https://liberty.ioCurated star highlights with fresh energy.en-usMon, 07 Sep 2026 22:18:07 -0400https://liberty.io/how-do-i-manually-change-the-resolution.htmlhttps://liberty.io/how-do-i-manually-change-the-resolution.htmlLots of online sources say simply to change the monitor resolution and launch the game and that it will adjust itself. However, this will cause all sorts of annoying issues due to my running two mo......Tue, 08 Sep 2026 02:16:32 -0400https://liberty.io/baldur-039-s-gate-ee-building-assasin-class.htmlhttps://liberty.io/baldur-039-s-gate-ee-building-assasin-class.htmlI always played a class that wears heavy armor, but now I decided to create some kind of assasin build, focusing on backstabbing etc. However I'm not sure which thief abilities should I invest to m......Tue, 08 Sep 2026 02:15:55 -0400https://liberty.io/what-do-i-do-with-eridium-after-maxing-out-my-sdus.htmlhttps://liberty.io/what-do-i-do-with-eridium-after-maxing-out-my-sdus.htmlSo, I've bought everything available at the Black Market in Sanctuary but enemies still keep dropping Eridium. It's gotten to the point where my HUD no longer displays my total Eridium count whenev......Tue, 08 Sep 2026 02:12:06 -0400https://liberty.io/how-much-does-luck-affect-the-various-games-of-chance-in-fallout-new-v.htmlhttps://liberty.io/how-much-does-luck-affect-the-various-games-of-chance-in-fallout-new-v.htmlDoes anyone know how luck affects the 3 casino games ( slots , BlackJack, roulette) in Fallout:NV? Does luck play a bigger role in one of the games more then the others? Is there some breakover p......Tue, 08 Sep 2026 02:11:42 -0400https://liberty.io/what-is-the-optimal-path-in-yoshis-valley.htmlhttps://liberty.io/what-is-the-optimal-path-in-yoshis-valley.htmlYoshis valley is an odd course in mario kart. Its a maze, that has 4-5 different ways to get through it. But is there a way that is noticeably faster than the others? Question is about the Mario ......Tue, 08 Sep 2026 02:07:06 -0400https://liberty.io/what-are-the-differences-between-marth-and-roy.htmlhttps://liberty.io/what-are-the-differences-between-marth-and-roy.htmlIn Super Smash Brothers Mêlée (SSBM), there are tens of characters in the roster to play as. Some characters have move-sets that are very similar to each other, but with different effects. These ...Tue, 08 Sep 2026 02:01:40 -0400https://liberty.io/java-minecraft-1-14-how-to-access-a-written-book-039-s-contents.htmlhttps://liberty.io/java-minecraft-1-14-how-to-access-a-written-book-039-s-contents.htmlI am currently modifying a datapack that changes the skullowner (tag) of a player_head to a written book's title to get that player's head skin. execute as @e[type=item,nbt={Item:{id:"minecraft:...Tue, 08 Sep 2026 01:57:17 -0400https://liberty.io/where-did-the-18-446-744-073-709-551-616-number-come-from.htmlhttps://liberty.io/where-did-the-18-446-744-073-709-551-616-number-come-from.htmlReading about No Mans Sky, and hearing about the 18,446,744,073,709,551,616 planets there are, I'm curious, where did that number come from? Does that mean there are 18,446,744,073,709,551,616 unique ...Tue, 08 Sep 2026 01:48:16 -0400https://liberty.io/how-to-create-a-line-of-wool-sorted-by-color.htmlhttps://liberty.io/how-to-create-a-line-of-wool-sorted-by-color.htmlI've been trying to figure out a way to create the best possible arrangement of wool colors, so far with no luck. Does anybody know a reference or an already made list of colors I could use? This......Tue, 08 Sep 2026 01:47:10 -0400https://liberty.io/is-it-possible-to-play-games-on-playstation-4-xbox-one-with-keyboard-a.htmlhttps://liberty.io/is-it-possible-to-play-games-on-playstation-4-xbox-one-with-keyboard-a.htmlI play games on my laptop. I tried playing on a PS3 and Xbox 360 on my friend's consoles and I am not at all comfortable with the controllers. Actually, I lost every round so I can't play. Can I c......Tue, 08 Sep 2026 01:46:48 -0400https://liberty.io/do-passives-stack-when-added-by-hellfire-amulet.htmlhttps://liberty.io/do-passives-stack-when-added-by-hellfire-amulet.htmlThe Hellfire Amulet introduced in patch 2.1 has a secondary affix that adds the effect a random passive ability for your class. If you do this on Monk and get Fleet Footed (Increase movement speed ......Tue, 08 Sep 2026 01:46:02 -0400https://liberty.io/war-horse-died-possible-to-get-it-back.htmlhttps://liberty.io/war-horse-died-possible-to-get-it-back.htmlAt some point I accidentally ran off a cliff with my War Horse which resulted in a death. After respawning, I noticed my War Horse was gone and the default Tennessee Walker was my main horse. How......Tue, 08 Sep 2026 01:37:13 -0400https://liberty.io/how-do-i-create-clickable-text-that-executes-a-command.htmlhttps://liberty.io/how-do-i-create-clickable-text-that-executes-a-command.htmlI want a line of text to appear in the chat, that when clicked on will execute a /fill command. I have used the following command to no avail: (~ = desired message or command) /tellraw @a {"text&...Tue, 08 Sep 2026 01:37:00 -0400https://liberty.io/what-blocks-can-endermen-pick-up-and-what-blocks-they-can-039-t.htmlhttps://liberty.io/what-blocks-can-endermen-pick-up-and-what-blocks-they-can-039-t.htmlI have seen Endermen pick up grass blocks, but I want to know what all blocks they can pick up and what blocks they can't pick up....Tue, 08 Sep 2026 01:28:46 -0400https://liberty.io/how-can-i-prevent-the-untimely-demise-of-john-039-s-wife.htmlhttps://liberty.io/how-can-i-prevent-the-untimely-demise-of-john-039-s-wife.htmlSo far the only "happy" end I found was the one where John and Molly are cured and sit in the park. Unfortunately, that involves John's wife comitting suicide. The only path that did not let John......Tue, 08 Sep 2026 01:25:36 -0400https://liberty.io/if-i-join-the-institute-what-happens-to-nick.htmlhttps://liberty.io/if-i-join-the-institute-what-happens-to-nick.htmlI met the Institute and I kind of like it, the only thing that i worry about is that if I join I could not interact more with Nick Valentine. Does anything change with Nick if I join the institute?...Tue, 08 Sep 2026 01:17:34 -0400https://liberty.io/can-charcoal-be-sold-and-where.htmlhttps://liberty.io/can-charcoal-be-sold-and-where.htmlI tried to sell them, but not even Belethor (General Goods, Whiterun) wants them. Where can I sell charcoal?...Tue, 08 Sep 2026 01:16:01 -0400https://liberty.io/how-can-i-save-character-customizations-in-saints-row-iv.htmlhttps://liberty.io/how-can-i-save-character-customizations-in-saints-row-iv.htmlIn Saints Row IV, I've noticed that I can save outfits by going to Wardrobe -> Outfits -> Save Outfit. Is there a way that I can do the same for character customizations? I'd like to be able to do......Tue, 08 Sep 2026 01:14:25 -0400https://liberty.io/can-039-t-find-screenshotted-photos-in-minecraft-technic-launcher.htmlhttps://liberty.io/can-039-t-find-screenshotted-photos-in-minecraft-technic-launcher.htmlI screenshotted some photos in Minecraft and I can't find them. I play Minecraft on a Technic Launcher and I have a Mac....Tue, 08 Sep 2026 01:08:12 -0400https://liberty.io/which-hm-is-more-powerful.htmlhttps://liberty.io/which-hm-is-more-powerful.htmlAfter Pokémon Sun and Moon I was planning to play Black and White. This got me wondering. Which HM out of Surf and Waterfall is more powerful in Black and White and Black and White 2?...Tue, 08 Sep 2026 00:55:22 -0400https://liberty.io/who-is-the-hero-that-uses-the-soulstone-at-the-end-of-diablo.htmlhttps://liberty.io/who-is-the-hero-that-uses-the-soulstone-at-the-end-of-diablo.htmlSpoiler alert! Don't read if you haven't completed the original Diablo from 1996....Tue, 08 Sep 2026 00:53:46 -0400https://liberty.io/how-do-i-launch-civ-5-in-the-tablet-touch-mode-by-default.htmlhttps://liberty.io/how-do-i-launch-civ-5-in-the-tablet-touch-mode-by-default.htmlI just got a Windows 8 touch screen laptop, and playing Civ V in the Touch Enabled mode is great. But every time I launch it from within Steam, it prompts me to pick either DirectX9, DirectX 10 &am......Tue, 08 Sep 2026 00:50:53 -0400https://liberty.io/how-can-i-get-the-80-coins-1000-stars-achievement.htmlhttps://liberty.io/how-can-i-get-the-80-coins-1000-stars-achievement.htmlIn Geometry Dash you can Unlock new icons with achievements. Some of those are "Collect 80 Secret Coins" or "Collect 1000 Stars". Now when I look at the Levels I only see 15. Each of them has only 3 ...Tue, 08 Sep 2026 00:49:04 -0400https://liberty.io/weird-symbol-under-my-character-after-empty-was-equipped.htmlhttps://liberty.io/weird-symbol-under-my-character-after-empty-was-equipped.htmlI was climbing the road to the shrine of Azura, south of Winterhold. At the top of the road, there was a frost troll. As the road is very steep, I decided to Fus Ro Dah his ass and watch him facero......Tue, 08 Sep 2026 00:47:43 -0400https://liberty.io/how-to-survive-early-uvhm-as-gaige.htmlhttps://liberty.io/how-to-survive-early-uvhm-as-gaige.htmlI'm playing as Gaige and I am in UVHM at level 53. My skills are distributed like that: http://bl2skills.com/mechromancer.html#514004101541000000000000415150150010 The only legendaries I have is a ...Tue, 08 Sep 2026 00:39:45 -0400https://liberty.io/how-do-you-determine-which-weapons-and-armor-a-companion-will-use.htmlhttps://liberty.io/how-do-you-determine-which-weapons-and-armor-a-companion-will-use.htmlIn Fallout: New Vegas, I've gotten the companion with the pneumatic glove, but she won't put on the body armor I give her. What are the restrictions for weapons and armor with companions? How can......Tue, 08 Sep 2026 00:39:00 -0400https://liberty.io/how-to-skip-battle-animations-in-civilization-v.htmlhttps://liberty.io/how-to-skip-battle-animations-in-civilization-v.htmlI know in strategic mode there are no battle animations. But how can I skip them in 3D mode?...Tue, 08 Sep 2026 00:29:51 -0400https://liberty.io/how-do-you-use-cloak-effectively.htmlhttps://liberty.io/how-do-you-use-cloak-effectively.htmlI chose the infiltrator class and have maxed out the cloaking ability. Overall the class and their cloak ability still seems disappointing when compared to some of the other class abilities. So fa......Tue, 08 Sep 2026 00:25:01 -0400https://liberty.io/how-do-i-make-the-water-rise-gradually-in-a-selected-area.htmlhttps://liberty.io/how-do-i-make-the-water-rise-gradually-in-a-selected-area.htmlI would like to know if there is any way to make water rise gradually in a certain area....Tue, 08 Sep 2026 00:17:03 -0400https://liberty.io/how-can-i-make-an-extremely-bright-light.htmlhttps://liberty.io/how-can-i-make-an-extremely-bright-light.htmlI'm trying to make a beacon/lighthouse which is visible from a distance at night (on far render). What is the best light source which will provide the brightest light / most visible to the human ey......Tue, 08 Sep 2026 00:14:35 -0400https://liberty.io/where-can-i-find-ebony-mine-in-skyrim.htmlhttps://liberty.io/where-can-i-find-ebony-mine-in-skyrim.htmlI'm looking to make a complete set of Daedric Armor and I need Ebony Ore to do so. Please help!!!! PS I already know about Shor's Stone and have discovered it already but I would also like to kn......Tue, 08 Sep 2026 00:14:12 -0400https://liberty.io/not-possible-to-connect-2-stations-sid-meier-039-s-railroads.htmlhttps://liberty.io/not-possible-to-connect-2-stations-sid-meier-039-s-railroads.htmlI Want to connect 2 stations in SidMeier's Railroad Bur when I buy a train to connect it, the City (Blythe) appears in black, and doesn't allow me to connect it with the Blythe Annex. The city is ...Tue, 08 Sep 2026 00:12:45 -0400https://liberty.io/how-is-your-rank-determined-in-the-campaign.htmlhttps://liberty.io/how-is-your-rank-determined-in-the-campaign.htmlLike Advanced Wars, after every mission in the campaign you are given a letter grade from E to S. Advanced Wars has a relatively simple formula for calculating points and rank, which can be cheesed......Tue, 08 Sep 2026 00:09:44 -0400https://liberty.io/best-strategy-for-killing-mgalekgolo-pairs.htmlhttps://liberty.io/best-strategy-for-killing-mgalekgolo-pairs.htmlI'm in a nasty situation on solo campaign where I have to face off against a pair of Mgalekgolo (hunter, mechanized infantry - the guys with the giant green ball cannons and shield) in a single-ele......Tue, 08 Sep 2026 00:06:42 -0400https://liberty.io/how-do-you-beat-megadragonbowser.htmlhttps://liberty.io/how-do-you-beat-megadragonbowser.htmlThis is the ultimate boss of Mario+Rabbids kingdom battle. He replenishes his health when we do 1600 damage to him total then I see lava bucklers and there making all the heroes dead.What do I do?...Tue, 08 Sep 2026 00:04:35 -0400https://liberty.io/can-i-stop-another-civ-039-s-trader-from-crossing-my-land.htmlhttps://liberty.io/can-i-stop-another-civ-039-s-trader-from-crossing-my-land.htmlI have an enemy who is crossing my land to trade with another civ. Can I stop them from crossing without going to war?...Tue, 08 Sep 2026 00:04:01 -0400https://liberty.io/conditional-covariance.htmlhttps://liberty.io/conditional-covariance.htmlSuppose we have two random variables, $X$ and $Y$, defined over nonnegative reals. Obviously, the following formula holds: $$\mathrm{Cov}(X,Y)=\mathbb{E}\left[XY\right]-\mathbb{E}\left[X\right]\ma......Mon, 07 Sep 2026 23:45:46 -0400https://liberty.io/about-the-definition-of-convergent-series-meaning.htmlhttps://liberty.io/about-the-definition-of-convergent-series-meaning.htmlFrom my textbook, the definition of convergent series is given as follow. If the sequence of partial sums {$S_n$} is convergent and $\displaystyle{\lim_{n \to \infty}} S_n$ exists, then the series......Mon, 07 Sep 2026 23:44:19 -0400https://liberty.io/understanding-the-proof-of-l-039-hopital-039-s-rule.htmlhttps://liberty.io/understanding-the-proof-of-l-039-hopital-039-s-rule.htmlThe following is an excerpt from Bartle and Sherbert's Introduction to Real Analysis: Okay. I am having a little trouble following this proof. What is $c$ and why is it in $(a,b)$? What confus......Mon, 07 Sep 2026 23:41:49 -0400https://liberty.io/matlab-equal-does-not-work.htmlhttps://liberty.io/matlab-equal-does-not-work.htmlHow to judge whether two whatever is equal? alphat and alpha are two kind big vectors. Why it turns 0, which means they are not equal?...Mon, 07 Sep 2026 23:34:08 -0400https://liberty.io/what-is-the-nature-of-skyrim-039-s-infinitely-generated-quests.htmlhttps://liberty.io/what-is-the-nature-of-skyrim-039-s-infinitely-generated-quests.htmlI've heard of Skyrim's "infinite quests" system. Are the quests quite varied, or are they just deliver/kill/protect/puzzle/etc. ones over and over? Just wondering about the depth of the generation, ...Mon, 07 Sep 2026 23:31:37 -0400https://liberty.io/the-cos-alpha-beta-formula-always-need-alpha-beta-or-not.htmlhttps://liberty.io/the-cos-alpha-beta-formula-always-need-alpha-beta-or-not.htmlI'm a beginner student study the proof of sum and difference trigonometry formula. There is a formula that: $$\cos(\alpha-\beta) = \cos(\alpha)\cos(\beta)+\sin(\alpha)\sin(\beta)$$ In the tutori......Mon, 07 Sep 2026 23:23:14 -0400https://liberty.io/how-can-i-delete-the-ps-plus-games-of-the-month-after-my-ps-plus-subsc.htmlhttps://liberty.io/how-can-i-delete-the-ps-plus-games-of-the-month-after-my-ps-plus-subsc.htmlI subscribed to PS Plus for two months and decided it was not for me. I downloaded all the games of the month then realized I don't want to actually play them anymore. Whenever I try downloading a ......Mon, 07 Sep 2026 23:14:00 -0400https://liberty.io/undo-command-in-minecraft.htmlhttps://liberty.io/undo-command-in-minecraft.htmlI would want to know if there is a sort of "undo" command in Minecraft (no mods) that undo one action at the time. For example, the player pressed a button that started a huge redstone system or he ...Mon, 07 Sep 2026 22:49:05 -0400https://liberty.io/when-does-a-rational-function-pass-through-the-horizontal-asymptote-ho.htmlhttps://liberty.io/when-does-a-rational-function-pass-through-the-horizontal-asymptote-ho.htmlSorry if this is a bit simple compared to everything here, but I can't really seem to find an answer. If I have $$f(x) = \frac{(x-2)(x-4)}{x(x-1)}$$ 1) When is the horizontal asymptote is crossed? ...Mon, 07 Sep 2026 22:46:28 -0400https://liberty.io/what-is-the-extraneous-solution-of-sqrt-a-a-6.htmlhttps://liberty.io/what-is-the-extraneous-solution-of-sqrt-a-a-6.htmlWhat is the extraneous solution of $$\sqrt a=a-6$$ The roots are $9$ and $4$. So I'm assuming that $4$ is the extraneous solution because when you plug it in to the equation you wind up with $2=-2$. ...Mon, 07 Sep 2026 22:37:01 -0400https://liberty.io/proving-directly-trace-matrix.htmlhttps://liberty.io/proving-directly-trace-matrix.htmlI am having difficulties in proving directly the following statement: I know that similar matrices have the same eigenvalues and that implies that their traces are the equal (if eigenvalues exist......Mon, 07 Sep 2026 22:33:29 -0400https://liberty.io/graph-theory-adjacency-vs-incident.htmlhttps://liberty.io/graph-theory-adjacency-vs-incident.htmlOkay, so I think if 2 vertices are adjacent to each other, they are incident to each other....or do I have it wrong? Is this just different terminology. I thought I was totally clear on this for my......Mon, 07 Sep 2026 22:25:24 -0400https://liberty.io/how-do-we-know-all-numbers-alternate-between-odd-and-even-numbers.htmlhttps://liberty.io/how-do-we-know-all-numbers-alternate-between-odd-and-even-numbers.htmlBasically, I tried proving that multiplying an odd and even number together gives you an even number to a friend of mine. This is what I said. Let's first take a random number $k$. It doesn't matt......Mon, 07 Sep 2026 22:22:40 -0400https://liberty.io/unkill-mettaton-neo-undertale-genocide.htmlhttps://liberty.io/unkill-mettaton-neo-undertale-genocide.htmlI killed mettaton neo when I hadn't gotten the required kills for Hotland... and I saved it how do I de kill her? I tried the time-travel thing and it did not work....Mon, 07 Sep 2026 22:21:09 -0400https://liberty.io/formula-for-a-very-steep-exponential-interpolation.htmlhttps://liberty.io/formula-for-a-very-steep-exponential-interpolation.htmlI have two points in the 2D space, e.g. point A is (3, 2) and point B is (30, 20) I want to get some points in between, aka, interpolating between A and B. But I don't want linear interpolation, I......Mon, 07 Sep 2026 22:12:18 -0400https://liberty.io/definite-integral-of-sine-squared-over-one-period.htmlhttps://liberty.io/definite-integral-of-sine-squared-over-one-period.htmlI'm working through a textbook on Fourier series ("The Intuitive Guide to Fourier Analysis and Spectral Estimation: with Matlab", by Langton and Levin), and I'm a bit stuck on the derivat......Mon, 07 Sep 2026 22:06:43 -0400https://liberty.io/do-specific-creatures-types-of-creatures-have-weaknesses-to-specific-t.htmlhttps://liberty.io/do-specific-creatures-types-of-creatures-have-weaknesses-to-specific-t.htmlDo specific creatures have weaknesses to specific types of attack, e.g. I have both a fire and shock based destruction spells. Would one work better on some creatures, and the other better on other......Mon, 07 Sep 2026 22:05:44 -0400https://liberty.io/calculate-radius-of-circle-that-by-given-length-of-square-that-is-insi.htmlhttps://liberty.io/calculate-radius-of-circle-that-by-given-length-of-square-that-is-insi.htmlin this picture a length of square edge is 8 cm. I want to calculate the radius of circle. i try to calculate it, but i don't know how. I calculate this:...Mon, 07 Sep 2026 22:01:40 -0400https://liberty.io/solve-the-equation-sqrt-cos-x-2-cos-x-1.htmlhttps://liberty.io/solve-the-equation-sqrt-cos-x-2-cos-x-1.htmlSolve this. Show work as detailed as possible. $$\sqrt{\cos x} = 2\cos x-1$$ My work: \begin{align*} 2\cos x & = \sqrt{\cos x}+1\\ \cos x & = \frac{\sqrt{\cos x}+1}{2}\\ x & = \c......Mon, 07 Sep 2026 21:59:21 -0400https://liberty.io/how-to-draw-greek-letters-on-paper-blackboard.htmlhttps://liberty.io/how-to-draw-greek-letters-on-paper-blackboard.htmlFor $\gamma$ (gamma), I've noticed people doing a sort of $\alpha$ (alpha) rotated by ninety degrees, which seems to be the standard on-paper-or-blackboard equivalent of $\gamma$. But for letters ......Mon, 07 Sep 2026 21:57:35 -0400https://liberty.io/in-dead-money-how-do-i-trap-father-elijah-in-the-vault.htmlhttps://liberty.io/in-dead-money-how-do-i-trap-father-elijah-in-the-vault.htmlThere's an achievement for trapping Father Elijah in the vault, but he has a knack for seeing right through stealth regardless of your preparations. Other guides suggest you should be able to just ......Mon, 07 Sep 2026 21:56:28 -0400https://liberty.io/why-normal-approximation-to-binomial-distribution-uses-np-5-as-a-condi.htmlhttps://liberty.io/why-normal-approximation-to-binomial-distribution-uses-np-5-as-a-condi.htmlI was reading about normal approximation to binomial distribution and I dunno how it works for cases when you say for example p is equal to 0.3 where p is probability of success. On most websites ......Mon, 07 Sep 2026 21:51:35 -0400https://liberty.io/is-there-a-way-to-calculate-lg-on-a-scientific-calculator.htmlhttps://liberty.io/is-there-a-way-to-calculate-lg-on-a-scientific-calculator.htmlTaking introduction to algorithms for computer science this semester and wanted to know if there is a way to calculate lg on scientific calculator? Thank you....Mon, 07 Sep 2026 21:50:37 -0400https://liberty.io/why-polynomial-functions-f-x-g-x-f-g-x.htmlhttps://liberty.io/why-polynomial-functions-f-x-g-x-f-g-x.htmlWhy polynomial functions f(x)+g(x) is the same notation as (f+g)(x)? I've seen the sum of polynomials as f(x)+g(x) before, but never seen a notation as with a operator in a prenthesis as (f+g)(x).......Mon, 07 Sep 2026 21:45:32 -0400https://liberty.io/distance-in-the-metric-induced-by-the-fisher-information-matrix.htmlhttps://liberty.io/distance-in-the-metric-induced-by-the-fisher-information-matrix.htmlFrom this (Section 2.1.2) paper I quote: "The Fisher information matrix defines a (Riemannian) metric on $\Theta$: the distance in this metric, between two very close values of $\theta$ is given b......Mon, 07 Sep 2026 21:44:41 -0400https://liberty.io/is-there-a-shortcut-for-raising-2-to-the-power-of-a-number-e-g-2-27.htmlhttps://liberty.io/is-there-a-shortcut-for-raising-2-to-the-power-of-a-number-e-g-2-27.htmlIn networking, when dealing with subnetting, you convert the net mask to binary and count the number of ones (for the example in the question there would be $27$ $1$'s) and to figure out how many s......Mon, 07 Sep 2026 21:32:16 -0400https://liberty.io/how-do-the-aiming-options-work-when-in-a-vehicle-in-grand-theft-auto-v.htmlhttps://liberty.io/how-do-the-aiming-options-work-when-in-a-vehicle-in-grand-theft-auto-v.htmlWhen in a vehicle, there are two aiming options - aim, and aim + fire. From testing, it seems like when "aim + fire" is chosen, holding down R1 on my PS4 controller automatically shoots - whereas w......Mon, 07 Sep 2026 21:25:01 -0400https://liberty.io/relations-between-optimization-versions-of-k-coloring-and-max-k-colora.htmlhttps://liberty.io/relations-between-optimization-versions-of-k-coloring-and-max-k-colora.htmlI am a tourist of Graph theory but I have this problem I am trying to solve, part of a research objective connected to quantum computing. I am trying to understand the relationship between: the ...Mon, 07 Sep 2026 21:23:26 -0400https://liberty.io/how-to-find-limits-involving-trigonometric-functions-as-x-to-0.htmlhttps://liberty.io/how-to-find-limits-involving-trigonometric-functions-as-x-to-0.htmlProblem: find the limit $lim _{x\rightarrow 0}\dfrac{\tan(3x)}{\sin(2x)}$ $lim _{x\rightarrow 0}\dfrac{(\sin(2x) + 3)}{(\cos(7x)-8)}$ Note I am able to solve the first one using l'Hopitals, but I ...Mon, 07 Sep 2026 21:16:38 -0400https://liberty.io/what-039-s-the-difference-between-a-roguelike-and-a-roguelite-game.htmlhttps://liberty.io/what-039-s-the-difference-between-a-roguelike-and-a-roguelite-game.htmlWhat exactly defines a Roguelike game and what is the difference between them and Roguelite games?...Mon, 07 Sep 2026 21:14:12 -0400https://liberty.io/is-my-answer-for-this-truth-table-boolean-expression-correct.htmlhttps://liberty.io/is-my-answer-for-this-truth-table-boolean-expression-correct.htmlI was given the following boolean diagram: I had to come out with the truth table and the simplified expression. I need help to check if my answers are correct below....Mon, 07 Sep 2026 21:11:21 -0400https://liberty.io/what-does-this-definition-of-permutation-mean.htmlhttps://liberty.io/what-does-this-definition-of-permutation-mean.htmlA simple question. They give the definition of permutation as "a one to one mapping of the set onto the set of positive integers $\{1, 2,3,4, \ldots n\}$." What does this definition exactly m......Mon, 07 Sep 2026 21:08:17 -0400https://liberty.io/which-type-of-followers-still-benefit-from-garrison-mission-xp.htmlhttps://liberty.io/which-type-of-followers-still-benefit-from-garrison-mission-xp.htmlMost of my followers are now level 100. I've currently got a mix of green, blue (rare), and purple (epic) followers. My question is: do they still benefit from Base XP or Bonus XP? I've tried answ......Mon, 07 Sep 2026 21:05:54 -0400https://liberty.io/why-are-my-npcs-disappearing-and-chest-loot-too.htmlhttps://liberty.io/why-are-my-npcs-disappearing-and-chest-loot-too.htmlI Received a Dryad after killing the Eye of Cthulhu, but it's now gone. There's still proof that I killed the Eye of Cthulu. The chair that made the Dryad's house is gone too! Also, my Goblin Tinke......Mon, 07 Sep 2026 21:05:09 -0400https://liberty.io/basis-of-a-subspace-meaning-of-the-term-039-unique-039.htmlhttps://liberty.io/basis-of-a-subspace-meaning-of-the-term-039-unique-039.htmlFollowing on from a previous question - Definition for Basis of a Subspace; it is often said that a basis of a subspace is a set of vectors that can be used to uniquely represent any vector in the ...Mon, 07 Sep 2026 20:38:38 -0400https://liberty.io/can-i-turn-off-my-ps4-with-my-vita-using-remote-play.htmlhttps://liberty.io/can-i-turn-off-my-ps4-with-my-vita-using-remote-play.htmlI've been using my Vita for Remote Play recently to the point that I haven't turned on my TV for days (go figure). However, despite how much I've been using it, while I know how to turn the PS4 on ......Mon, 07 Sep 2026 20:38:10 -0400https://liberty.io/help-setting-up-a-differential-equation-with-rate-in-rate-out.htmlhttps://liberty.io/help-setting-up-a-differential-equation-with-rate-in-rate-out.htmlI'm in a differential equations class and I am not getting it. It's been over a year since any calculus classes and I am struggling to set up the following problem. If some one can explain to me the ...Mon, 07 Sep 2026 20:36:48 -0400https://liberty.io/are-there-any-benefits-for-going-after-non-lethal-takedowns-in-cyberpu.htmlhttps://liberty.io/are-there-any-benefits-for-going-after-non-lethal-takedowns-in-cyberpu.htmlFor my first playthrough, I'm planning to play stealthily. I won't run and gun cause mayhem, but sneak around and take people down without alerting anyone. I've noticed when grabbing people, I have......Mon, 07 Sep 2026 20:36:42 -0400https://liberty.io/prove-that-a-horizontal-asymptote-can-never-be-crossed.htmlhttps://liberty.io/prove-that-a-horizontal-asymptote-can-never-be-crossed.htmlThis is a lot simpler of a problem than others posted here, but I was bored in class and decided to work out why a horizontal asymptote exists. Bear in mind that I am still fairly low on the “math ......Mon, 07 Sep 2026 20:34:40 -0400https://liberty.io/getting-delphine-esbern-039-unstuck-039.htmlhttps://liberty.io/getting-delphine-esbern-039-unstuck-039.htmlSo I've gotten myself into the documented bug with Delphine & Esbern getting stuck @ the Karthspire. I used the PC console code of setstage MQ203 280 as I COULDN'T get them to get passed the f......Mon, 07 Sep 2026 20:31:16 -0400https://liberty.io/pokestops-not-working.htmlhttps://liberty.io/pokestops-not-working.htmlPokestops aren't working for me. Every time I spin it, it just says "Try again later". Even when I wait for a few seconds to spin it, I get the same results. I don't have any connectivity problems,......Mon, 07 Sep 2026 20:28:34 -0400https://liberty.io/how-to-find-3-1000-bmod-7.htmlhttps://liberty.io/how-to-find-3-1000-bmod-7.htmlSorry this is a really simple problem but I couldnt figure it out. I'm trying to find the value of $3^{1000}\bmod 7$. I know the actual value is 4, but I used a calculator. How would I simplify this ...Mon, 07 Sep 2026 20:26:26 -0400https://liberty.io/example-of-a-covariance-matrix.htmlhttps://liberty.io/example-of-a-covariance-matrix.htmlCan someone provide an example of a covariance matrix for any set of data? For example, if given: 2 3 4 5 1 8 9 7 6 how would I take this 3x3 matrix and convert it to the covariance matrix? I s......Mon, 07 Sep 2026 20:23:25 -0400https://liberty.io/what-are-the-possible-mann-manor-gifts-spawn-places.htmlhttps://liberty.io/what-are-the-possible-mann-manor-gifts-spawn-places.htmlSo I've been playing on a couple 24/7 Mann Manor servers (I know!) to get some of the ghostchievements and scarechievements I missed from previous years. I got the pumpkin hat, the paper mask, the ...Mon, 07 Sep 2026 20:20:09 -0400https://liberty.io/integrate-sec-4x.htmlhttps://liberty.io/integrate-sec-4x.htmlHow do I go about doing this? I try doing it by parts, but it seems to work out wrong: $\eqalign{ & \int {\sec 4xdx} \cr & u = \sec 4x \cr & {{du} \over {dx}} = 4\sec 4x\tan......Mon, 07 Sep 2026 20:10:48 -0400https://liberty.io/examples-of-infinite-boolean-rings.htmlhttps://liberty.io/examples-of-infinite-boolean-rings.htmlI'm attempting to list examples of infinite boolean rings and I need some clarification. Firstly, is it possible to take an infinite direct product of the integers mod $2$ to get a boolean ring? ......Mon, 07 Sep 2026 20:01:11 -0400https://liberty.io/formula-for-sequence-0-0-0-0-1-0-0-0-0-1-ldots.htmlhttps://liberty.io/formula-for-sequence-0-0-0-0-1-0-0-0-0-1-ldots.htmlThere is a sequence with the values $0, 0, 0, 0, 1, 0, 0, 0, 0, 1, \ldots$ (basically there are always four 0s followed by a 1, then it repeats). Is there a function for this sequence? Here are two ...Mon, 07 Sep 2026 19:48:33 -0400https://liberty.io/domain-and-range-of-composite-functions.htmlhttps://liberty.io/domain-and-range-of-composite-functions.htmlWould I be correct in assuming that the domain of the composite function $(f∘g)(x)$ is the intersection of the range of $g$ and the domain of $x$? If not, how do I find the domain of a composite fu......Mon, 07 Sep 2026 19:40:20 -0400https://liberty.io/how-do-i-give-players-already-enchanted-tools-armour-weapons.htmlhttps://liberty.io/how-do-i-give-players-already-enchanted-tools-armour-weapons.htmlI'm making a map where I want players to be able to choose there kits/classes. The problem I'm having with it though is giving players already enchanted Tools/Armour/Weapons. I'm not sure if you c......Mon, 07 Sep 2026 19:39:06 -0400https://liberty.io/help-me-find-a-good-potions-calculator-closed.htmlhttps://liberty.io/help-me-find-a-good-potions-calculator-closed.htmlTrying to find a good potions calculator. I used to have one but lost it when my comp crashed, it had a list of the reagents and you input the number you had and it gave a readout of craftable poti......Mon, 07 Sep 2026 19:34:26 -0400https://liberty.io/proof-of-the-polynomial-remainder-theorem.htmlhttps://liberty.io/proof-of-the-polynomial-remainder-theorem.htmlMy textbook states that $f(x)$ can always be written as $$f(x) = q(x)g(x) + r(x)$$ but it doesn't provide any proof of this and I cannot seem to find it anywhere. And what does it actually say, t......Mon, 07 Sep 2026 19:18:20 -0400https://liberty.io/poisson-distribution-lambda-or-mu.htmlhttps://liberty.io/poisson-distribution-lambda-or-mu.htmlThe number of goals in a hockey game is modelled using a Poisson process with rate 1.5 per minute. (a) What is the distribution for the number of goals in the first quarter (12 minutes)? Write dow......Mon, 07 Sep 2026 19:11:59 -0400https://liberty.io/what-are-the-applications-of-the-mean-value-theorem.htmlhttps://liberty.io/what-are-the-applications-of-the-mean-value-theorem.htmlI'm going through my first year of teaching AP Calculus. One of the things I like to do is to impress upon my students why the topics I introduce are interesting and relevant to the big picture of ...Mon, 07 Sep 2026 19:07:10 -0400https://liberty.io/why-is-the-set-of-all-sets-a-paradox-in-layman-039-s-terms.htmlhttps://liberty.io/why-is-the-set-of-all-sets-a-paradox-in-layman-039-s-terms.htmlI've heard of some other paradoxes involving sets (i.e., "the set of all sets that do not contain themselves") and I understand how paradoxes arise from them. But this one I do not under......Mon, 07 Sep 2026 19:02:49 -0400https://liberty.io/how-can-i-find-out-what-missions-are-available-in-borderlands.htmlhttps://liberty.io/how-can-i-find-out-what-missions-are-available-in-borderlands.htmlAs I make my way through the main storyline, Claptrap will randomly appear in the top-right and say something like: Greetings, Person X has more jobs for you at Place Y. Or similar to that. ...Mon, 07 Sep 2026 18:59:53 -0400https://liberty.io/drawing-direction-fields-online.htmlhttps://liberty.io/drawing-direction-fields-online.htmlI am looking for a convenient and free online tool for plotting Direction Fields and Solution Curves of Ordinary Differential Equations. I tried the "Slope Field Plotter" on Geogebra; it worked tol......Mon, 07 Sep 2026 18:47:57 -0400https://liberty.io/multiplying-a-matrix-by-a-row-vector.htmlhttps://liberty.io/multiplying-a-matrix-by-a-row-vector.htmlIs multiplying a matrix by a row vector the same as multiplying it by a column vector? Or are there any differences between the two?...Mon, 07 Sep 2026 18:46:28 -0400https://liberty.io/how-do-you-jungle-in-smite.htmlhttps://liberty.io/how-do-you-jungle-in-smite.htmlI'm not very familiar with jungling in Smite. Assuming that you've picked an appropriate jungler, what does the jungler do during the course of the game? Some information I'm looking for is: Star......Mon, 07 Sep 2026 18:33:10 -0400https://liberty.io/solving-lyapunov-equation-matlab-has-different-solution-why.htmlhttps://liberty.io/solving-lyapunov-equation-matlab-has-different-solution-why.htmlI need to solve the lyapunov equation i.e. $A^TP + PA = -Q$. With $A = \begin{bmatrix} -2 & 1 \\ -1 & 0 \end{bmatrix}$ and $Q = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$. Hence.......Mon, 07 Sep 2026 18:23:01 -0400https://liberty.io/how-do-i-read-strawberry-facts.htmlhttps://liberty.io/how-do-i-read-strawberry-facts.htmlIn Fruit Ninja, to unlock one of the achievements, you have to "Read three strawberry facts". What does that mean? Somehow, I got that achievement; how did I do it?...Mon, 07 Sep 2026 18:10:35 -0400https://liberty.io/getting-the-sequence-1-0-1-0-1-0-1-0-ldots-without-trig.htmlhttps://liberty.io/getting-the-sequence-1-0-1-0-1-0-1-0-ldots-without-trig.htmlWhat's the simplest way to write a function that outputs the sequence: {1, 0, -1, 0, 1, 0, -1, 0, ...} ... without using any trig functions? I was able to come up with a very complex sequence ...Mon, 07 Sep 2026 17:58:55 -0400https://liberty.io/the-two-definitions-of-a-compact-set.htmlhttps://liberty.io/the-two-definitions-of-a-compact-set.htmlIn general, $A$ is compact if every open cover of $A$ contains a finite subcover of $A$. In $R$, $A$ is compact if it is closed and bounded. The second is very easy to understand because I can ea......Mon, 07 Sep 2026 17:51:45 -0400https://liberty.io/what-should-the-width-of-the-border-be-closed.htmlhttps://liberty.io/what-should-the-width-of-the-border-be-closed.htmlYou have made a rectangular stained glass window that is $2$ feet by $4$ feet. You have 7 square feet of clear glass to create a border of uniform width around the window. What should the width of ......Mon, 07 Sep 2026 17:49:44 -0400https://liberty.io/find-the-function-arcsin-cos-x.htmlhttps://liberty.io/find-the-function-arcsin-cos-x.htmlQuestion is from Spivak's Calculus 15-18. It asks to find the function $\arcsin(\cos x)$. Answer below: I have problem with the highlighted part. If that is true, then why is it our answer for ......Mon, 07 Sep 2026 17:48:29 -0400