What are the values of the mass $m$ such that $mx''+25x = 12 \cos(36\pi t)$ will exhibit resonance?
Differential equation with resonance
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction I am just starting out learning mathematical induction and I got this homework question to prove with induction but I am not managing. $$\sum_{k=1}^n\frac1{\sqrt k}&lt;2\sqrt n$$ Please help! Replace a xtick by a letter in Tikz Unity Tweak tool fails to start with the error "com.canonical.unity.webapps schema is missing" com.canonical.unity.webapps   In order to work properly, Unity Tweak Tool recommends you install the necessary packages Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism. I think I'm supposed to prove that both $T$ and $I_V$ are isomorphic, but I'm not sure and even if that's the right way to go, how am I supposed to prove that $I_V$ is isomorphic. Or am I going about this all wrong. Please help. $X$ is a Hausdorff space and $\sim$ is an equivalence relation.  If the quotient map is open, then $X/{\sim}$ is a Hausdorff space if and only if $\sim$ is a closed subset of the product space $X \times X$.  Necessity is obvious, but I don't know how to prove the other side. That is, $\sim$ is a closed subset of the product space $X \times X$ $\Rightarrow$ $X/{\sim}$ is a Hausdorff space. Any advices and comments will be appreciated. How do I kill mobs using /kill without them dropping loot? I have a spawn area I am hoping to make a safe haven, so I have a command block on a clock that kills each hostile mob type. This works to keep the place free of any hostile mobs, however every night I see rotten flesh, bones, arrows, and string everywhere.  I would like to add something to my command blocks so that they are killed without dropping loot. How can I accomplish this?  Note that I want mobs to drop loot generally elsewhere in the world, so /gamerule doMobLoot false will not do the trick for me. I'm hoping for a command that only applies to the mobs killed by the command block, and not anything else. What does "Suit yourself" mean? Proof that in a field $x=0$ is equivalent to $x=-x$ Let $F$ be a field and $x\in F$. If $x=-x$ and $1\neq -1$, then $$0=\frac{x+x}{1+1}=\frac{1+1}{1+1}x=x.$$ This means that the statement in the title is true if and only if $1\neq -1$. But how do we know that $1\neq -1$ for an arbitary field? Books about matroids Could you recommend any approachable books/papers/texts about matroids (maybe a chapter from somewhere)? The ideal reference would contain multiple examples, present some intuitions and keep formalism to a necessary minimum.  I would appreciate any hints or appropriate sources. Add/Show comments focuses text box by default If I open a post using the mobile theme, which has many comments, there is a link at the footer "add/show n more comments". If this link is clicked, the comments are loaded and displayed.   At the moment the text area is automatically focused which is not a great experience (in my opinion), as you have to close the editor and scroll back to the top if you just wanted to read the comments, without adding a new one.  Would it be possible to either   not focus the text area by default and to load only the comments add a new link for adding a comment How can I learn the basics of SharePoint 2013 in a few days? I have very little knowledge of SharePoint, and want to learn about SharePoint 2013.  Most of the resources that I've found are either about what's new in 2013, or they have a bunch of links to SharePoint 2010.  I also don't have the time to read a thousand page book.  A hundred or so would be fine.  Can anyone recommend a resource (site / book / video / tutorial) for a beginner to learn the basics of SharePoint 2013 in a few days?  I've downloaded a Kindle book, "Getting Started With SharePoint 2013."  It's perfect for absolute beginners, who just want to know how to upload &amp; download documents, but I'm looking for more than that. How to remove the "Could not connect to the iTunes store" error message when your network does not allow access to the iTunes Store Loading .sql files from within PHP Random place change in row with restrictions Can I mask an input text in a bat file? What is tail recursion? Whilst starting to learn lisp, I've come across the term tail-recursive. What does it mean exactly? As I show below, typical alien depictions include an elongated, pale face, two dark elliptical eyes, and a small mouth.  Who first used this design for an alien?  Where does this design come from? Has the disputed flag message changed? I know how disputed flags work. Today, I reviewed a "not an answer" flag and marked it as invalid.   I've later seen a disputed message with this reason:     invalid flag         disputed - a moderator reviewed your flag, but found no evidence to   support it   Given that disputed flags are in the ,  Is this message applicable only to my flag or is this message also for the original flagger?  Or put otherwise, are all disputed flags now shown this message (or similar decline reason)?  I've run out of flags for today to test this further. "At" vs. "in" before verb In a document I found the following sentence:     listeners are more accurate at understanding speech spoken in their own accent...   Would it be an error to use "in" instead of "at"?  Actually in this case "at" sounds better than "in", but in general before verb is "at" always used? I've seen this Kuratowski definition for ordered pairs, but can't fathom why it implies an order to $x$ and $y$  $(x,y):=\{\{x\}, \{x,y\}\}$  As I understand sets, $\{\{x\}, \{x,y\}\}$ is also $\{\{x,y\}, \{x\}\}$. Only when I think about the Axiom of Union does $\{\{x\}, \{x,y\}\}$ "collapse down" to $S = \{x, y\}$, but that doesn't give me much either. All I can see is some as yet hidden message in the set saying "I am the set $\{x,y\}$ and my order of $x$ first is indicated by having $\{x\}$ along for the ride."