It seems, that in The Hobbit movie (Battle of Five Armies), Thranduil leads a impressive force of Mirkwood elves to reclaim his treasure in Lonely Mountain, but he doesn't help in the Pelennor Fields battle. Heres his army in the Hobbit movie:   Dain's army is featured:    My question is why didn't these Elves and Dwarves help Gondor in the Battle of the Pelennor fields? After 60 long years, maybe their forces would have been built up to counter the Sauron-threat..? I have not read the books in a long time, so I cannot seem to think of an answer.
During The Great Battle of the Last Alliance, there were an estimated 100,000 elves that fought with the armies of Isildur. This was one of the first scenes in the first LOTR movie. However, in the trilogy, it appears that only a small number of elves show up to Helms Deep and overall left the majority of the fighting to the humans. Why did the elves not participate during the rest of the war?
White cloudy areas on bottom of new stainless steel skillet I just bought my first few pot and pans "Calaphon" stainless steel trip-ply  I used my new 10" skillet tonight, and cooked pork chops. I heated the pan first, added olive oil, let it heat, then added chops. After I was done, cleaned it immediately under water, and noticed white cloud looking areas on the bottom of the skillet. They won’t wash or rub off  Do I need to return these? I did buy them for the look as well. How do I parse a string to a float or int? In Python, how can I parse a numeric string like "545.2222" to its corresponding float value, 545.2222? Or parse the string "31" to an integer, 31?  I just want to know how to parse a float str to a float, and (separately) an int str to an int. Assuming one wants to travel through China, what are the rules for visa-free access? To be more specific:   How does the 24-hour visa free transit work? How does the 72-hour version work? What does a person ineligible for either of these programs have to do to transit China? Do the programs apply to flights only or do they also work for transit on land? Would a visitor save much hassle by using visa free transit instead of just getting a visa?      NB: this is intended as a canonical question on transiting China The ship flying away from Rey in her flashback of being left on Jakku looks like one of the ships in the group that takes her away when she is captured.  If so, and it is a First Order ship that dropped her off, this is an interesting Easter egg. Groups of order $pq$ without using Sylow theorems If $|G| = pq$,  $p,q$ primes, $p \gt q, q \nmid p-1 $, then how do I prove $G$ is cyclic without using Sylow's theorems? I am using Blender to mix the video from my camera with the audio from my external recording setup.  It works great mostly and I am very pleased with it.  But the problem is that I can't start the audio recorder an even number of thirtieths of a second from when I started the camera.  And Blender seems to only let me move the audio track in the VSE by whole frames (1/30 of a second).  Here are a couple screenshots:   The track on top is the external audio and the one on the bottom is the camera's audio.  Between the two screenshots I have only moved the audio track by one frame.  But as you can see, I need to move it by about 1/2 frame to line up the audio properly with the video.  So can I move a track in the VSE by fractions of a frame? All I want to see are the specs Is there a way to see the processor and speed of a Cisco UCS B230 Blade Server without the enclosure that runs it? The enclosure that we have does not power on and all I need is to see what cpu and processor speed is in it. $(a_n+a_{n+1})$ is convergent implies $(a_n/n)$ converges to $0$ Let $(a_n)$ be a sequence such that $(a_n+a_{n+1})$ is convergent. Prove that $(a_n/n)$ converges to $0$.   $(a_n+a_{n+1})$ convergent to $L$ means that for all $\epsilon$, there exists $N$ such that for all $n\geq N$, $|L-a_n-a_{n+1}|&lt;\epsilon$, or in other words $L-\epsilon&lt;a_n+a_{n+1}&lt;L+\epsilon$. How to proceed from here? Can polymorph and true polymorph change a PC's race and sex? How do I completely uninstall Google Chrome and Chromium? I'm having a problem with Chrome and one of its extensions, so I want to completely uninstall everything. I've uninstalled Chrome through the Software Center, but when I reinstall it, all of my extensions and preferences are still there.   If I want to start over from scratch, what do I need to do? Avoid trailing zeroes in printf() share login/logout sessions across two installs? Can I have two UK visas simultaneously? I have a visitor UK visa valid until October 2017.  I also want to apply for a Tier 4 student visa. My studies in the UK start in September 2017.  If I apply for the student visa in June, will they simply issue an overlapping student visa, or will they cancel my visitor visa and I will not be able to come to the UK until September?  I am worried because in a similar situation with Schengen visas, my existing visa was canceled. Conditional probability and venn diagram What are the alternatives to Notepad++ on Ubuntu? Why is DarkGray lighter than Gray? What is the capacity of this circuit? I simply can't figure out what the capacity of this circuit is.  I can do the math myself, I just need a hint how to create an equivalent circuit where it is obvious what is parallel and what is in series... Gauss's Lemma for polynomials claims that a non-constant polynomial in $\mathbb{Z}[X]$ is irreducible in $\mathbb{Z}[X]$ if and only if it is both irreducible in $\mathbb{Q}[X]$ and primitive in $\mathbb{Z}[X]$.   I wonder if this holds for multivariable case.      Is it true that a non-constant polynomial in $\mathbb{Z}[X_1,\dots,X_n]$ is irreducible in $\mathbb{Z}[X_1,\dots,X_n]$ if and only if it is both irreducible in $\mathbb{Q}[X_1,\dots,X_n]$ and primitive in $\mathbb{Z}[X_1,\dots,X_n]$?    Thank you for your help. I'm setting up a child theme in WordPress and I can't make add_action to be fired within functions.php.  Functions.php is called and I can run code from within. Any idea on what I'm doing wrong?  $debug_msg = "Hi there!";  function test_function() {     error_log($debug_msg, 0);  } add_action('init', 'test_function', 20); macOS Mojave won't install updates past 10.14.1 due to requirement for APFS formatting I have a MBP 2012 I upgraded from High Sierra to Mojave after it came out as GA. I don't recall if I was asked about upgrading to APFS when Id id that, but at this time the main volume is Mac OS Extended (Journaled).  My current About This Mac...version is Mojave 10.14.1 (18B75). Now, when updates are advertised from the App Store, I'm unable to upgrade because 10.14.3 is required.  No OS updates show in the App Store, and when I searched for the updaters (10.14.2 Combo, etc), I can't install because the installer reports "macOS 10.14.2 Update can't be installed on this disk. This Mac can only install macOS on APFS-formatted drives."  I tried the search results recommending to boot in Recovery Mode and use Disk Utility, but APFS is not available as a type.  I have good backups and I can reformat the boot volume if I need to, but I have not done this before. Should I get a 10.14.3 installer to do this and boot from an external drive? The only guies and message boards I've found just keep saying to install 10.14.3 (I can't) or convert the disk in Recovery Mode (APFS is not available as an option.)  Any known-good ways to get my 10.14.1 upgraded so I can keep getting App Store updates?