Is it correct to state that Frodo killed Sauron? Which is the role of Gollum/Smeagol? Frodo was the one in charge of destroying the Ring in the flames of Mount Doom (Amon Amarth of Mordor), but Gollum actually bit Frodo's finger and fell into the flames.
The LOTR wiki  Eru Ilúvatar intervened in the history of Arda:   creating Elves and Men removing Aman from the spherical Earth resurrecting Gandalf making Gollum trip      In a letter written by Tolkien, he stated that Eru again intervened, this time in the Third Age, causing Gollum to trip and fall into the fires of Mount Doom while still holding the One Ring, thus destroying it.   Is this correct? If so, what letter is this, and exactly what did Tolkien say?
unblock slime presta valve My Son's bike has slime inner tubes.  The bike has been sitting in the garage since last summer and the front tyres valve now seems blocked.  Its has what feels like 15-20 psi in it but I can not get the valve to let any air out or take any more in.  I have no idea at this point how to get it to unblock the valve so I can use it again.  For that matter I don't know how I could get the tire off as it has a reasonable (not ridable) amount of air in it without slashing the tyres (nice kings 2.2 which are pretty new).  I have tried putting the pump on it and putting a bit of air into it to try and clear the blockage but that didn't do anything.  Any ideas please? Why is the t-test designed for small samples? How does wizard & cleric spell preparation and casting work? In 3.X wizards had spellbooks, while clerics had their entire spell list, but they both memorized/prepared spells every day from those lists, and had a certain number of slots for preparing spells in.  Now in 5e preparing spells and spell slots aren't the same thing. What's going on here? How does their spellcasting work now? Get Edge / Vertex / Face from mouse position As far as I can tell, it's something like this:  damage reduction = armor / (armor + 100)   Is this accurate? What is the correct pronunciation of TeX and LaTeX? Is it tex(tech)? Or Is it tex(like touch)?  Lay-TeX? or La-TeX?  Should I use TeX pronunciation in LaTeX? Derivative of function with 2 variables Let $p, q \in \mathbb R$ be positive reals for which $p + q = 1$. How to prove that for any two natural numbers $n, m$ the following inequality is true?  $(1 - p^n)^m + (1 - q^m)^n \ge 1$  I don't have a big knowledge about solving inequalities, so I tried to use cauchy-schwarz inequality, binomial theorem and some other baisc techniques, but it lead me nowhere. I've been thinking about it for a long time and now I'm completly stuck. I've been trying to find this darn series of books for ages, I read them back in early 2001-02 and can't really remember much of them. I think there were 10-ish books, it was an easy read but a long series. On early publications, the covers, were mainly yellow, with small pictures of whatever happens in that book.  The book began with two siblings, a brother and a sister, running in a forest. She conjures up what can only be remembered as a golem type creature. He then uses a high magic 'blast' and wipes out the golem, knackering himself. His sister laughs at him for being 'powerful' but expending himself too much on one big magic blast. The beginning I remember vividly, the rest, not so much.  The story continues as a conflict happens, I believe two worlds are involved? The brother and sister are split up, but this is where my memory becomes vague.  The mechanics of the world seems that there are gems, or stones, set in the backbone, which in turn give access to magic. When the person uses them, they can draw too much, which ends up exhausting them. The 'big bad evil king' kills their father, and destroys their farm early on in the story. In the Upcoming Halloween Update Posted By SOOPUR SELL (supercell), there have been sneak peeks released showing new skeleton traps for TH 8+. I also remember the Santa Strike from one of the Christmas Updates. My question is when these holiday events finish, do we lose the money we spent on the Traps or do we keep them forever? How to change color for a block of texts? I am trying to write a script that will delete all comments and everything in between inside C files in my current directory. I've been using sed, and this is what I have so far:   sed -i '/ * [^()] */d' *.c  This works when the comments are on the same line as an asterisk or backslash.   However it doesn't work when there is a commented line without a slash or asterisk.   I know sed goes line by line, I just don't know how to tell it to keep deleting until it sees a */. In English, the number 0 is treated as plural. It is then:   0 seconds 1 second    1.2 seconds   2 seconds     Shouldn't it be "nobody want to go there," instead of "nobody wants to go there"?  I also saw in TOEFL that "any __" should be used with a singular.  But I see it very common that it is a plural also.  Why is that?  (updated: example, "we don't have any apples any more" vs "If you get any apple, please let me know.") Add a dependency in Maven Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $ Problem: Show that $\int_{0}^{\infty}|\frac{ \sin x}{x}|=\infty $ .  Here is what i have tried :  I found out that for all $x&gt;0$ , $x-\frac{x^3}{6} &lt; \sin x &lt;x $  . So $1-\frac{x^2}{6}&lt;\frac{ \sin x}{x}&lt;1$ . So applying integration to both side from $0$ to $M$ we have $M-\frac{M^3}{18}&lt;\int_{0}^{M}|\frac{ \sin x}{x}|&lt; M$ . Now we send $M \rightarrow \infty$ and observe that left-hand side goes to infinity . Hence proved .  Please point out if there is anything wrong with my approach . I will also be delighted if could provide alternative solutions . Thank you . We have $q, p$ prime and $tq = (p-1)(p+1)$ for some positive integer $t$. The book I'm reading says that because $q$ is prime, it divides $p-1$ or $p+1$.   Question: Why exactly does it matter that $q$ is prime here? How to match all words of one column against words in another column? postgresql - replace all instances of a string within text field Establishing a Basis for $F[x]/(f(x))$ Hypothesis:   $f(x) = a_0 + a_1 x + \ldots + a_n x^n \in F[x]$ s.t. $f(x)$ irreducible over field $F$. $deg(f(x)) = n \ge 1$. Let $V = (f(x)) \subset F[x]$.   Goal: Show that $\mathcal{B} = \{1 + V, x + V, x^2 + V, \ldots , x^{n-1} + V\}$ forms a basis for $E = F[x]/V$  Attempt:   Linear Independence: If this set weren't linearly independent, then a non-trivial $b_i \in F$ would satisfy  $$ b_0 + b_1x + \ldots + b_{n-1} x^{n-1} + V = 0 + V $$   But this would then imply that $b_0 + b_1x + \ldots + b_{n-1} x^{n-1}  \in 0 + V$. But this would contradict $V = (f(x))$ since it is impossible that $f(x)\,\,|\,\,b_0 + b_1x + \ldots + b_{n-1} x^{n-1}$ of strictly lower degree.  Now how would I show that this set spans $F[x]/V$? How long can you store used cooking oil How long can you store used cooking oil then re-use it? I deep fried a turkey one year ago and have had it refrigerated since.