I hope this kind of question will qualify for the purpose of this website. What is the purpose of alternate levels in BIT.TRIP. Runner 2 ? By alternate levels I mean those levels that stray from the "main path" on the world map and you have to "pay" some gold to play them.  It seems to me that the quantity of gold demanded is not so big and you can easily play them normally, also they are not more difficult (like the vault ones) or special in any other way.  EDIT: It looks to me that I was not so clear on my question. I was not talking about the alternate exits, I was talking about the levels on the WORLD MAP that are  "locked" and you have to pay gold to get to play them.
Is there any point in taking the alternate exits in Bit Trip Runner 2?  I can't see any benefit to doing so in terms of unlocking a different path in the overworld, so is it just for your own benefit?
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed? Last year I hired someone to do some work for our website but accidentally lost the PSD files since then. It's a fairly basic concept but I am fairly inexperienced with using masks.  How can I create the black circular gradient area as shown in this image below? I need to get as close as possible where it matches existing images on the site, why I am hoping its not too hard.  Thank you! What are the rules and limits of Accio spell? We know that Accio spell (aka ) has some limits:   It can be blocked (e.g. Harry couldn't Accio the Diadem in RoR in Deathly Hallows). Many more failures are listed on Wikia.   But what are the exact full rules and limitations governing the spell in Harry Potter world?   Distance?  Line-of-sight?  Knowing exact or approximate location?  Specificity of item (e.g. "Accio Broom" seemed to work for Weasleys in OotP to bring their locked-up brooms - why not just a random broom?) Types of Accio-able stuff? Can you Accio water? Lump of earth? Gases/liquids/etc...? Can you Accio based on jQuery selector (or an SQL where clause), for lack of a better description? E.g. "Accio the book that has the word 'Flammel'"? "Accio biggest green ball from this room"? Can you Accio ALL items of a kind? (the reason I thought of this whole question was seeing "Accio all guns" comment in ). Can you Accio vague stuff? ("Accio meal"). Other rules that can be inferred.   NOTE: While Wikia article has some of the info, it is clearly very lacking in details on specific rules based on specific instances in canon. I'm looking for a fully comprehensive, organized ruleset for the charm, not merely 1-2 tidbits in Wikia article. What does \s! do? 1st example:  \starttypescript [\s!serif] [paratype]   \definefontsynonym [ParatypeSerif-Regular] [\s!name:PTSerif-Regular] [\s!features=\s!default]   \definefontsynonym [ParatypeSerif-Italic] [\s!name:PTSerif-Italic] [\s!features=\s!default]   \definefontsynonym [ParatypeSerif-Bold] [\s!name:PTSerif-Bold] [\s!features=\s!default]   \definefontsynonym [ParatypeSerif-BoldItalic] [\s!name:PTSerif-BoldItalic] [\s!features=\s!default] \stoptypescript   2nd example:  \definefont[SerifS][\s!file:GenBkBasR at \smallfontsize]   Is \s! only related to fonts? Should I use it in my typescript files? How do I rigorously show $f(z)$ is analytic if and only if $\overline{f(\bar{z})}$ is? I'm doing a bit of self study, but I'm uncomfortable with a certain idea. I want to show that $f(z)$ is analytic if and only if $\overline{f(\bar{z})}$ is analytic, and by analytic I mean differentiable at each point. Here $f$ is a complex valued function.  What I do is write $f(z)=u(x,y)+iv(x,y)$, where $u$ and $v$ are real functions of two variables. Then $\overline{f(\bar{z})}=u(x,-y)-iv(x,-y)$.  These two forms look very similar, in the sense the one function being differentiable should immediately imply the other is differentiable, since the only thing really changing might be a $-$ sign popping out due to the chain rule.   How can I more rigorously express that $f(z)$ is analytic iff $\overline{f(\bar{z})}$ using this? Many thanks. let $x,y,z,w&gt;0$,show that $$(x+y)^3+(y+z)^3+(z+w)^3+(w+x)^3\ge 8(x^2y+y^2z+z^2w+w^2x)$$  it seem use AM-GM inequality to solve it,But I can't it,Thanks What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$? For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical solution of ordinary least squares. Or, for PCA, its eigenvectors are the principal components of the data.  I understand how to calculate $A^TA$, but I was wondering if there's an intuitive interpretation of what this matrix represents, which leads to its important role? Moment of inertia: why $\mathrm{dI}=r^2\mathrm{dm}$ instead of $\mathrm{dI}=m\mathrm{dr^2}$? Does payment in goods count as "income" for tax purposes? Can someone help me elucidate the definition of "income" from a tax perspective? More specifically, if Joe is paid for his work in avocados instead of dollars, then would Joe be exempt from paying any income tax for the year? Or would the value of avocados earned for the year be translated into dollars which would then be considered Joe's annual income? If so, what guidelines would one use to make this translation? (Make the assumption that Joe does not sell the avocados (for dollars) at a later date and either eats them or trades them for other real property)  What if he was paid in gold instead of avocados? Is there a way to disable the hotkeys? Brie Cheese and expiration date I have a Brie Cheese that has not been opened. It shows an expiration date that is 6 weeks ago. Is it still safe to eat? Minimize the sum of distances between two point and a circle Let's $A$,$B$ and $O$ be random point in a plane, such that they are not colinear. Let's $c$ be a circle centered on $O$, such that points $A$ and $B$ are outside of it. Find a point $X$ that lies on the circle $c$ and the sum $AX + BX$ is minimal.  First I tried to minimize the function:  $$f(x,y) = \sqrt{(A.x - x)^2 + (A.y - y)^2} + \sqrt{(B.x - x)^2 + (B.y - y)^2}$$ with  constraint $$g(x,y) = x^2 + y^2 - r^2 = 0$$  By moving $O$ to $(0,0)$ and do the same with $A$,$B$ so the relative distance will not change.  But these works when we know the coordinates of $A$,$B$ and the radius of the circle. Yet this isn't the right way because the problem is to construct that point.  Later I tried to approach using geometry.  The smallest distance from the point $A$ to the circle is the intersection of the circle $c$ and the ray $OA$, this is the same for $B$. Then we construct circles centered on $A$ and $B$ that are tangent to $c$. If the two circle intersect we'll get a common point for the both $A$ and $B$ and the distance will be minimal. Using computer I find the point X should be somewhere around the intercetion of the circle $c$ and the ray from $O$ to the new point.   Sometimes the optimal point differs just a bit and also this method fails when the two circles do not intersect each other Suppose $X$ is binomial $B(n,p)$. How can I find the probability that $X$ is even ?  I know $$P(X = k ) = \frac{ n!}{(n-k)!k!} p^k(1-p)^{n-k} $$  where $X=1,....,n$. Are they just asking to find $P(X = 2m )$ for some $m &gt; 0$ ? How to convert decimal to hexadecimal in JavaScript Why doesn't Spotlight show invisible files that I know exist? I am running Mac OS X 10.8 (Mountain Lion) and had to edit an invisible file as part of an Android project. While I eventually found it, Spotlight was of no help, since it could not find an invisible file when searching for the exact name (.classpath) and with the 'File Visibility' option set to 'Visible or Invisible'.  Why didn't Spotlight work in this instance? Hi there! I'm looking for a help drawing this diagram. Any ideas? Say I have a module $M$ over a ring $R$ that is   $1.$ finitely-generated, i.e. $\exists$ finite $X \subset M$ such that $M = \sum_{i=1}^{n} Rx_{i}, x_{i}\in X$ (but $X$ is not necessarily free)  $2.$ free, i.e. $\exists$ a basis $Y \subset M$ a.k.a. $Y$ is free and generates M, (but $Y$ is not necessarily finite).  Now I want to show, that there exists a finite basis for $M$. For vector spaces, this would obviously be trivial, but for some  $R$-Modul, I'm not sure how to proceed.   Furthermore, is every minimal generating subset of $M$ a basis? Can my familiar use a Ring of Spell Storing? Can the familiar options from the Pact of the Chain warlock (quasit, imp, sprite, pseudodragon) attune with a ring of spell storing?  If so, can I cast a spell requiring concentration into the ring and then have the familiar maintain concentration on the spell? Most of the recipes I'm using (mainly Modernist; stocks, caramelized vegetables, confit) suggest cooking at 15psi. My pressure cooker has two settings 12psi and 7psi. I've always had success just using 12psi in recipes where it says 15psi. However recently the 12psi mode has broken on my PC. I can now only cook at 7psi. How can I convert my recipes to use this lower pressure?  For example I would cook a chicken stock at 12psi for 90mins, I presume at 7psi the cooking time would need to be longer but by how much?