output is something like this:  A player has won the game!   But I want the output to be something like  JasonSPQR has won the game!   Using the @p parameter When is it appropriate to end a question without a question mark? I have seen both usages.    Stay tuned on our Facebook page to know more  Stay tuned to our Facebook page to know more    But don’t know which one is more appropriate. Please help me figure it out. Thanks Why isn't an infinite, flat, nonexpanding universe filled with a uniform matter distribution a solution to Einstein's equation? Merging arrays with the same keys Full-wave bridge rectifier with capacitor filter and ripple voltage According to various sources, the ripple voltage of a full-wave bridge rectifier is   $$ V_r = \frac{V_s}{2}fCR $$  where \$V_s\$ is the peak of the input voltage source, \$f\$ is the frequency, \$C\$ is the capacitor and \$R\$ the resistor.  I have simulated this circuit on PSPICE, circuitlab, and built it in real life:   \$R\$ is \$4.7K\$ and \$C\$ is \$10 uF\$. Voltage source is sine wave with \$0 V\$ offset, \$5V\$ amplitude and \$40 Hz\$ frequency.  All 3 experiments give me a ripple voltage of approximately \$0.65V\$, but the formula gives me \$1.330 V\$ (twice as much).  What am I missing? How do electromagnetic waves wave? Electromagnetic waves have a physical crest and trough as observed in microwaves and radio waves. I understand that is electromagnetic field vectors that wave, not the photon. But how do they wave? What does causes them to change direction? OpenSSL and error in reading openssl.conf file I want to know if my server is running Subversion 1.5.  How can I find that out?  Also would be nice to know my SVN client version number. svn help hasn't been helpful.  Note: I don't want my project's revision number, etc. This question is about the Subversion software itself.