https://liberty.ioCurated star highlights with fresh energy.en-usMon, 07 Sep 2026 10:21:49 -0400https://liberty.io/division-isn-039-t-associative.htmlhttps://liberty.io/division-isn-039-t-associative.htmlConsider the following fraction: $$\frac{\frac{\frac{a}{b}}{c}}{a}$$ How to explain that: $$\frac{\frac{\frac{a}{b}}{c}}{a} \ne \frac{\frac{a^2}{b}}{c}$$ Obviously, you get different results. ......Mon, 07 Sep 2026 14:05:44 -0400https://liberty.io/is-it-possible-to-get-the-horadric-cube-with-a-level-lower-than-70.htmlhttps://liberty.io/is-it-possible-to-get-the-horadric-cube-with-a-level-lower-than-70.htmlIs it possible to get the cube right at the start of a season journey with level 10 for example?...Mon, 07 Sep 2026 14:03:57 -0400https://liberty.io/why-does-it-make-no-sense-to-define-addition-on-points-in-geometry.htmlhttps://liberty.io/why-does-it-make-no-sense-to-define-addition-on-points-in-geometry.htmlHere is a simple question: Why does it not make sense to define addition on points in geometry? To be a bit more specific: assume we are talking only about standard Euclidean geometry. It is clea......Mon, 07 Sep 2026 13:56:01 -0400https://liberty.io/is-it-possible-to-respec-all-skill-points-duplicate.htmlhttps://liberty.io/is-it-possible-to-respec-all-skill-points-duplicate.htmlPossible Duplicate: Is there any way to respec? In town, there is an NPC that lets me respec the last 3 skills I chose, but I want to respec everything. Is there a way to reset my skill point......Mon, 07 Sep 2026 13:53:47 -0400https://liberty.io/what-would-be-the-most-significant-way-to-farm-neural-sensors-in-warfr.htmlhttps://liberty.io/what-would-be-the-most-significant-way-to-farm-neural-sensors-in-warfr.htmlI've been on a crafting spree in Warframe, and a lot of the things that I am trying to make require 2 at most, which doesn't seem like a lot, but when they are rare drops, it makes it a hassle. Any......Mon, 07 Sep 2026 13:40:08 -0400https://liberty.io/how-do-i-kill-the-crab-boss.htmlhttps://liberty.io/how-do-i-kill-the-crab-boss.htmlIn the Beach world, the end boss is at least one (I think three, though, if the cutscene is any indication) crab. I have no idea how to fight it! No matter what I do, it seems to hurt me, and I am ......Mon, 07 Sep 2026 13:39:49 -0400https://liberty.io/how-to-test-weapons-in-battlefield-3-without-affecting-accuracy-score.htmlhttps://liberty.io/how-to-test-weapons-in-battlefield-3-without-affecting-accuracy-score.htmlDo you know of any time when the game is [not] counting the bullets you fire or registering any hits or misses? Would the time when there is this "Waiting for players" message be suitable? The reas......Mon, 07 Sep 2026 13:37:06 -0400https://liberty.io/differentiation-of-fractions-and-negative-powers-y-3-sqrt-3-x.htmlhttps://liberty.io/differentiation-of-fractions-and-negative-powers-y-3-sqrt-3-x.htmlI am stuck with this concept, just can't get my head around it. I am differentiating fractions and negative powers, I have this question to solve which I just cannot figure out: $$y=-3/\sqrt[3]{x}......Mon, 07 Sep 2026 13:30:02 -0400https://liberty.io/software-to-explore-abstract-algebra-and-or-category-theory-closed.htmlhttps://liberty.io/software-to-explore-abstract-algebra-and-or-category-theory-closed.htmlIs there any software that lets one explore group theory, ring theory, and category theory visually and theoretically that is tailored for education purposes? I'm not talking about using software l......Mon, 07 Sep 2026 13:17:16 -0400https://liberty.io/integral-of-cosh-3-x.htmlhttps://liberty.io/integral-of-cosh-3-x.htmlWhat is the integral of $\cosh^3(x)$? And how exactly can I calculate it? I've tried setting $\cosh^3(x)=(\frac{e^x+e^{-x}}{2})^3$ but all I get in the end is one long fraction....Mon, 07 Sep 2026 13:16:30 -0400https://liberty.io/where-can-i-see-the-approval-rating-of-my-companions.htmlhttps://liberty.io/where-can-i-see-the-approval-rating-of-my-companions.htmlI'm pretty much constantly seeing notifications like "Solas approves" or "Cassandra disapproves", but I still have no idea on how much my companions approve or disapprove of myself in general. I as......Mon, 07 Sep 2026 13:16:12 -0400https://liberty.io/why-the-axioms-for-a-topological-space-are-those-axioms.htmlhttps://liberty.io/why-the-axioms-for-a-topological-space-are-those-axioms.htmlThis question might have even been asked here before, I don't really know, so sorry if it's duplicate. I've started to study topological spaces and I've found the axioms for such spaces kind of har......Mon, 07 Sep 2026 13:15:07 -0400https://liberty.io/concave-down-increasing-example.htmlhttps://liberty.io/concave-down-increasing-example.htmlI'm looking for a concave down increasing-function, see the image in the right lower corner. Basically I need a function f(x) which will rise slower as x is increasing. The x will be in range of [......Mon, 07 Sep 2026 13:13:33 -0400https://liberty.io/proving-existence-of-inverse-function-using-the-rule-of-differentiatin.htmlhttps://liberty.io/proving-existence-of-inverse-function-using-the-rule-of-differentiatin.htmlI am working from a textbook that gives us that The derivative of the inverse function is $$ \frac{dx}{dy} = \large{\frac{1}{\frac{dy}{dx}}}.\qquad (*)$$ $$$$ Now I am stuck on part $(a)$ of the ...Mon, 07 Sep 2026 13:03:24 -0400https://liberty.io/questions-tagged-chinese-remainder-theorem.htmlhttps://liberty.io/questions-tagged-chinese-remainder-theorem.htmlQ&A for people studying math at any level and professionals in related fields...Mon, 07 Sep 2026 12:58:11 -0400https://liberty.io/when-to-use-which-z-score-equation.htmlhttps://liberty.io/when-to-use-which-z-score-equation.htmlin some exam past papers I have been doing I have come across the statistics equation z=(sample mean - mean)/standard deviation as well as the equation z = (sample mean - mean)/(standard devia......Mon, 07 Sep 2026 12:54:30 -0400https://liberty.io/resultant-from-40-n-and-30-n-vectors.htmlhttps://liberty.io/resultant-from-40-n-and-30-n-vectors.htmlIf $F_1$ has magnitude 30 N and $F_2$ has magnitude 40 N, what is the exact magnitude and direction of the resultant vector? I think I should apply the Pythagorean theorem to get the magnitude, so......Mon, 07 Sep 2026 12:34:26 -0400https://liberty.io/how-do-you-unlock-the-4-extra-characters.htmlhttps://liberty.io/how-do-you-unlock-the-4-extra-characters.htmlIn Super Mario Party, you have 4 extra characters that are locked at the beginning of the game. Without a single player mode to speak of, how do you unlock them?...Mon, 07 Sep 2026 12:08:46 -0400https://liberty.io/in-which-branch-of-mathematics-does-logarithm-belong-arithmetic-or-alg.htmlhttps://liberty.io/in-which-branch-of-mathematics-does-logarithm-belong-arithmetic-or-alg.htmlI'm currently working on an iOS & Android application for GCE O Level students. I have to classify everything neatly such that Maths never appears to be a messy subject to study and so should I ...Mon, 07 Sep 2026 12:08:10 -0400https://liberty.io/application-of-cauchy-davenport.htmlhttps://liberty.io/application-of-cauchy-davenport.htmlLet $ p $ be a prime number and $ A \subset \mathbb{Z}/p\mathbb{Z} $. Suppose $ 0 \notin A $ and for $ a \in A $ define $ d(a)= \min\{k|-a \in \underbrace{A+A+ \dots +A}_\text{k times} \} $. I wan......Mon, 07 Sep 2026 12:06:33 -0400https://liberty.io/how-to-fix-mouse-slow-sensitivity-in-minecraft-java.htmlhttps://liberty.io/how-to-fix-mouse-slow-sensitivity-in-minecraft-java.htmlI have a problem with my mouse control since yesterday. When I move my mouse the screen moves slowly like a movie animation. I don't know what to do. I clicked every buttons in Minecraft. Do I need......Mon, 07 Sep 2026 12:02:28 -0400https://liberty.io/is-gts-on-pokemon-oras-unsafe.htmlhttps://liberty.io/is-gts-on-pokemon-oras-unsafe.htmlI have been going everywhere for some tips on Pokemon ORAS and everyone is saying that Pokemon GTS is unsafe. I want to know why because I've been thinking of putting up Shiny Pokemon, and I don'......Mon, 07 Sep 2026 12:02:24 -0400https://liberty.io/cycle-decomposition-into-disjoint-cycles.htmlhttps://liberty.io/cycle-decomposition-into-disjoint-cycles.htmlIn this link here it says that a cycle be decomposed a product of disjoint cycles. However say you consider the element of $S_4$ (The symmetric group of order 24) given by $(12)(13)(14) = (1432)$. ......Mon, 07 Sep 2026 12:00:32 -0400https://liberty.io/how-do-i-make-it-so-when-one-player-dies-everyone-dies.htmlhttps://liberty.io/how-do-i-make-it-so-when-one-player-dies-everyone-dies.htmlI'm trying to make something like the life link challenge for a realm but can't use a plugin on it so I've been trying to make it using command blocks. it's in 1.14.4 so old commands won't work...Mon, 07 Sep 2026 11:50:35 -0400https://liberty.io/how-to-neutralise-eliminate-lydia-boyle-without-attracting-any-guards-.htmlhttps://liberty.io/how-to-neutralise-eliminate-lydia-boyle-without-attracting-any-guards-.htmlSo... when you do the "Lady Boyle's Last Party" Mission, and you do not have shadow kill, and your given target is Lydia Boyle (the one in red), you will be led to music room. There, she will ask y......Mon, 07 Sep 2026 11:41:37 -0400https://liberty.io/what-is-the-best-set-up-for-insane-mode-in-castle-crashers.htmlhttps://liberty.io/what-is-the-best-set-up-for-insane-mode-in-castle-crashers.htmlI'm pretty new to this game and I got to insane mode(my friend helped me) but when I play on insane mode it seems that I'm under powered.(and I don't know how to juggle that well) So I was wonderin......Mon, 07 Sep 2026 11:37:46 -0400https://liberty.io/how-to-take-the-derivative-of-a-power.htmlhttps://liberty.io/how-to-take-the-derivative-of-a-power.htmlSo I'm trying to solve this problem: Take the derivative of $2^{t^{3}}$ This is the relevant text from my textbook which makes sense to me. The trick seems to convert anything in the form of $b^......Mon, 07 Sep 2026 11:30:11 -0400https://liberty.io/sine-and-cosine-power-series.htmlhttps://liberty.io/sine-and-cosine-power-series.htmlI have read that sine and cosine can be represented as power series. Power series, as I understand them, are infinite series that can be represented as: $\sum_{j=0}^{\infty} a_j (x-x_0)^j$ where ......Mon, 07 Sep 2026 11:28:03 -0400https://liberty.io/why-can-039-t-i-change-my-skin.htmlhttps://liberty.io/why-can-039-t-i-change-my-skin.htmlI play Minecraft PE on my Kindle Fire, however, I cannot change my skin; It is staying on the default, Alex. Does anyone know how I might go about fixing this? The version I'm running is MCPE 16.2...Mon, 07 Sep 2026 11:23:06 -0400https://liberty.io/calculating-sample-size-for-a-one-sample-dichotomous-outcome.htmlhttps://liberty.io/calculating-sample-size-for-a-one-sample-dichotomous-outcome.htmlI'm trying to calculate a required sample sizes for a project using a one sample, dichotomous outcome formula. I'm confused by the intuition of the formula where a less probable result requires fewer ...Mon, 07 Sep 2026 11:18:19 -0400https://liberty.io/integral-dependence.htmlhttps://liberty.io/integral-dependence.htmlA module theoretical equivalence of integral dependence states as follows: Let $S$ be a ring and $R \subseteq S$ be a subring, and $1\in R$. Then $x \in S$ is integral over $R$ if and only if $R[x......Mon, 07 Sep 2026 11:14:33 -0400https://liberty.io/what-is-the-minimum-degree-of-a-polynomial-given-the-initial-condition.htmlhttps://liberty.io/what-is-the-minimum-degree-of-a-polynomial-given-the-initial-condition.htmlA polynomial $ p(x)$ is such that $p(0) =5, p(1) = 4, p(2) = 9 $ and $p(3) = 20 $. What is the minimum degree it can have? The problem can easily be solved by hit and trial method. First assuming......Mon, 07 Sep 2026 11:07:05 -0400https://liberty.io/need-examples-to-understand-choice-function-and-choice-structure.htmlhttps://liberty.io/need-examples-to-understand-choice-function-and-choice-structure.htmlWould you please give me a concrete example for the following definitions? Specifically I don't understand why a choice function is defined as $c: B \rightarrow P(X)$. For any nonempty set $X$, le......Mon, 07 Sep 2026 11:06:50 -0400https://liberty.io/how-do-you-interact-with-the-green-plant-like-things.htmlhttps://liberty.io/how-do-you-interact-with-the-green-plant-like-things.htmlThese: They can be found in the walls and ceilings all throughout the game and seem to be the key to access the last bits of collectibles, at least as far as I can see. They seem to be places as ......Mon, 07 Sep 2026 11:03:42 -0400https://liberty.io/why-is-the-definition-of-inner-product-the-way-it-is.htmlhttps://liberty.io/why-is-the-definition-of-inner-product-the-way-it-is.htmlI have recently started looking at inner products. However, I'm still struggling to intuitively understand the definition. I am aware that in most cases we generalize concepts because they are use......Mon, 07 Sep 2026 10:47:29 -0400https://liberty.io/do-you-have-to-kill-dean.htmlhttps://liberty.io/do-you-have-to-kill-dean.htmlI'm in the Sierra Madre (Dead Money add-on), and I was trying to be a nice guy -- I really was. But when the time came that I could decide whether to kill my companions or let them live and disable......Mon, 07 Sep 2026 10:47:16 -0400https://liberty.io/is-the-thrill-digger-minigame-deterministic.htmlhttps://liberty.io/is-the-thrill-digger-minigame-deterministic.htmlIn Skyward Sword, in the Edlin Volcano area near the Bokoblin tower, there is a cave where one can play the game Thrill Digger. My question is: can one predict the layout of the board based on: ...Mon, 07 Sep 2026 10:37:20 -0400https://liberty.io/derivative-of-natural-log-vs-base-10-log.htmlhttps://liberty.io/derivative-of-natural-log-vs-base-10-log.htmlConsider the logarithmic function with base $10.$ $$ y=\log{\left(x\right)} $$ wherein the derivative with respect to $x$ is: $$ f'\left(x\right)=\frac{1}{x} $$ Now consider the natural logarith......Mon, 07 Sep 2026 10:26:43 -0400https://liberty.io/database-of-fol-statements-and-proofs.htmlhttps://liberty.io/database-of-fol-statements-and-proofs.htmlIs there a database somewhere of simple FOL statements, with their proofs written out in a Hilbert-style deduction system, or perhaps a tool to take such statements and produce proofs? While I see ...Mon, 07 Sep 2026 10:21:37 -0400https://liberty.io/the-final-state-of-1000-light-bulbs-switched-on-off-by-1000-people-pas.htmlhttps://liberty.io/the-final-state-of-1000-light-bulbs-switched-on-off-by-1000-people-pas.htmlThere are 1000 light bulbs and 1000 tutors. All light bulbs are off. Tutor 1 goes flipping light bulb 1,2,3,4... tutor 2 then flips 2,4,6,8... tutor 3 then 3,6,9...etc until all 1000 tutors have ......Mon, 07 Sep 2026 10:18:54 -0400https://liberty.io/user-calvin-lin-mathematics-stack-exchange.htmlhttps://liberty.io/user-calvin-lin-mathematics-stack-exchange.htmlQ&A for people studying math at any level and professionals in related fields...Mon, 07 Sep 2026 10:17:57 -0400https://liberty.io/proving-gradient-of-a-function-is-always-perpendicular-to-the-contour-.htmlhttps://liberty.io/proving-gradient-of-a-function-is-always-perpendicular-to-the-contour-.htmlCan someone give an explanation of how such a proof would go, given a function example: $y = f(x)$...Mon, 07 Sep 2026 10:14:54 -0400https://liberty.io/what-039-s-the-point-of-a-kingdom-past.htmlhttps://liberty.io/what-039-s-the-point-of-a-kingdom-past.htmlIt seems to indicate that you should replicate the Kingdom, based on this image, but nothing seems to happen when you do. What's the point of this image?...Mon, 07 Sep 2026 10:14:03 -0400https://liberty.io/what-is-the-relation-between-production-meals-and-total-export-price.htmlhttps://liberty.io/what-is-the-relation-between-production-meals-and-total-export-price.htmlI'm playing Tropico 4 right now, but I'm pretty sure it's the same for all Tropico games. I've finished the normal campain, but I'm still wondering what these numbers are about. So let's take an e......Mon, 07 Sep 2026 10:05:07 -0400https://liberty.io/why-dominated-convergence-theorem-is-related-to-the-superiority-of-leb.htmlhttps://liberty.io/why-dominated-convergence-theorem-is-related-to-the-superiority-of-leb.htmlI read the following paragraph from wikipedia: In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which almost everywhere convergence of a sequence of ...Mon, 07 Sep 2026 09:59:19 -0400https://liberty.io/how-to-enable-steam-overlay-while-playing-dungeons-of-dredmor.htmlhttps://liberty.io/how-to-enable-steam-overlay-while-playing-dungeons-of-dredmor.htmlFor some reasons I cannot access to Steam overlay and other Steam features (F12->screenshot) while playing Dungeons of Dredmor. Do you know how to fix it? Just to be precise the in-game option in ......Mon, 07 Sep 2026 09:52:45 -0400https://liberty.io/for-numbers-divisible-by-three-why-is-the-sum-of-their-digits-able-to-.htmlhttps://liberty.io/for-numbers-divisible-by-three-why-is-the-sum-of-their-digits-able-to-.htmlWhen you add the digits of any number that is divisible by three, that sum of those digits also appears to be divisible by three (with no remainder). For example a number (which I randomly grab fr......Mon, 07 Sep 2026 09:48:20 -0400https://liberty.io/darboux-theorem.htmlhttps://liberty.io/darboux-theorem.htmlDarboux's Theorem states that" If $f$ is differentiable on $[a,b]$ and if $k$ is a number between $f^{\prime}(a)$ and $f^{\prime}(b)$, then there is at least one point $c\in (a,b)$ such that $f^{\p......Mon, 07 Sep 2026 09:27:24 -0400https://liberty.io/properties-of-dictionary-order-topology.htmlhttps://liberty.io/properties-of-dictionary-order-topology.htmlProperties of dictionary order topology Choose the correct option My attempt : According to Munkres the order topology on $\mathbb{R} \times \mathbb{R}$ has as basis the collection of all ......Mon, 07 Sep 2026 09:24:48 -0400https://liberty.io/getting-attributes-bonuses-5-5-5-in-elder-scrolls-oblivion.htmlhttps://liberty.io/getting-attributes-bonuses-5-5-5-in-elder-scrolls-oblivion.htmlI have just completed the recommended quests for the Mages Guild to get accepted into the Arcane University. Now, I think it's time to work on leveling up the mage class character that I have. I'm ...Mon, 07 Sep 2026 09:16:41 -0400https://liberty.io/how-to-prove-that-mathbb-z-2z-times-z-2z-is-not-cyclic.htmlhttps://liberty.io/how-to-prove-that-mathbb-z-2z-times-z-2z-is-not-cyclic.htmlHow to prove that $\mathbb{Z/2Z\times Z/2Z}$ is not cyclic? Here is what I did, what is wrong with it if anything and is there a better way to prove it? A group $G$ is cyclic if $\exists\ a \in G$ ......Mon, 07 Sep 2026 08:44:47 -0400https://liberty.io/steam-purchase-issue.htmlhttps://liberty.io/steam-purchase-issue.htmlWhen you attempt to purchase Realm of the Mad God's "Beginner's Package", it lists the purchase as buying "2600 Gold". The package contains more than just gold, so what does this mean?...Mon, 07 Sep 2026 08:42:36 -0400https://liberty.io/finding-the-measure-of-an-angle-given-area-and-diameter.htmlhttps://liberty.io/finding-the-measure-of-an-angle-given-area-and-diameter.htmlAlright, so i've been trying to tackle this problem. The answer to this problem is 40 degrees (3). Now i'm trying to figure out how. I decided to start with finding the area of the whole circle wh......Mon, 07 Sep 2026 08:33:44 -0400https://liberty.io/how-do-i-set-a-kill-command-on-a-block.htmlhttps://liberty.io/how-do-i-set-a-kill-command-on-a-block.htmlYou can set a /kill command on a command block, I know that, but how do I do it? I am making a map, so please help!...Mon, 07 Sep 2026 08:28:24 -0400https://liberty.io/area-enclosed-between-3-curves.htmlhttps://liberty.io/area-enclosed-between-3-curves.htmlQuestion: What is the area of the region enclosed by the curves: $$2y = 4\sqrt{x},\quad y = 3,\quad \text{and} \quad 2y + 2x = 6. $$ I have tried calculate all the definite integrals but I am not ......Mon, 07 Sep 2026 08:16:18 -0400https://liberty.io/why-do-some-players-play-league-of-legends-in-window-mode.htmlhttps://liberty.io/why-do-some-players-play-league-of-legends-in-window-mode.htmlWhile watching this current LoL live world championship (Intel extreme masters), I noticed some players play in window mode. Why is that? What are the benefits of playing LoL in window mode?...Mon, 07 Sep 2026 08:07:51 -0400https://liberty.io/what-is-the-solution-of-a-2-b-2-closed.htmlhttps://liberty.io/what-is-the-solution-of-a-2-b-2-closed.htmlHow to solve $a^2=b^2$? Should I consider if the number is negative or positive?...Mon, 07 Sep 2026 08:02:27 -0400https://liberty.io/when-does-order-of-partial-derivatives-matter.htmlhttps://liberty.io/when-does-order-of-partial-derivatives-matter.htmlI've taken multivariate calculus and am wondering if I can see a specific function where the order of taking the partial derivative matters. I've been told that there are some exceptions where $ \d......Mon, 07 Sep 2026 08:01:33 -0400https://liberty.io/when-do-people-use-nydus-worm.htmlhttps://liberty.io/when-do-people-use-nydus-worm.htmlI'm not a Zerg player, but I've never seen Nydus worm used against me either. When do people actually use it?...Mon, 07 Sep 2026 08:00:11 -0400https://liberty.io/using-dimensional-analysis-to-convert-oz-to-l.htmlhttps://liberty.io/using-dimensional-analysis-to-convert-oz-to-l.htmlI'm having trouble deciding whether this table has enough information to convert between fluid $oz$ and $L$. I'm inclined to say it doesn't, but my homework problem has me considering otherwise....Mon, 07 Sep 2026 07:31:00 -0400https://liberty.io/recommended-free-software-to-draw-both-histogram-and-graph-paper-grid.htmlhttps://liberty.io/recommended-free-software-to-draw-both-histogram-and-graph-paper-grid.htmlIs there any software for drawing both the graph (histogram, ogive or other statistical graphs) and the graph paper grid behind it? I want to draw graph that look like image below. Thanks!...Mon, 07 Sep 2026 07:29:28 -0400https://liberty.io/what-is-the-value-of-6.htmlhttps://liberty.io/what-is-the-value-of-6.htmlI know this is not absolute value, so what do the parentheses mean? If it was absolute value, it would have lines so I can rule that out. And I guess I should mention, the question I was asked is ......Mon, 07 Sep 2026 07:27:12 -0400https://liberty.io/even-function-divided-by-odd-function-is-an-odd-function-proof.htmlhttps://liberty.io/even-function-divided-by-odd-function-is-an-odd-function-proof.htmlAn Even function divided by Odd function is an Odd function,that is a fact. However is there a means to prove this?...Mon, 07 Sep 2026 07:17:44 -0400https://liberty.io/moving-minecart-once-hopper-has-items-and-then-becomes-empty.htmlhttps://liberty.io/moving-minecart-once-hopper-has-items-and-then-becomes-empty.htmlHere's a rough outline of what I want Empty cart stays still under an empty hopper Hopper gets x items in it, the cart stays still Once the hopper has emptied all its items into the cart, the c......Mon, 07 Sep 2026 07:15:53 -0400https://liberty.io/why-was-the-inverse-sine-ratio-used-and-not-sine.htmlhttps://liberty.io/why-was-the-inverse-sine-ratio-used-and-not-sine.htmlFrom what point should I look when determining what trig ratio to use? If they can use hypotenuse over opposite, they can also use opposite over hypotenuse. Were should I look to determine the corr......Mon, 07 Sep 2026 07:11:40 -0400https://liberty.io/how-many-diamonds-can-a-diamond-ore-drop-in-minecraft.htmlhttps://liberty.io/how-many-diamonds-can-a-diamond-ore-drop-in-minecraft.htmlMy friends and I are having an argument on how many diamonds a Diamond Ore can drop (on avg. or maximum) without any fortune levels on a pickaxe. My friend says there will always drop only one, but......Mon, 07 Sep 2026 07:09:00 -0400https://liberty.io/why-is-there-no-product-quotient-rule-for-integration.htmlhttps://liberty.io/why-is-there-no-product-quotient-rule-for-integration.htmlSo it's known that there's no product rule and quotient rule for integration. But is there a reason why they don't exist, and the rules exist for differentiation?...Mon, 07 Sep 2026 07:07:36 -0400https://liberty.io/if-i-buy-a-ubisoft-game-on-steam-can-i-play-the-game-through-uplay-clo.htmlhttps://liberty.io/if-i-buy-a-ubisoft-game-on-steam-can-i-play-the-game-through-uplay-clo.htmlI just bought Assassin's Creed Unity on Steam, but the place I was playing can't install the game on Steam but the game is already installed in Uplay, can I play the game from Uplay instead of from......Mon, 07 Sep 2026 07:05:42 -0400https://liberty.io/which-diy-recipes-can-you-self-learn.htmlhttps://liberty.io/which-diy-recipes-can-you-self-learn.htmlAn overwhelmingly vast majority of DIY recipes in the game can be found by buying them from Nook's Cranny, finding them in the balloon presents or beach bottles, or getting them from crafting villa......Mon, 07 Sep 2026 06:57:38 -0400https://liberty.io/is-it-possible-to-switch-sides-in-ingress.htmlhttps://liberty.io/is-it-possible-to-switch-sides-in-ingress.htmlI chose to play as Enlightened, but it appears that nearly all of the portals in a nearby city are already controlled by Enlightened. In order to get experience I need to hack enemy portals, not fr......Mon, 07 Sep 2026 06:49:47 -0400https://liberty.io/an-extension-of-the-four-4-039-s-game.htmlhttps://liberty.io/an-extension-of-the-four-4-039-s-game.htmlWhen I was in lower school I remember playing the Four $4$'s game and we got to around $10$. For those of you who don't know the Four $4$'s game is one where you have to use four $4$'s and you have......Mon, 07 Sep 2026 06:46:17 -0400https://liberty.io/what-is-a-good-estimate-of-total-play-time-for-zelda-skyward-sword-dup.htmlhttps://liberty.io/what-is-a-good-estimate-of-total-play-time-for-zelda-skyward-sword-dup.htmlI want to complete Skyward Sword before Christmas, I'm trying to get a good grasp on how much time I need to finish it off. At the very least, I want to beat the game, but I tend to get most of the......Mon, 07 Sep 2026 06:45:39 -0400https://liberty.io/represent-f-x-1-x-as-a-power-series-around-x-1.htmlhttps://liberty.io/represent-f-x-1-x-as-a-power-series-around-x-1.htmlAs stated on the title, my question is: (a) represent the function $ f(x) = 1/x $ as a power series around $ x = 1 $. (b) represent the function $ f(x) = \ln (x) $ as a power series around $ x = 1 ......Mon, 07 Sep 2026 06:42:56 -0400https://liberty.io/stole-the-temptress-how-can-i-upgrade-it.htmlhttps://liberty.io/stole-the-temptress-how-can-i-upgrade-it.htmlI just stole the Temptress, looks like a cross between a Porsche and a Lamborghini I think. This is the car I would like to keep with as much damage resistance I can buy. I am trying to upgrade it. I ...Mon, 07 Sep 2026 06:42:07 -0400https://liberty.io/how-long-does-original-game-boy-battery-backed-memory-last.htmlhttps://liberty.io/how-long-does-original-game-boy-battery-backed-memory-last.htmlI have a Nintendo Game Boy Pocket (which plays original monochrome Game Boy games and is probably not capable of playing Game Boy Advance or similar "advanced" cartridges.) At any rate it is the or......Mon, 07 Sep 2026 06:41:47 -0400https://liberty.io/what-specific-bonus-loyalty-powers-are-available.htmlhttps://liberty.io/what-specific-bonus-loyalty-powers-are-available.htmlI know that the concept of Bonus Powers earned from loyal squadmates to enhance Shepards abilities has been retained. But what I can't find any information on is what specific powers are availiable......Mon, 07 Sep 2026 06:38:30 -0400https://liberty.io/an-introduction-to-tensors.htmlhttps://liberty.io/an-introduction-to-tensors.htmlAs a physics student, I've come across mathematical objects called tensors in several different contexts. Perhaps confusingly, I've also been given both the mathematician's and physicist's definiti......Mon, 07 Sep 2026 06:37:42 -0400https://liberty.io/can-the-value-of-9-be-found-duplicate.htmlhttps://liberty.io/can-the-value-of-9-be-found-duplicate.htmlI saw this question on an fb page and I couldn't solve it. Question: What is the value of $(-9!)$? a)$362800$ b)$-362800$ c) Can not be calculated The first options seems to be incorrect,which ...Mon, 07 Sep 2026 06:37:19 -0400https://liberty.io/what-do-you-call-numbers-such-as-100-200-500-1000-10000-50000-as-oppos.htmlhttps://liberty.io/what-do-you-call-numbers-such-as-100-200-500-1000-10000-50000-as-oppos.htmlThere are different categories of numbers that we use every day. Integers that written in decimal notation have $1, 2$ or $5$ as the leading figure, followed by none, one or more zeros. These are ......Mon, 07 Sep 2026 06:34:31 -0400https://liberty.io/permutations-with-forbidden-positions-sit-n-students-in-a-row.htmlhttps://liberty.io/permutations-with-forbidden-positions-sit-n-students-in-a-row.htmlSuppose we have $N$ students $(N>20)$ that should be seated in a row. ($1-n$ seats) $1.$ In how many ways can we arrange such that student number $2$ won't sit on chair number $1,3$ or $7......Mon, 07 Sep 2026 06:31:54 -0400https://liberty.io/how-can-you-give-a-player-a-speed-boost-when-they-are-sprinting-in-min.htmlhttps://liberty.io/how-can-you-give-a-player-a-speed-boost-when-they-are-sprinting-in-min.htmlI'm trying to make a vanilla KitPvP server, and I want to make a kit that gives you normal walking speed, but when you are sprinting, you have a speed boost. Is that possible? If so, then how?...Mon, 07 Sep 2026 06:30:28 -0400https://liberty.io/where-can-i-find-a-large-number-of-fish.htmlhttps://liberty.io/where-can-i-find-a-large-number-of-fish.htmlNearly every crafting/carry capacity upgrade needs fish bones/skin for the final, end-game items. I want to stop carrying animal bits as soon as possible, since my inventory is full of stuff I may ......Mon, 07 Sep 2026 06:29:04 -0400https://liberty.io/cdf-of-pareto-distribution.htmlhttps://liberty.io/cdf-of-pareto-distribution.htmlI want to compute the CDF of a Pareto distribution In particular, I have a Pareto distribution with p.d.f. $$f(x) = \lambda x^{-(\lambda + 1)},$$ and I want to find the CDF of $f$. When I perform ...Mon, 07 Sep 2026 06:24:58 -0400https://liberty.io/radians-negative-and-positive-values.htmlhttps://liberty.io/radians-negative-and-positive-values.htmlRecently I have been reading books on DSP where I came across Polar co-ordinates. I understand that on Polar graph (4 quadrants) we have $0, \frac{\pi}{2}, \pi, \frac{3}{2\pi}$ and $2 \pi$ radians ......Mon, 07 Sep 2026 06:23:31 -0400https://liberty.io/parametric-equation-of-a-circle-using-a-line.htmlhttps://liberty.io/parametric-equation-of-a-circle-using-a-line.htmlConsider the unit circle $$ x^2+y^2=1. $$ How can I parametrize it using the line $y=m(x+1)$, where $m$ is its slope?...Mon, 07 Sep 2026 06:08:08 -0400https://liberty.io/number-of-occurrences-in-contiguous-subarrays.htmlhttps://liberty.io/number-of-occurrences-in-contiguous-subarrays.htmlHow to count the number of occurrences of each element in all contiguous subarrays? For an array $[1,2,3]$, the contiguous subarrays are: $[1]$, $[2]$, $[3]$ $[1,2]$, $[2,3]$ $[1,2,3]$ $1$ occu......Mon, 07 Sep 2026 06:07:51 -0400https://liberty.io/what-are-the-domain-s-of-self-inverse-functions.htmlhttps://liberty.io/what-are-the-domain-s-of-self-inverse-functions.htmlA self inverse function is a function $f$, such that $y=f(x)$, with the special property that $ff(x)=x$, or written another way, $f(x) = f^-1(x)$ Example: Imagine there's a function $f$, such that......Mon, 07 Sep 2026 06:06:25 -0400https://liberty.io/give-a-serious-explanation-of-the-difference-between-an-equation-and-a.htmlhttps://liberty.io/give-a-serious-explanation-of-the-difference-between-an-equation-and-a.htmlWhat's the difference between an equation and a function? I mean, I am not seeking for a high school-like answer like "an equation has an equals sign". I want to know what is the fundamental differ......Mon, 07 Sep 2026 06:03:27 -0400https://liberty.io/what-do-you-get-for-tsanna-039-s-sacrificial-offering-in-chapter-7.htmlhttps://liberty.io/what-do-you-get-for-tsanna-039-s-sacrificial-offering-in-chapter-7.htmlIn Chapter 7 - Tsanna offers to sacrifice Evindra to give you the blessings of Lamashtu. If you do it, what benefit do you see for the final battle?...Mon, 07 Sep 2026 06:01:33 -0400https://liberty.io/infinite-sum-and-partial-sum-not-equal-in-wolframalpha.htmlhttps://liberty.io/infinite-sum-and-partial-sum-not-equal-in-wolframalpha.html$$\sum_{n=0}^{\infty} |(-0.8)^n \theta(n)-(-0.8)^{n-1} \theta(n-1)|$$ $\theta(n) = 1$ for $n \geq 0$ and 0 otherwise. My attempt to calculate this summation numerically with Python yielded 10. To ......Mon, 07 Sep 2026 05:57:56 -0400https://liberty.io/how-do-i-use-the-undermounted-shotgun-attachment-for-assault-rifles.htmlhttps://liberty.io/how-do-i-use-the-undermounted-shotgun-attachment-for-assault-rifles.htmlIn call of duty: modern warfare 3 (PC version) when playing multiplayer. You can select at weapon level 20 the shotgun attachment for the assault rifle. How do you fire it? Does it happen automati......Mon, 07 Sep 2026 05:56:05 -0400https://liberty.io/is-it-worth-it-to-upgrade-the-clan-castle.htmlhttps://liberty.io/is-it-worth-it-to-upgrade-the-clan-castle.htmlI was wondering if the clan castle building is worth the resources to upgrade it. I rarely attack getting all my resources from farming and use all them for upgrading defenses. I'm questioning th......Mon, 07 Sep 2026 05:53:21 -0400https://liberty.io/mega-stone-of-chosen-starter-pokemon-buyable.htmlhttps://liberty.io/mega-stone-of-chosen-starter-pokemon-buyable.htmlIf I am choosing Charmander as my starter, will I be able to buy the Charizardite Mega Stone again? So I could buy another one and trade it to someone else. Edit: I just found this site and it sa......Mon, 07 Sep 2026 05:49:33 -0400https://liberty.io/my-world-keeps-not-responding-correctly-how-do-i-fix-that.htmlhttps://liberty.io/my-world-keeps-not-responding-correctly-how-do-i-fix-that.htmlI was using a lan server on my favorite world and when i saved and exited the world everything worked fine. Then later i tried to enter the world and it glitched out a bit at the load screen and wh......Mon, 07 Sep 2026 05:45:41 -0400https://liberty.io/find-max-vertical-distance.htmlhttps://liberty.io/find-max-vertical-distance.htmlWhat is the maximum vertical distance between the line $y = x + 20$ and the parabola $y = x^2$ for $−4 ≤ x ≤ 5?$ What steps do I take to solve this? Do I have to use the distance formula and wh......Mon, 07 Sep 2026 05:37:02 -0400https://liberty.io/quote-from-mathematician-poet.htmlhttps://liberty.io/quote-from-mathematician-poet.htmlI read once a quote by a mathematician (or scientist) who was also a poet and it was something similar to: As a mathematician I try to make complicated things obvious, as a poet I try to make ob......Mon, 07 Sep 2026 05:23:40 -0400https://liberty.io/when-to-play-the-old-hunters-during-the-first-run-or-ng.htmlhttps://liberty.io/when-to-play-the-old-hunters-during-the-first-run-or-ng.htmlI'm doing my first Bloodborne run. I beat the boss of Byrgenwerth. Currently I have the option of playing the new DLC, The Old Hunters. If I waited until I finish my first run, it means I have to......Mon, 07 Sep 2026 05:21:14 -0400https://liberty.io/do-i-need-to-play-the-previous-games.htmlhttps://liberty.io/do-i-need-to-play-the-previous-games.htmlDarksiders II is out for free on XboxLive. Do I need to play Darksiders to understand whats going on? Or is the game completely different to the first?...Mon, 07 Sep 2026 05:14:34 -0400https://liberty.io/quick-way-of-selling-at-the-trading-post.htmlhttps://liberty.io/quick-way-of-selling-at-the-trading-post.htmlIs there a way to quickly sell goods at the trading post in GW2? I know there is the sell at trading post option by right clicking the desired item but that loads up the trading post every time and......Mon, 07 Sep 2026 04:59:15 -0400https://liberty.io/what-039-s-a-good-trophy-army-for-a-town-hall-8-closed.htmlhttps://liberty.io/what-039-s-a-good-trophy-army-for-a-town-hall-8-closed.htmlI've maxed out my troops for town hall 8 and I'm trying to do a big push, any suggestions?...Mon, 07 Sep 2026 04:56:49 -0400