I am preparing a document to send to print. I was asked to add bleed. Is it necessary for a no background document?  The image on the design will not go all the way to the edge.  Or should I add a white background layer and add the bleed to that?
I'm starting to do designs meant for printing, but I'm fairly new to this medium so I don't really understand how bleed works and how much bleed should I specify for:   Business cards Large format prints (42 inches and bigger) Magazines   Should I extend the design into the bleed areas?
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $? How do I show via inductive proof (and without the use of the binomial theorem) that $$ {n\choose k} \in {\mathbb{N}} $$ $$\text{ for  all }\: n,k \in \mathbb{N}_0\: \text{ with }\: n≥k .$$ For my induction proof, I would show that$$  {n\choose k-1}+{n\choose k} = {n+1 \choose k}   $$ is true. However, how do I start the induction correctly with the base cases and the hypothesis? As far as I know, I cannot simply assume $$ {n\choose k-1}+{n\choose k}, $$  so how do I come to this derivation? Which is more polite, "Would you" or "Could you"? Suppose you want to ask someone to do something, say to tell you the way to a station. Which is more polite, "Would you tell me the way to the station?" or "Could you tell me the way to the station?"? If you willingly fall on your turn does it cost movement?  As a DM I'm thinking about how to handle things such as creatures who are immune to being prone, diving into the water from a height, or a flying creature diving off a cliff and taking a fall before taking flight. There are many circumstances where you can fall without taking damage or being knocked prone afterward, and I'm not sure how to determine movement following the dive.  For example, my character walks up to a ledge above a 10 foot drop to the ground below. After taking 5 feet of movement to step off the ledge, I allow myself to fall. When I hit the ground have I used 15 feet of movement or just 5? How do you beta test an iphone app? How can you beta test an iPhone app?  I can get it on my own device, and anyone that gives me a device, I can run it on theirs, but is there a way to do a limited release via the app store for beta testing?  Related: Also, see  on getting your app onto phones without using the App Store. Too many SE sites causes confusion have already been created through .  have already completed their beta stage and are waiting for launch.  are in public beta stage.  are in commitment phase in   proposals are listed in   Now it is really confusing to find a suitable site to ask a question. As an example - I host a blog using . Now I have a question about this hosting. I want to post it in a . Where will I post? I have 2 options available now.     Are developers trying anything to solve this confusing matter? Notification that ‘someone might be watching what you browse’ How prove this inequality $\frac{a}{b+3}+\frac{b}{c+3}+\frac{c}{d+3}+\frac{d}{a+3}\le 1$ Question:  let $a,b,c,d\ge 0$,such $$a^2+b^2+c^2+d^2=4$$ show that $$\dfrac{a}{b+3}+\dfrac{b}{c+3}+\dfrac{c}{d+3}+\dfrac{d}{a+3}\le 1$$  My try: By Cauchy-Schwarz inequality,we have $$\sum_{cyc}\dfrac{a}{b+3}\le\sqrt{(\sum_{cyc}a^2)\left(\sum_{cyc}\dfrac{1}{(b+3)^2}\right)}$$ then we have only prove this $$\sum_{cyc}\dfrac{1}{(a+3)^2}\le \dfrac{1}{4}?$$ This is  not true,in fact, we have $$\sum_{cyc}\dfrac{1}{(a+3)^2}\ge \dfrac{1}{4}?$$ because we have $$\dfrac{1}{(a+3)^2}\ge\dfrac{5-a^2}{64}$$ this is true because $$\Longleftrightarrow \dfrac{(a-1)^2(a^2+8a+19)}{64(a+3)^2}\ge 0$$ so $$\sum_{cyc}\dfrac{1}{(a+3)^2}\ge\sum_{cyc}\dfrac{5-a^2}{64}=\dfrac{1}{4}$$ can see:  This methods is from: can  see:  By the way I have see this three variable inequality  let $a,b,c$ be non-negative numbers such that $$a^2+b^2+c^2=3$$  show that $$\dfrac{a}{b+2}+\dfrac{b}{c+2}+\dfrac{c}{a+2}\le 1$$  proof: By expanding,the inequality becomes $$ab^2+bc^2+ca^2\le abc+2$$ without loss of generality,assume that  $$\min(a,b,c)\le b\max(a,b,c)$$ then \begin{align*} 2-ab^2-bc^2-ca^2+abc&amp;=2-ab^2-b(3-a^2-b^2)-ca^2+abc\\ &amp;=(b^3-3b+2)-a(b^2-ab+ca-bc)\\ &amp;=(b-1)^2(b+2)-a(b-a)(b-c)\ge 0 \end{align*} Equality occurs for $(a,b,c)=(1,1,1)$ and also for $(a,b,c)=(0,1,\sqrt{2})$ or any cyclic permutation.  so my Four-inequality  variable inequality,can use this methods $$\dfrac{a}{b+3}+\dfrac{b}{c+3}+\dfrac{c}{d+3}+\dfrac{d}{a+3}\le 1$$ $$\Longleftrightarrow a^2cd+3a^2c+3a^2d+9a^2+ab^2d+3ab^2+abc^2-abcd+3ac^2+9ac+3b^2d+9b^2+3bc^2+bcd^2+3bd^2+9bd+9c^2+3cd^2+9d^2-81\le 0$$ $$\Longleftrightarrow a^2cd+3a^2c+3a^2d+ab^2d+3ab^2+abc^2+3ac^2+9ac+3b^2d+3bc^2+bcd^2+3bd^2+9bd+3cd^2\le 45$$ $$\Longleftrightarrow a^2(cd+3c+3d)+ab^2d+3ab^2+abc^2+3ac^2+9ac+3b^2d+3bc^2+bcd^2+3bd^2+9bd+3cd^2\le 45$$ $$\Longleftrightarrow (4-b^2-c^2-d^2)(cd+3c+3d)+ab^2d+3ab^2+abc^2+3ac^2+9ac+3b^2d+3bc^2+bcd^2+3bd^2+9bd+3cd^2\le 45$$  Then  I can't  Thank you  very  much How do I bypass "this connection is not private" warnings in safari? I've seen many variants of this problem online, but not quite the same as this, so I don't believe this is a duplicate.  The famous differential equation problem models a skydiver jumping out of a plane as  $$m \frac{dv}{dt} = -mg-cv$$ where m is the mass of the skydiver, g is acceleration due to gravity (9.81 m/s) and c is the coefficient of air resistance.  Here is my question:     Suppose the skydiver exits the stationary helicopter at an altitude of 2000m and opens the parachute at 500m. For this exercise, the parachute opens instantaneously. Suppose m= 70kgs, the coefficient of air resistance is c = 14 for a free falling body and c = 105 after the parachute opens. When does the skydiver open the parachute? When does the Skydiver hit the ground?   So my attempt at a solution kinda starts like this, but this is where I get stuck:  Let's assume that s(t) is the distance the body falls in time t from its initial point of release, then $v = \frac{ds}{dt}$ and $a = \frac{dv}{dt} = \frac{d^2s}{dt^2}$. Thus we have a second order differential equation: $m \frac{d^2s}{dt^2} = -mg-c\frac{ds}{dt}$. By simply manipulation, we get $m \frac{d^2s}{dt^2} + c\frac{ds}{dt} = mg$. I originally started thinking of finding the integrating factor, however, this seems more complicated and won't help produce the equation that I need.  Would anyone be able to help? Much thanks in advanced! Is there anything to do during an 8 hour after-midnight layover in Dubai? We are planning a trip with an 8 hour layover in Dubai spanning from 1am-9am. I am thinking about going to see the city, but is it worth it to do it given the very late night hours? Will at least the outside attractions accessible?   Will Burj Khalifa be visible in the middle of the night?  Will at least some of the malls be open?  Will there be anything to do at night?  I have seen other questions about layovers in Dubai (), but none of them is asking about a night-only stay. How do I get the Minecraft GUI scale to go back to Auto? I have been playing Minecraft, and I went into the settings to see what could be changed. I was in display and I saw the GUI scale was set to "Auto", which was fairly large. I cycled through the scales until I got back to auto, but the GUI scale was stuck at normal size and wouldn't allow me to make it large again. I know this isn't such a big problem, but I really like big font and this is a constant bother to me. Meaning of convolution? I have installed Apache(LAMP) web server on my ubuntu machine and I want to do the above mentioned thing.I have tried creating symbolic links in the /var/www directory but it only shows files but not directories inside the directory linked.I want to redirect /var/www to my home folder so that I can access all the files and directories contained therein.Please help me. I can't download apps from the Play Store on my Android device (maybe due to a network issue), so I'm wondering how could I download the APK file of an app on my PC from ? Mesh imported to Unity is inside out Visited links within spoilers are not hidden anymore Is there a Term to describe the relationship between two people when they share an Alma Mater?  For example; Neil Armstrong is an alumnus of Purdue University. I am an alumnus of Purdue University. Both Neil and I are alumni of Purdue University, which is to say we share an alma mater. So, I'm looking for a term to describe my relationship to to Neil with out needing to explicitly reference the university. Is co-alumni a real term? Is it appropriate to say that Neil and I are co-alumni? Is there something better? Further, is there a way to specifically describe the relationship between two people from the same graduating class?  Thank You in advance! I just found this identity but without any proof, could you just give me an hint how I could prove it? $$2^n = \sum\limits_{k=0}^n 2^{-k} \cdot \binom{n+k}{k}$$  I know that $$2^n = \sum\limits_{k=0}^n \binom{n}{k}$$ but that didn't help me More than one optional argument for newcommand The \newcommand macro allows to use an optional argument for the first parameter #1 with:  \newcommand{\mycommand}[3][defaultfor1]{blah blah blah}   Is it possible to have more than one option with \newcommand? Given the functional dependencies of a relation is there more then one way to normalize it?