Why the purple and red light entering the prism is broken at different angles?
Why do prisms work (why is refraction frequency dependent)?
TV show that starts with debris encompassing Earth I am trying to count the number of bit-strings of length 8 with 3 consecutive zeros or 4 consecutive ones. I was able to calculate it, but I am overcounting. The correct answer is $147$, I got $148$.  I calculated it as follows:  Number of strings with 3 consecutive zeros = $2^5+5\times2^4 = 112$, because the 3 zeros can start at bit number 1, 2, 3, .., 6  Number of strings with 4 consecutive ones = $2^4+4\times2^3 = 48$, I used the same reasoning.  Now I am trying to count the number of bit-strings that contain both 3 consecutive zeros and 4 consecutive 1s. I reasoned as follows:   the strings can be of the following forms: 0001111x, 000x1111, x0001111..thus there are $2+2+2 = 6$ possibilities for bit-strings where the 3 consecutive zeros come first. Symmetrically there are $6$ bit-strings where the 4 consecutive ones come first.  Thus the answer should be = $112+48-12 = 148$.  clearly there's something wrong with my reasoning, if someone could point it out, that would be awesome. Thanks Whenever I am given a system type with a certain transfer function, I am always asked to proceed to find out the 1. impulse response and 2. step response of the system. My question is, what is so special about these two response types that other responses, like for example parabolic response, is not what I am asked to find out? Is there a streaming API for JSON? Is DOM the only way to parse JSON? Adverb sentence query There are three random variables, $x,y,z$. The three correlations between the three variables are the same. That is,  $$\rho=\textrm{cor}(x,y)=\textrm{cor}(x,z)=\textrm{cor}(y,z)$$  What is the tightest bound you can give for $\rho$? Windows 7 finding location of installed program I'm trying to make a command block that spawns an item in front of you if you are holding an item with a specific name. I've got these two working scripts;  /testfor @p[r=10] {Inventory:[{tag:{display:{Name:"Item Name"}}}]}  /testfor @p[r=10] {SelectedItemSlot:0,Inventory:[{Slot:0b,­id:"minecraft:diamond_sword"}]­}   but I can't get them together. The block should only look for an item in the active slot. Statistics module doesn't show the "Enable access log" checkbox I dont know what to do to show "Enable access log" option.  I activated logging all messages and checked all statistics permissions.  Thanks. Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why? $\mathbb R^*$ refers to $\mathbb R$ without zero.  Please explain the statement "$\mathbb R$  is not a group under multiplication, it is a group under addition." in the . Basically:   Why is multiplicative group $(\mathbb R^*, ×)$ a group? Why is $(\mathbb R, ×)$ not group? Why are $(\mathbb R^*, +)$ and $(\mathbb R, +)$ groups? Current  enables one to upgrade to macOS Mojave from a stable release, but I want to try out a fresh installation instead of upgrading with previous data, so that I can assess it better.  I've downloaded an application named "macOS Mojave Beta" from the App Store, and running it would presumably result in an upgrade. Now I wonder what to do next. Would  and booting from it be a good idea, when I'm working with a Beta version? The world I've been playing crashed recently and took the level.dat with it, so I've recreated it, however I have no idea what my seed used to be, and I really don't want to end up with another corrupted game world from exploring with the wrong seed.  How can I recover the seed which was used to generate my world? pm-hibernate freezes and/or fails to resume on Dell XPS 13, 14.04, 3.19 kernel I'm having trouble understanding what I'm doing wrong here: I'm trying to set up two network Locations, one for my home network via my cable modem and a second for Wi-Fi tethering via my mobile phone. What I'd like to be able to do is change the Location (under the Apple menu &gt; Location) and have my Mac automatically connect to the proper Wi-Fi network: either my home network SSID or my WiFi tethering SSID. I defined two locations, switched between them, and set the preferred network list for each location. But when I change the preferred network list for one Location, it changes the list for the other Location as well! Am I doing something wrong or is it really not possible to maintain a separate list of Preferred Networks for each network Location? It seems doubtful it's not possible since just about every other netrok setting depends on the location... I am using OS X 10.7.2. Calculate the area on a sphere of the intersection of two spherical caps What is the function of this circuit? Just wondering if someone can give me an explanation for this capacitor layout - what is it's function? The chip to the right is an ADC.  Circled in blue.    I'm guessing it is well known but i don't know how to search for it. Installing node with apt-get or downloading the Linux Binaries (.tar.gz) What is the difference between installing node.js with 'sudo apt-get install nodejs' or downloading the Linux Binaries (.tar.gz) and following  instructions?  Is the outcome the same? The adjective ones I have heard recently are    forward straightforward forthcoming frank   I was wondering if each of them has positive, negative or neutral meaning?  What are other similar terms that are used for positive, neutral and negative intention? How do I escape a percentage sign in T-SQL? How to print only last column? echo -e 'one two three\nfour five six\nseven eight nine' one two three four five six seven eight nine   how can I do some "MAGIC" do get this output?:  three six nine   UPDATE: I don't need it in this specific way, I need a general solution so that no matter how many columns are in a row, e.g.: awk always displays the last column.