https://track.liberty.ioFresh celebrity buzz with instant attention value.en-usMon, 07 Sep 2026 22:20:59 -0400https://track.liberty.io/selling-loot-in-ultima-7.htmlhttps://track.liberty.io/selling-loot-in-ultima-7.htmlHow do I sell things in Ultima 7? Is there a place where I can sell things like weapons, armor, potions, gems, other stuff?...Tue, 08 Sep 2026 02:20:29 -0400https://track.liberty.io/what-happens-when-i-get-attacked-by-another-player.htmlhttps://track.liberty.io/what-happens-when-i-get-attacked-by-another-player.htmlI'm currently in the grace period where I have a "shield" that prevents attacks from other players. When this expires, I assume that I'll start getting attacked. What happens when another player ...Tue, 08 Sep 2026 02:19:28 -0400https://track.liberty.io/what-main-stat-should-i-get-for-sands-with-yanfei.htmlhttps://track.liberty.io/what-main-stat-should-i-get-for-sands-with-yanfei.htmlI'm building Yanfei as a main dps carry for my team, and I have heard that Yanfei struggles with getting her burst frequently. Yet when I ask for other's opinions on what main stat to put on the sa......Tue, 08 Sep 2026 02:16:32 -0400https://track.liberty.io/what-happened-to-the-female-krogan.htmlhttps://track.liberty.io/what-happened-to-the-female-krogan.htmlSo...how the heck does this character die? I never saw anything to indicate she was wounded, except she was in the caravan when a ship crashed into it on Tuchanka. Other players have indicated she ......Tue, 08 Sep 2026 02:06:20 -0400https://track.liberty.io/do-removed-games-still-count-towards-achievements-status-on-steam.htmlhttps://track.liberty.io/do-removed-games-still-count-towards-achievements-status-on-steam.htmlI already know that it doesn't count any games with 0 achievements, but I've deleted some games with unlocked achievements from my Steam profile using help.steampowered.com. I want to know if these ...Tue, 08 Sep 2026 01:58:57 -0400https://track.liberty.io/where-are-screenshots-saved-in-eu4.htmlhttps://track.liberty.io/where-are-screenshots-saved-in-eu4.htmlI took a screenshot in Europa Universalis 4 but I can't seem to find the location of the image file! Where is it?...Tue, 08 Sep 2026 01:57:51 -0400https://track.liberty.io/what-does-the-heart-in-gyms-mean.htmlhttps://track.liberty.io/what-does-the-heart-in-gyms-mean.htmlI have been playing Pokemon Go for a while now, and I am quite new to the new gym style. Whenever I battle another persons Pokemon, the heart inches down a little. What does it mean?...Tue, 08 Sep 2026 01:54:58 -0400https://track.liberty.io/what-is-the-point-of-delays-on-redstone-repeaters.htmlhttps://track.liberty.io/what-is-the-point-of-delays-on-redstone-repeaters.htmlI think that redstone in Minecraft is quite confusing, so I'm learning about it. Then I came across redstone repeaters. I read about them and it says they repeat signals and can delay ticks. What d......Tue, 08 Sep 2026 01:53:51 -0400https://track.liberty.io/how-do-i-download-the-wolf-among-us-episode-2-without-paying-again.htmlhttps://track.liberty.io/how-do-i-download-the-wolf-among-us-episode-2-without-paying-again.htmlI have the season pass on Xbox 360 for The Wolf Among Us. Episode 2 of this is listed as available for download in-game and it's release has been widely publicised in the press. However, when I s......Tue, 08 Sep 2026 01:47:20 -0400https://track.liberty.io/how-does-wild-card-side-bets-really-work-spoiler.htmlhttps://track.liberty.io/how-does-wild-card-side-bets-really-work-spoiler.htmlThis is my first playthrough and I think I have done things backwards compared to what the designers intended. I scoured all of the wasteland and did all the DLC before I even set foot in New Vegas......Tue, 08 Sep 2026 01:34:13 -0400https://track.liberty.io/how-many-secret-levels-are-there-and-how-do-i-unlock-them.htmlhttps://track.liberty.io/how-many-secret-levels-are-there-and-how-do-i-unlock-them.htmlI know there's at least one secret level, but I've been having a lot of trouble figuring out if there's any other secret levels. My google-fu is failing me, since any search for "Secret levels&...Tue, 08 Sep 2026 01:33:15 -0400https://track.liberty.io/fallout-4-saves-are-scrambled-up-in-the-load-list-xbox-one-how-do-i-fi.htmlhttps://track.liberty.io/fallout-4-saves-are-scrambled-up-in-the-load-list-xbox-one-how-do-i-fi.htmlOk so...I cant make it to lv 25 to upgrade my deliverer to its fullest potential....and it's because every new save I make vanishes to the bottom of the list or somewhere besides the top...not only......Tue, 08 Sep 2026 01:32:27 -0400https://track.liberty.io/do-resource-potions-stack.htmlhttps://track.liberty.io/do-resource-potions-stack.htmlWith regards to the new resource potions in CoC (the ones you can store in your Clan Castle, and applies to all collectors for 1 day) - are they able to be stacked more than once. e.g. If I activa......Tue, 08 Sep 2026 01:13:04 -0400https://track.liberty.io/is-there-any-way-to-get-2-dragon-eggs-on-bedrock-without-cheating-or-d.htmlhttps://track.liberty.io/is-there-any-way-to-get-2-dragon-eggs-on-bedrock-without-cheating-or-d.htmlRecently I was playing Minecraft with one of my friends. I was playing on my switch, I didn't know what they were playing on. We went and beat the dragon and before that, I took the egg from a prev......Tue, 08 Sep 2026 01:07:08 -0400https://track.liberty.io/hearthstone-hero-replacers.htmlhttps://track.liberty.io/hearthstone-hero-replacers.htmlIs there a quick way to find all the cards that replace your hero and hero power, like Magister Dawngrasp in the crafting interface?...Tue, 08 Sep 2026 01:03:42 -0400https://track.liberty.io/can-i-build-all-ideology-wonders-in-my-original-capital-in-civilizatio.htmlhttps://track.liberty.io/can-i-build-all-ideology-wonders-in-my-original-capital-in-civilizatio.htmlCan I somehow build all ideology wonders ( Statue of Liberty, Prora and Kremlin ) into my original capital in Civilization 5? I understand that I need two revolutions to change the ideology twice b......Tue, 08 Sep 2026 01:01:16 -0400https://track.liberty.io/why-can-039-t-i-switch-equipment-vanity-items-or-clothes.htmlhttps://track.liberty.io/why-can-039-t-i-switch-equipment-vanity-items-or-clothes.htmlIs there any reason I can't switch inventory items? For example, when I hold a helmet, to put it on, I hold it to the equipment menu (the one with my head on it). It opens I put it over my other h......Tue, 08 Sep 2026 00:56:31 -0400https://track.liberty.io/how-can-i-summon-an-armor-stand-with-arms.htmlhttps://track.liberty.io/how-can-i-summon-an-armor-stand-with-arms.htmlI need help on getting armor stands with arms in Minecraft. Whenever I try it just says "Unable to summon object". I am playing Minecraft 1.11.2 and thus am looking for a command for that is not 1.......Tue, 08 Sep 2026 00:48:54 -0400https://track.liberty.io/what-039-s-the-point-of-the-quad-rocket-alt-fire.htmlhttps://track.liberty.io/what-039-s-the-point-of-the-quad-rocket-alt-fire.htmlI'm at Gen 4 so have to use the Quad Rocket to head to 5, and I have no clue why anyone would ever use the alt-fire (zoom) mode. The rockets simply seem to travel slower, and in a larger spread. ...Tue, 08 Sep 2026 00:47:13 -0400https://track.liberty.io/are-the-steam-region-locks-backwards-compatible-are-there-any-workarou.htmlhttps://track.liberty.io/are-the-steam-region-locks-backwards-compatible-are-there-any-workarou.htmlJust recently, there has been an update to Steam's region locking, which affects gifting where games that are region locked can be activated on accounts outside the countries it is locked to, but c......Tue, 08 Sep 2026 00:46:36 -0400https://track.liberty.io/transferring-clash-of-clans-from-android-to-amazon-fire-tablet.htmlhttps://track.liberty.io/transferring-clash-of-clans-from-android-to-amazon-fire-tablet.htmlI am trying to get my Clash of Clans account from Android to my Amazon Fire tablet. I have downloaded the Clash of Clans' apk but it will not allow me to sign in. Is there a way I can get Google Play ...Tue, 08 Sep 2026 00:40:18 -0400https://track.liberty.io/questions-tagged-around-the-clock-at-bikini-bottom.htmlhttps://track.liberty.io/questions-tagged-around-the-clock-at-bikini-bottom.htmlQ&A for passionate videogamers on all platforms...Tue, 08 Sep 2026 00:34:48 -0400https://track.liberty.io/blue-creepers-does-anyone-know-why-closed.htmlhttps://track.liberty.io/blue-creepers-does-anyone-know-why-closed.htmlAll my creepers are blue for some reason. All the other mobs are okay in color except creepers every creeper is dark blue completely why?...Tue, 08 Sep 2026 00:32:56 -0400https://track.liberty.io/burnout-paradise-constant-crashing-on-vista-windows-7.htmlhttps://track.liberty.io/burnout-paradise-constant-crashing-on-vista-windows-7.htmlI know this has little to do with gaming, but more to do with lack of gaming. On both my Vista PC as my Windows 7 laptop, Burnout Paradise crashes 9 times out of 10 just a few frames after going in......Tue, 08 Sep 2026 00:19:49 -0400https://track.liberty.io/is-there-a-way-to-transfer-xbox-360-hdd-contents-to-a-pc-hard-drive.htmlhttps://track.liberty.io/is-there-a-way-to-transfer-xbox-360-hdd-contents-to-a-pc-hard-drive.htmlI'm running out of space on my 360's HDD. There are several installed downloaded games on it. To clear up space, rather than deleting games (and then later redownloading from Xbox Live when needed......Tue, 08 Sep 2026 00:12:05 -0400https://track.liberty.io/is-the-notorious-n-2-n-41-prime-generator-the-last-of-its-type.htmlhttps://track.liberty.io/is-the-notorious-n-2-n-41-prime-generator-the-last-of-its-type.htmlThe polynomial $n^2+n+41$ famously takes prime values for all $0\le n\lt 40$. I have read that this is closely related to the fact that 163 is a Heegner number, although I don't understand the argu......Mon, 07 Sep 2026 23:48:52 -0400https://track.liberty.io/what-digit-appears-in-unit-place-when-2-320-is-multiplied-out.htmlhttps://track.liberty.io/what-digit-appears-in-unit-place-when-2-320-is-multiplied-out.htmlIs there a way to answer the following preferably without a calculator What digit appears in unit place when $2^{320}$ is multiplied out ? a)$0$ b)$2$ c)$4$ d)$6$ e)$8$ ---- Ans(d)...Mon, 07 Sep 2026 23:41:16 -0400https://track.liberty.io/gta-iv-lag-on-powerful-laptop.htmlhttps://track.liberty.io/gta-iv-lag-on-powerful-laptop.htmlI get about 15-20 FPS in GTA IV. I should be able to run it on the highest setting with over 60 FPS. I have tried to lower all the settings to low, but it doesn't improve my performance at all, not......Mon, 07 Sep 2026 23:38:09 -0400https://track.liberty.io/applearcade-the-oregon-trail-what-does-wagon-grease-do.htmlhttps://track.liberty.io/applearcade-the-oregon-trail-what-does-wagon-grease-do.htmlIn the AppleArcade version of the Oregon Trail, the purpose of wagon grease is described as increasing the wagon's resistance to damage. When used, the wagon glows green for a moment with some + sy......Mon, 07 Sep 2026 23:24:31 -0400https://track.liberty.io/mantra-of-retribution-vs-conviction.htmlhttps://track.liberty.io/mantra-of-retribution-vs-conviction.htmlI'm wondering which of these to take on my lvl 60 monk who's currently farming Act 1 of Inferno (killed the Butcher). I could take MoR with the Transgression rune for the nice bonus to attack speed......Mon, 07 Sep 2026 23:23:06 -0400https://track.liberty.io/is-there-a-geometric-interpretation-of-the-product-integral.htmlhttps://track.liberty.io/is-there-a-geometric-interpretation-of-the-product-integral.htmlRiemann's "way to the Integral" is loosely speaking the limit of sums of this kind \begin{equation} \sum_if(x_i)\Delta x_i \end{equation} Now, if we replace the sum with a product and the multiplic......Mon, 07 Sep 2026 23:08:03 -0400https://track.liberty.io/what-were-some-major-mathematical-breakthroughs-in-2016-closed.htmlhttps://track.liberty.io/what-were-some-major-mathematical-breakthroughs-in-2016-closed.htmlAs the year is slowly coming to an end, I was wondering which great advances have there been in mathematics in the past 12 months. As researchers usually work in only a limited number of fields in ...Mon, 07 Sep 2026 23:06:25 -0400https://track.liberty.io/square-root-long-division-method-root-24-trouble.htmlhttps://track.liberty.io/square-root-long-division-method-root-24-trouble.htmlI'm trying to get a grasp of the long division method of square roots without a calculator via pen and paper, but i'm having some trouble. I've been trying to increase understanding with practice, ......Mon, 07 Sep 2026 23:01:27 -0400https://track.liberty.io/how-do-i-allow-other-players-on-my-server-to-use-commands-like-telepor.htmlhttps://track.liberty.io/how-do-i-allow-other-players-on-my-server-to-use-commands-like-telepor.htmlI play on the DivineJourney modpack with a friend, but he wants to constantly spawn things in. Is there any way to allow him to be able to use the teleport command, but not be able to spawn in item......Mon, 07 Sep 2026 22:55:07 -0400https://track.liberty.io/what-are-the-units-in-age-of-mythology-saying.htmlhttps://track.liberty.io/what-are-the-units-in-age-of-mythology-saying.htmlWhat are the units saying in Age of Mythology? For example, when I click on a Hoplite he says "Prostagma". What does that mean? Is there a resource that has all the unit's quotes for all the races (...Mon, 07 Sep 2026 22:53:56 -0400https://track.liberty.io/evaluate-sum-k-0-nk-n-k.htmlhttps://track.liberty.io/evaluate-sum-k-0-nk-n-k.htmlEvaluate $\sum_{k=0}^nk(n-k)$ I have $\sum_{k=0}^nkn-\sum_{k=0}^nk^2$ then im suppose to use the identity of $\left( \begin{array}{c} r \\ r \end{array} \right)+\left( \begin{array}{c} r+1 \\ r ......Mon, 07 Sep 2026 22:44:44 -0400https://track.liberty.io/how-can-you-prove-that-1-05-50-100-without-a-calculator.htmlhttps://track.liberty.io/how-can-you-prove-that-1-05-50-100-without-a-calculator.htmlIs there a way to prove that $1.05^{50} < 100$ without a calculator? I have tried this... $$1.05^{50}<10^2$$ $$(\frac{105}{100})^{50}<10^2$$ $$(\frac{21}{20})^{50}<10^2$$ $$\frac{21^{......Mon, 07 Sep 2026 22:42:51 -0400https://track.liberty.io/is-it-possible-to-rename-characters-in-castle-crashers.htmlhttps://track.liberty.io/is-it-possible-to-rename-characters-in-castle-crashers.htmlIs it possible to rename characters in Castle Crashers? All created characters are named "profile name(number)" and are hard to distinguish....Mon, 07 Sep 2026 22:35:45 -0400https://track.liberty.io/do-polynomials-with-complex-coefficients-need-to-have-complex-conjugat.htmlhttps://track.liberty.io/do-polynomials-with-complex-coefficients-need-to-have-complex-conjugat.htmlFrom the Complex conjugate root theorem we get that if a polynomial in one varaible with real coefficients has as solution $a + bi$ , than $a-bi$ must also be a solution...however, what happens if......Mon, 07 Sep 2026 22:21:03 -0400https://track.liberty.io/can-you-get-a-refund-either-rp-or-ip-on-a-champion-if-you-do-not-like-.htmlhttps://track.liberty.io/can-you-get-a-refund-either-rp-or-ip-on-a-champion-if-you-do-not-like-.htmlI bought a champion the other day with RP and I'm not particularly fond of them. Does Riot state a return policy (I didn't notice one) on refunding a champ for the price that I paid for it?...Mon, 07 Sep 2026 22:18:52 -0400https://track.liberty.io/i-don-039-t-understand-why-this-card-trick-works.htmlhttps://track.liberty.io/i-don-039-t-understand-why-this-card-trick-works.htmlSo a friend of mine showed me a very interesting card trick that I don't quite understand. You have 52 normal cards from any regular deck you can buy anywhere. The Ace is worth 1 while 2 through 1......Mon, 07 Sep 2026 22:16:08 -0400https://track.liberty.io/probability-of-winning-a-contest.htmlhttps://track.liberty.io/probability-of-winning-a-contest.htmlThis is my first question so apologies if its unclear/vague. There exists a contest with me in it, and $5$ others, thus $6$ people in total, along with $5$ prizes. A person can only win one prize,......Mon, 07 Sep 2026 22:11:07 -0400https://track.liberty.io/common-symbols-in-linear-algebra.htmlhttps://track.liberty.io/common-symbols-in-linear-algebra.htmlI would like to clarify what symbols are the most commonly used for the following concepts in linear algebra: Linear transformations from $V$ to $U$, and the set of all transformations. A $m$-by-$n$ ...Mon, 07 Sep 2026 22:10:47 -0400https://track.liberty.io/where-can-i-find-ainethach.htmlhttps://track.liberty.io/where-can-i-find-ainethach.htmlThis guy hired thugs to kill me. I read the contract and the guy was called Ainethach. Where can I find him?...Mon, 07 Sep 2026 22:01:39 -0400https://track.liberty.io/filling-a-rectangle-with-congruent-squares-in-two-columns.htmlhttps://track.liberty.io/filling-a-rectangle-with-congruent-squares-in-two-columns.htmlI have a rectangle. This rectangle is divided into two columns; the widths of these columns are not necessarily equal, and are not known. I want to fill the rectangle with squares. The number of sq......Mon, 07 Sep 2026 22:01:08 -0400https://track.liberty.io/how-do-i-get-a-coupon-for-the-lumiose-city-boutique.htmlhttps://track.liberty.io/how-do-i-get-a-coupon-for-the-lumiose-city-boutique.htmlIt seems that I've finally been able to get into the shop, but the prices are incredibly expensive. There was a woman who mentioned being able to get a discount card, but no mention of how to get ......Mon, 07 Sep 2026 22:01:01 -0400https://track.liberty.io/find-all-solutions-of-ax-0-in-parametric-vector-form.htmlhttps://track.liberty.io/find-all-solutions-of-ax-0-in-parametric-vector-form.htmlHow can I find all solutions of $Ax = 0$ in parametric vector form where A is row equivalent to the matrix $\begin{pmatrix} -1&-4&0&-4\\2&-8&0&8 \end{pmatrix}$...Mon, 07 Sep 2026 21:56:34 -0400https://track.liberty.io/an-example-for-the-partition-of-unity-for-a-circle.htmlhttps://track.liberty.io/an-example-for-the-partition-of-unity-for-a-circle.htmlI am trying to wrap my head around on what partition of unity means and trying to understand some examples of it. I have an engineering background so most of the abstract discussions are a little h......Mon, 07 Sep 2026 21:53:14 -0400https://track.liberty.io/is-the-sum-of-two-singular-matrices-also-singular.htmlhttps://track.liberty.io/is-the-sum-of-two-singular-matrices-also-singular.htmlIf $A$ and $B$ are $n \times n$ singular matrices, is $A+B$ also singular?...Mon, 07 Sep 2026 21:49:22 -0400https://track.liberty.io/christoffel-symbols-and-metric.htmlhttps://track.liberty.io/christoffel-symbols-and-metric.htmlFor Christoffel symbol and metric, we've the following identity $$\large \frac{1}{2}g^{\alpha\gamma}(g_{\alpha\beta,\mu}+g_{\alpha\mu,\beta}- g_{\beta\mu,\alpha})={\mathrm\Gamma^{\gamma}}_{\bet......Mon, 07 Sep 2026 21:47:21 -0400https://track.liberty.io/when-should-you-buy-cull-and-on-which-champions.htmlhttps://track.liberty.io/when-should-you-buy-cull-and-on-which-champions.htmlI play a lot of adc, especially Vayne, and I know she is a late game champion and needs a few items. I don't currently use Cull because I don't see other people build it, but I don't understand why......Mon, 07 Sep 2026 21:43:03 -0400https://track.liberty.io/use-de-morgan-039-s-laws-to-simplify-the-following-sets.htmlhttps://track.liberty.io/use-de-morgan-039-s-laws-to-simplify-the-following-sets.htmlSimplify the following sets: $$ℝ\setminus \bigcap\limits_{n=1}^∞ (-1/n,1/n)\tag1$$ $$\bigcup\limits_{n=1}^∞ (ℝ\setminus[1/n,2+1/n])\tag2$$ For the first problem, I used De Morgan's law, and it e......Mon, 07 Sep 2026 21:38:31 -0400https://track.liberty.io/is-categories-and-sheaves-a-good-followup-to-aluffi-039-s-algebra-chap.htmlhttps://track.liberty.io/is-categories-and-sheaves-a-good-followup-to-aluffi-039-s-algebra-chap.htmlI'm about to finish Aluffi's "algebra: chapter 0" and am a bit confused as to what should be my next move. I've been planning to read Tom Dieck's Algebraic Topology for some time now. I glimpsed at......Mon, 07 Sep 2026 21:13:42 -0400https://track.liberty.io/why-is-1-1-1-duplicate.htmlhttps://track.liberty.io/why-is-1-1-1-duplicate.htmlI apologize if this is too obvious, but I crave for a reasonable definition/explanation - why is $(-1)(-1)=1$? Something akin to the reason $a^{-1}=\frac{1}{a}$, I.e. because $a^{-1}a^1=a^{1-1=0}......Mon, 07 Sep 2026 20:56:21 -0400https://track.liberty.io/what-are-the-dominant-weapon-armor-configurations.htmlhttps://track.liberty.io/what-are-the-dominant-weapon-armor-configurations.htmlI'm playing through Final Fantasy X HD Remaster (which should be the same as the FFX International.) I wondered is there an accepted dominant Weapon/Armor configuration? As far as the best abiliti......Mon, 07 Sep 2026 20:50:05 -0400https://track.liberty.io/how-do-damage-multipliers-stack.htmlhttps://track.liberty.io/how-do-damage-multipliers-stack.htmlI've been wondering how multipliers stack since I got hold of Old Faithful, which deals x2 damage when the enemy hit was on full health. Do we know how this interacts with stuff like sneak attacks? (...Mon, 07 Sep 2026 20:46:05 -0400https://track.liberty.io/is-the-mace-of-the-insolent-comparable-to-the-blue-flame-sword.htmlhttps://track.liberty.io/is-the-mace-of-the-insolent-comparable-to-the-blue-flame-sword.htmlI've read on various forums that the Blue Flame Sword for sorcery casters can scale insanely well (innate magic damage, magic infusion, and crystal magic weapon). If done correctly, this can be the ...Mon, 07 Sep 2026 20:44:49 -0400https://track.liberty.io/how-to-maximize-the-profit-for-the-given-equation.htmlhttps://track.liberty.io/how-to-maximize-the-profit-for-the-given-equation.htmlIt is a maximize profit question. Basically: There is a play which costs $180$ Each attendee costs $0.4$ Ticket price affects the overall attendance. When the ticket price is $5$, then there are ......Mon, 07 Sep 2026 20:37:18 -0400https://track.liberty.io/1-minus-percentage-what-is-this-called.htmlhttps://track.liberty.io/1-minus-percentage-what-is-this-called.htmlI'm trying to convert a percentage: The original percentage represents how bad the condition of a asset is (in other words, a high number is bad). I would like to convert the percentage to represen......Mon, 07 Sep 2026 20:30:44 -0400https://track.liberty.io/incapacitating-dahl-quest.htmlhttps://track.liberty.io/incapacitating-dahl-quest.htmlTowards the end of the game, you can incapacitate Dahl instead of outright killing him. This opens up an option to leave the station, as well as allow for any crew members you've saved to leave. I......Mon, 07 Sep 2026 20:25:37 -0400https://track.liberty.io/i-dismissed-jenassa-now-i-can-039-t-find-her-at-the-drunken-huntsman-w.htmlhttps://track.liberty.io/i-dismissed-jenassa-now-i-can-039-t-find-her-at-the-drunken-huntsman-w.htmlPossible Duplicate: How do I find my follower if and when they leave me? I paid Jenassa 500 gold and hired her as a companion. This was before I became the thane of Dragonsreach. I was really ......Mon, 07 Sep 2026 20:23:59 -0400https://track.liberty.io/circle-least-squares-fit.htmlhttps://track.liberty.io/circle-least-squares-fit.htmlSo my question is this: Find the equation of the circle that gives the best least squares circle fit to the points $(-1,-2), (0,2.4), (1.1,-4),$ and $(2.4,-1.6).$ So far I have this general equa......Mon, 07 Sep 2026 20:20:28 -0400https://track.liberty.io/do-ps1-or-ps2-memory-cards-die-over-time-like-cartridges.htmlhttps://track.liberty.io/do-ps1-or-ps2-memory-cards-die-over-time-like-cartridges.htmlI have a PS1, PS2, PSP and a PS3. With an adapter (official, made by Sony), I was able to copy my old file saves from my old games into my PS3, so I can keep them without being erased for long time......Mon, 07 Sep 2026 20:19:33 -0400https://track.liberty.io/is-it-worth-it-to-get-better-at-contest-math.htmlhttps://track.liberty.io/is-it-worth-it-to-get-better-at-contest-math.htmlI have never done well in math competitions, and am now past the point at which I can participate in them. I am asking if it is worth it to go back and practice such types of problems until I gain ......Mon, 07 Sep 2026 20:14:54 -0400https://track.liberty.io/how-to-find-the-domain-of-this-function.htmlhttps://track.liberty.io/how-to-find-the-domain-of-this-function.htmlf(x)= $\frac{(\sqrt{x}-\sqrt{x-1} )}{( \sqrt{x}+\sqrt{x-1} )}\;$ first off $\sqrt{x}$ is defined for: $$x > 0 \tag{1}$$ and $\sqrt{x-1}$ is defined for: $$x \ge 1 ......Mon, 07 Sep 2026 20:13:34 -0400https://track.liberty.io/magnitude-of-cross-product-given-2-vector-magnitudes-and-angle-between.htmlhttps://track.liberty.io/magnitude-of-cross-product-given-2-vector-magnitudes-and-angle-between.htmlif the magnitude of vector U is 6 and the magnitude of vector V is 9, and the angle between these vectors is 60 degrees, what is ||U x V||? Why is the answer not 54Sin(60)?...Mon, 07 Sep 2026 20:05:04 -0400https://track.liberty.io/how-can-i-soft-reset.htmlhttps://track.liberty.io/how-can-i-soft-reset.htmlI've already completed the game 3 times and I only recently found out about Soft Resetting. I wanted to try it but after 17 on Heatran, I got really Impatient. If anyone has an easily explained tu......Mon, 07 Sep 2026 20:03:01 -0400https://track.liberty.io/what-is-a-homomorphism.htmlhttps://track.liberty.io/what-is-a-homomorphism.htmlI am starting to see the term everywhere I look, but every time I do, I get confused and can't get past it. I've seen various definitions: ("linear" homomorphism, i think) $$f:S\rightarrow T $$ $$\...Mon, 07 Sep 2026 19:57:13 -0400https://track.liberty.io/prerequisites-for-atiyah-macdonald.htmlhttps://track.liberty.io/prerequisites-for-atiyah-macdonald.htmlI am currently doing a one semester course on groups and rings where we have learned about (so far): Definitions of groups, subgroups, cyclic and normal subgroups, the symmetric group, homomorphis......Mon, 07 Sep 2026 19:56:34 -0400https://track.liberty.io/difficulty-in-understanding-find-e-n-where-n-min-n-0-x-n-x-0.htmlhttps://track.liberty.io/difficulty-in-understanding-find-e-n-where-n-min-n-0-x-n-x-0.htmlIt is Question 30 on page 168 in Ross's book (Introduction to Probability Models-11th edition) Let $X_i, i\ge 0$ be independent and identically distributed random variables with probability mass ...Mon, 07 Sep 2026 19:49:12 -0400https://track.liberty.io/which-buildings-have-lots-of-ingredients.htmlhttps://track.liberty.io/which-buildings-have-lots-of-ingredients.htmlI'm prioritizing improvement of the Alchemy and Enchanting skills because they can enhance practically everything else, including each other. I'm focusing on creating potions with a Paralyze effect......Mon, 07 Sep 2026 19:46:21 -0400https://track.liberty.io/classification-of-finite-abelian-groups.htmlhttps://track.liberty.io/classification-of-finite-abelian-groups.htmlI'm new to group theory and struggling with understanding what is required in an example problem I'm working through. I need to classify the following using the classification og finite abelian gr......Mon, 07 Sep 2026 19:42:19 -0400https://track.liberty.io/how-can-i-talk-to-neloth-without-him-attacking-me.htmlhttps://track.liberty.io/how-can-i-talk-to-neloth-without-him-attacking-me.htmlEvery time I walk into the mushroom area, Neloth and his assistant try to kill me. I need to talk to them for the quest Path of Knowledge, but I'm not able to....Mon, 07 Sep 2026 19:41:38 -0400https://track.liberty.io/do-diamonds-spawn-less-in-the-mountains-and-extreme-hills-biomes.htmlhttps://track.liberty.io/do-diamonds-spawn-less-in-the-mountains-and-extreme-hills-biomes.htmlI don't know if diamonds spawn less in mountains and extreme hills biomes or not, but I always seem to get extreme-hilly unlucky (sorry) with finding diamonds in those biomes. The other day I spent......Mon, 07 Sep 2026 19:40:58 -0400https://track.liberty.io/deducing-pa-039-s-axioms-in-zfc.htmlhttps://track.liberty.io/deducing-pa-039-s-axioms-in-zfc.htmlRecently I've stumbled across this claim: Peano axioms can be deduced in ZFC I found a lot of info regarding this claim (e.g. what would (one version of) the natural numbers look like within the ...Mon, 07 Sep 2026 19:09:21 -0400https://track.liberty.io/proof-of-a-determinant-identity.htmlhttps://track.liberty.io/proof-of-a-determinant-identity.htmlI have a matrix identity that I wish to prove, which relates the determinant of a matrix to determinants of sub-matrices (essentially, cofactors of the larger matrix). In general terms, consider the ...Mon, 07 Sep 2026 19:07:57 -0400https://track.liberty.io/find-the-maximum-and-minimum-value-of-variance-duplicate.htmlhttps://track.liberty.io/find-the-maximum-and-minimum-value-of-variance-duplicate.htmlLet $X$ be an arbitrary random variable takes values in $\{0,1,2,...,10\}$. Then the minimum and maximum values of variance of random variable $X$ are $0$ and $30$ $1$ and $30$ $0$ and $25$ $1$......Mon, 07 Sep 2026 19:06:11 -0400https://track.liberty.io/where-can-i-find-iron-gold-and-diamond-in-survival-mode.htmlhttps://track.liberty.io/where-can-i-find-iron-gold-and-diamond-in-survival-mode.htmlWhere can I find Iron, Gold, and Diamond in Minecraft Pocket Edition Survival Mode? I can only find gravel, dirt, wood, sand, and cobblestone....Mon, 07 Sep 2026 18:57:56 -0400https://track.liberty.io/matchmaking-claiming-i-have-to-reconnect-to-a-finished-game.htmlhttps://track.liberty.io/matchmaking-claiming-i-have-to-reconnect-to-a-finished-game.htmlToday I played 2 competitive matches in CS:GO. After the first competitive match ended, and tried to start the second game, it told me I still had a game going, and should reconnect from the main m......Mon, 07 Sep 2026 18:50:05 -0400https://track.liberty.io/prove-the-converse-of-wilson-039-s-theorem-duplicate.htmlhttps://track.liberty.io/prove-the-converse-of-wilson-039-s-theorem-duplicate.html... namely that if $n > 1$ and $(n − 1)!\equiv−1\pmod{n}$, then $n$ is prime. This is for a number theory class I'm in at Penn State. My idea is to follow accordingly, but I can't get it concre......Mon, 07 Sep 2026 18:42:15 -0400https://track.liberty.io/using-the-arnoldi-iteration-to-find-the-k-largest-eigenvalues-of-a-mat.htmlhttps://track.liberty.io/using-the-arnoldi-iteration-to-find-the-k-largest-eigenvalues-of-a-mat.htmlI'm trying to obtain a general understanding of this algorithm which determines the k-largest eigenvalues of a matrix $A\in \mathbb{R}^{n\times n}$. How I see it: power iteration: take random ...Mon, 07 Sep 2026 18:31:05 -0400https://track.liberty.io/does-collecting-keys-and-dogtags-have-any-purpose-other-than-trophies.htmlhttps://track.liberty.io/does-collecting-keys-and-dogtags-have-any-purpose-other-than-trophies.htmlIs there a specific reason to collect all of these car keys, or all of the dog tags? To put it simply, are these only in the game for those try-hard gamers that think they have to get everything in a ...Mon, 07 Sep 2026 18:29:29 -0400https://track.liberty.io/droprate-of-prideful-gear-from-celestials.htmlhttps://track.liberty.io/droprate-of-prideful-gear-from-celestials.htmlAs PvP season 15 is dawning upon us, Blizzard has decided to give us a chance at next seasons gear by letting us do Celestials and getting a chance for the gear. What are the drop rates of the items ...Mon, 07 Sep 2026 18:23:27 -0400https://track.liberty.io/which-npcs-can-point-me-to-san-francisco.htmlhttps://track.liberty.io/which-npcs-can-point-me-to-san-francisco.htmlI want to travel to San Francisco. Unfortunately it's been a long time and I forgot where it is and people in other towns don't want to tell me. I have asked for directions and got plenty, but none......Mon, 07 Sep 2026 18:21:40 -0400https://track.liberty.io/how-many-different-eulerian-circuits-are-there-in-this-graph.htmlhttps://track.liberty.io/how-many-different-eulerian-circuits-are-there-in-this-graph.htmlI'm trying to figure out how many different Eulerian circuits there are in the following graph. I have found one Eulerian circuit so far (see photo below, start- and end point to the far left). How ...Mon, 07 Sep 2026 17:59:37 -0400https://track.liberty.io/orthogonal-art-gallery-problem.htmlhttps://track.liberty.io/orthogonal-art-gallery-problem.htmlHere is a problem: One should position the least amount of cameras in an art gallery. The walls in the gallery are represented only by horizontal and vertical line segments. I am trying to find the ...Mon, 07 Sep 2026 17:54:04 -0400https://track.liberty.io/find-the-projection-of-b-onto-the-column-space-of-a.htmlhttps://track.liberty.io/find-the-projection-of-b-onto-the-column-space-of-a.html$A= \left[ {\begin{array}{ccccc} 1 & 1 \\ 1 & -1 \\ -2 & 4 \end{array} } \right] $ and $b = \left[ {\begin{array}{cccc} 1 \\ 2 \\ 7 \end{array} } \right] $ ......Mon, 07 Sep 2026 17:53:50 -0400https://track.liberty.io/minecraft-sound-effects.htmlhttps://track.liberty.io/minecraft-sound-effects.htmlI am doing a Minecraft animation and I need Minecraft sound effects does anyone know any safe website where java Minecraft sounds can be downloaded?...Mon, 07 Sep 2026 17:40:18 -0400https://track.liberty.io/markov-chains-and-stochastic-matrix.htmlhttps://track.liberty.io/markov-chains-and-stochastic-matrix.htmlGive an example of a $2\times 2$ regular transition matrix $T$ and an initial state probability vector $x$ such that all the entries in $T^{1000}$x is still different from the steady state vector w......Mon, 07 Sep 2026 17:36:34 -0400https://track.liberty.io/the-case-of-being-vacuously-true-trivially-true-and-the-empty-set.htmlhttps://track.liberty.io/the-case-of-being-vacuously-true-trivially-true-and-the-empty-set.htmlLet's suppose that we need to prove a statement of the form $\forall x(x\in A\longrightarrow\phi)$, where $\phi$ is any property (for example when we need to prove that $A\subseteq A\cup B$). Is it ...Mon, 07 Sep 2026 17:28:27 -0400https://track.liberty.io/is-it-correct-to-say-that-square-root-of-0-9-is-0-9-itself.htmlhttps://track.liberty.io/is-it-correct-to-say-that-square-root-of-0-9-is-0-9-itself.htmlWhen I calculate Square Root of 0.9, it comes around 0.9486832980505138. Though I have heard people occasionally saying that the square root of 0.9 is 0.9 itself. Would it be correct to make a stat......Mon, 07 Sep 2026 17:15:56 -0400https://track.liberty.io/find-the-remainder-when-123412341234-written-1234-times-is-divided-by-.htmlhttps://track.liberty.io/find-the-remainder-when-123412341234-written-1234-times-is-divided-by-.htmlFind the remainder when $123412341234$...(written $1234$ times) is divided by $13$ I divided $1234$ by $13$ and I got the answer $12$ which is the correct answer but what is the approach behind so......Mon, 07 Sep 2026 17:05:39 -0400https://track.liberty.io/intuitive-explanation-of-double-expectation.htmlhttps://track.liberty.io/intuitive-explanation-of-double-expectation.htmlThis has been bugging me for some time. The famous result in probability is like $E[Y] = E[E[Y|X]]$ Can someone write an intuitive explanation of the above?...Mon, 07 Sep 2026 17:04:22 -0400https://track.liberty.io/the-proper-symbol-to-denote-proper-subset.htmlhttps://track.liberty.io/the-proper-symbol-to-denote-proper-subset.html⊂ and ⊃ symbols Some authors use the symbols ⊂ and ⊃ to indicate subset and superset respectively; that is, with the same meaning and instead of the symbols, ⊆ and ⊇ Other authors prefer to use the ...Mon, 07 Sep 2026 17:01:57 -0400https://track.liberty.io/how-to-avoid-introducing-a-spurious-solution.htmlhttps://track.liberty.io/how-to-avoid-introducing-a-spurious-solution.htmlSuppose I have $\sqrt{r-x}-\frac{x}{\sqrt{r-x}}-o=0$ with $r,x$ and $o$ real. To solve I multiply by $\sqrt{r-x}$. I assume therefore $r>x$ $r-x-x-o\sqrt{r-x}=0$ $r-2x=o\sqrt{r-x}$ Squaring......Mon, 07 Sep 2026 16:56:17 -0400https://track.liberty.io/show-that-the-inverse-of-a-strictly-diagonally-dominant-matrix-is-mono.htmlhttps://track.liberty.io/show-that-the-inverse-of-a-strictly-diagonally-dominant-matrix-is-mono.htmlI have been struggling with this problem for awhile. Given that $A$ is a strictly diagonally dominant matrix with positive diagonal entries and non-positive off-diagonal entries, show that $A$ is ...Mon, 07 Sep 2026 16:56:12 -0400https://track.liberty.io/why-do-the-ivs-change-based-on-level.htmlhttps://track.liberty.io/why-do-the-ivs-change-based-on-level.htmlI know how IVs in Pokemon Go work, but I don't understand why when I check my Pokemon's IVs on an IV calculator, I get multiple IV combinations back. For instance, say I check IVs on a Pikachu. T......Mon, 07 Sep 2026 16:56:06 -0400https://track.liberty.io/can-a-system-of-linear-equations-be-inconsistent-even-if-the-last-colu.htmlhttps://track.liberty.io/can-a-system-of-linear-equations-be-inconsistent-even-if-the-last-colu.htmlI have a simple question which is troubling me. I have seen this theorem in Linear Algebra which I quote here : The Row Echelon Form of an Inconsistent System: An augmented matrix corresponds t......Mon, 07 Sep 2026 16:55:39 -0400https://track.liberty.io/how-can-one-prove-that-pi-4-pi-5-e-6.htmlhttps://track.liberty.io/how-can-one-prove-that-pi-4-pi-5-e-6.htmlA proof of the inequality using properties of $\pi$ and $e$, for example, is what I'm looking for. Not calculator approximations showing the inequality holds....Mon, 07 Sep 2026 16:48:24 -0400https://track.liberty.io/meaning-of-limit-as-h-approaches-0.htmlhttps://track.liberty.io/meaning-of-limit-as-h-approaches-0.htmlI am learning differentiation, and am having some trouble understanding what is meant by h approaching zero, from a positive or negative direction. If I understand correctly, h is one point on the ......Mon, 07 Sep 2026 16:40:34 -0400