https://track.liberty.ioFresh celebrity buzz with instant attention value.en-usMon, 07 Sep 2026 05:17:52 -0400https://track.liberty.io/proving-that-0-cdot-x-0-using-field-axioms.htmlhttps://track.liberty.io/proving-that-0-cdot-x-0-using-field-axioms.htmlConsider the following axiomatic definition of a field: A field is a set $F$ together with two binary operations $+$ and $\cdot$ on $F$ such that $(F,+)$ is an Abelian group with identity $0$ an......Mon, 07 Sep 2026 09:12:19 -0400https://track.liberty.io/how-to-prove-that-the-derivative-of-heaviside-039-s-unit-step-function.htmlhttps://track.liberty.io/how-to-prove-that-the-derivative-of-heaviside-039-s-unit-step-function.htmlHere is a problem from Griffith's book Introduction to E&M. Let $\theta(x)$ be the step function $$\theta = \begin{cases} 0, & x \le 0, \\ 1, & x \gt 0. \end{cases} $$ The qu......Mon, 07 Sep 2026 09:06:25 -0400https://track.liberty.io/what-should-i-do-with-nuggets.htmlhttps://track.liberty.io/what-should-i-do-with-nuggets.htmlI visited the quarry and acquired some silver & gold nuggets. I'd like to sell them, but only if there's nothing more useful I can do with them. I also am not sure where to sell them since the ...Mon, 07 Sep 2026 09:04:34 -0400https://track.liberty.io/simpsons-tapped-out-finding-maggie.htmlhttps://track.liberty.io/simpsons-tapped-out-finding-maggie.htmlIn the minigame where you have to find Maggie somewhere in Springfield, I always manage to locate her, but when I tap on her on the screen, nothing happens. A few times now I've had her in the cent......Mon, 07 Sep 2026 09:00:21 -0400https://track.liberty.io/cantor-set-and-fractals.htmlhttps://track.liberty.io/cantor-set-and-fractals.htmlI have read that the Cantor set is considered a fractal. I am referring to the Cantor set in which the middle third of a real line is removed recursively. I see that this is recursively defined, bu......Mon, 07 Sep 2026 08:52:02 -0400https://track.liberty.io/how-to-find-where-a-function-is-increasing-at-the-greatest-rate.htmlhttps://track.liberty.io/how-to-find-where-a-function-is-increasing-at-the-greatest-rate.htmlGiven the function $f(x) = \frac{1000x^2}{11+x^2}$ on the interval $[0, 3]$, how would I calculate where the function is increasing at the greatest rate? Differentiating the function will give its ...Mon, 07 Sep 2026 08:48:48 -0400https://track.liberty.io/are-there-any-treasure-vaults-to-break-into.htmlhttps://track.liberty.io/are-there-any-treasure-vaults-to-break-into.htmlWhile on my travels in Skyrim i found one place (Markarth) which reminded me of Vivec from Morrowind, in the sense that there was a secured area with the possibility of gold and loot behind locked ......Mon, 07 Sep 2026 08:45:07 -0400https://track.liberty.io/cash-register-key-locations.htmlhttps://track.liberty.io/cash-register-key-locations.htmlOn the map Interchange, I am looking for the cash register keys to unlock them for roubles, however, I haven't had any luck on finding any of them. What are their spawn locations (picture would be......Mon, 07 Sep 2026 08:44:36 -0400https://track.liberty.io/how-do-i-increase-the-maximum-amount-of-weight-my-character-can-carry-.htmlhttps://track.liberty.io/how-do-i-increase-the-maximum-amount-of-weight-my-character-can-carry-.htmlIn Skyrim, as with most RPGs, I find myself overwhelmed by a compulsive desire to obtain all of the things. All of them. To this end, I wound up picking up five iron warhammers...only to find out t......Mon, 07 Sep 2026 08:42:34 -0400https://track.liberty.io/when-do-multi-parries-happen.htmlhttps://track.liberty.io/when-do-multi-parries-happen.htmlDoing a regular parry is already hard enough, and I can only ever do it by accident, but there are some instances where I was hit by what I think were multi hit projectiles or moves, but somehow pa......Mon, 07 Sep 2026 08:41:37 -0400https://track.liberty.io/has-prof-otelbaev-shown-existence-of-strong-solutions-for-navier-stoke.htmlhttps://track.liberty.io/has-prof-otelbaev-shown-existence-of-strong-solutions-for-navier-stoke.htmlModerator Notice: I am unilaterally closing this question for three reasons. The discussion here has turned too chatty and not suitable for the MSE framework. Given the recent pre-print......Mon, 07 Sep 2026 08:31:26 -0400https://track.liberty.io/probability-of-one-normdist-being-greater-than-another-duplicate.htmlhttps://track.liberty.io/probability-of-one-normdist-being-greater-than-another-duplicate.htmlI have two independant normally distributed random variables. X ~ N(657, 3) Y ~ N(661, 2) P(x > y) = ? How do I calculate the probability of X being greater than Y? Using R for simulating, I am ...Mon, 07 Sep 2026 08:30:41 -0400https://track.liberty.io/backwards-epsilon.htmlhttps://track.liberty.io/backwards-epsilon.htmlWhat does the $\ni$ (backwards element of) symbol mean? It doesn't appear in the Wikipedia list of mathematical symbols, and a Google search for "backwards element of" or "backwards epsilon" turns......Mon, 07 Sep 2026 08:30:38 -0400https://track.liberty.io/deriving-the-formula-for-the-radius-of-the-circle-inscribed-in-an-equi.htmlhttps://track.liberty.io/deriving-the-formula-for-the-radius-of-the-circle-inscribed-in-an-equi.htmlI am trying to derive the formula for the radius of the circle inscribed in an equilateral triangle from scratch. Given $2*n$ = length of a side $H$ = the altitude of the triangle = $h + a......Mon, 07 Sep 2026 08:27:41 -0400https://track.liberty.io/is-there-a-way-to-earn-resources-fast.htmlhttps://track.liberty.io/is-there-a-way-to-earn-resources-fast.htmlIn Metal Gear Solid 5: The Phantom Pain, is there a quick/easy method to getting resources to upgrade Mother Base and unlocking Mission 46? Can I somehow buy resources?...Mon, 07 Sep 2026 08:18:25 -0400https://track.liberty.io/killing-animals-in-dishonored-will-that-ruin-achievements.htmlhttps://track.liberty.io/killing-animals-in-dishonored-will-that-ruin-achievements.htmlCan I kill animals, such as the dogs, and still get the achievements? I'm looking at one achievement that says I can kill "no one". I'm not sure if that includes the animals or not....Mon, 07 Sep 2026 08:12:05 -0400https://track.liberty.io/can-you-turn-weather-off-in-minecraft.htmlhttps://track.liberty.io/can-you-turn-weather-off-in-minecraft.htmlThe arrival of Minecraft Beta 1.5 brought weather conditions. However, it can at times be inconvenient when you're trying to screenshot something and show it off (as it reduces lighting and obstructs ...Mon, 07 Sep 2026 08:11:54 -0400https://track.liberty.io/can-an-autonomous-differential-equation-be-nonhomogeneous.htmlhttps://track.liberty.io/can-an-autonomous-differential-equation-be-nonhomogeneous.htmlWhen a differential equation $\dfrac{dy}{dt}=f(y)$ does not depends on $y$ then it is autonomous, and it can't be non-homogeneous? Can anyone explain this? Thanks!...Mon, 07 Sep 2026 08:07:45 -0400https://track.liberty.io/speed-of-a-particle-given-parametric-equations-of-x-and-y.htmlhttps://track.liberty.io/speed-of-a-particle-given-parametric-equations-of-x-and-y.htmlSo my $x(t)=\pi t +\cos(2\pi t -(\pi/2))$, and my $y(t)=\pi t +\sin(2\pi t -(\pi/2))$. I implicitly derived and got $$\frac{dy}{dt}=\frac{(\pi+\cos(2\pi t -(\pi/2))*2\pi)}{(\pi-\sin(2\pi t -(\pi/2)......Mon, 07 Sep 2026 08:03:09 -0400https://track.liberty.io/what-is-the-trick-to-the-final-boss-fight-in-uncharted-3.htmlhttps://track.liberty.io/what-is-the-trick-to-the-final-boss-fight-in-uncharted-3.htmlThis may seem like a bit of a weird question, especially considering I beat the game on Crushing last night, but here goes... What is the trick to winning the final boss fight against Talbot on the ...Mon, 07 Sep 2026 08:00:14 -0400https://track.liberty.io/notation-for-set-of-constant-functions.htmlhttps://track.liberty.io/notation-for-set-of-constant-functions.htmlI have a constant function that always returns the same integer value. How do I represent a set of functions where each function is a constant function that returns some arbitrary constant? For exa......Mon, 07 Sep 2026 07:55:21 -0400https://track.liberty.io/ivoerth-039-s-path-from-a-bygone-era.htmlhttps://track.liberty.io/ivoerth-039-s-path-from-a-bygone-era.htmlHow do you unlock this quest for Chapter 3, if you are on Ivoerth's path?...Mon, 07 Sep 2026 07:54:15 -0400https://track.liberty.io/are-proofs-by-contradiction-and-counterexample-two-different-technique.htmlhttps://track.liberty.io/are-proofs-by-contradiction-and-counterexample-two-different-technique.htmlNew to proofs. Suppose I want to prove $f: \mathbb Z \to \mathbb Z$ as $f(n) = 2n$ for all $n$ is not onto. Are the two arguments below valid, separate proofs? Are they invalid iterations of a sin......Mon, 07 Sep 2026 07:51:04 -0400https://track.liberty.io/proving-equation-has-only-one-solution.htmlhttps://track.liberty.io/proving-equation-has-only-one-solution.htmlSo i want to prove that $$x^2e^x=1$$ has at least one solution for $$x\in\mathbb{R}$$ I am kinda lost and would appreciate any help. This is suppose to be solved using basic calculus but i am not......Mon, 07 Sep 2026 07:45:05 -0400https://track.liberty.io/completing-the-lost-patrol-bos-side-quest.htmlhttps://track.liberty.io/completing-the-lost-patrol-bos-side-quest.htmlI seem to be having a problem completing the Brotherhood of Steel sidequest Lost Patrol, and I'm wondering if I've hit a bug/if anyone knows how to workaround it/has experienced the same problem/et......Mon, 07 Sep 2026 07:35:31 -0400https://track.liberty.io/how-to-use-a-bank-in-neverwinter-without-being-in-a-guild.htmlhttps://track.liberty.io/how-to-use-a-bank-in-neverwinter-without-being-in-a-guild.htmlI read that it is possible to deposit up to 16 items in bank, but when I approach the bank in Protector's Enclave it denies me access for "not being in a guild" Is it possible to use the bank to s......Mon, 07 Sep 2026 07:26:30 -0400https://track.liberty.io/what-is-the-difference-between-tekkit-and-normal-minecraft.htmlhttps://track.liberty.io/what-is-the-difference-between-tekkit-and-normal-minecraft.htmlI have the normal minecraft loader, and a lot of people tell me about Tekkit, what is the difference?...Mon, 07 Sep 2026 07:24:39 -0400https://track.liberty.io/what-happens-to-the-gem-when-i-salvage-an-item-with-a-gem-in-it.htmlhttps://track.liberty.io/what-happens-to-the-gem-when-i-salvage-an-item-with-a-gem-in-it.htmlI currently have no gold (just went shopping in the auction house... bought me some fancy and expensive weapon), but want to remove a gem from an item since I want to use it in another item. I'm ......Mon, 07 Sep 2026 07:10:03 -0400https://track.liberty.io/if-m-6x-5-what-equation-is-equivalent-to-6x-5-2-10-18x-15-in-terms-of-.htmlhttps://track.liberty.io/if-m-6x-5-what-equation-is-equivalent-to-6x-5-2-10-18x-15-in-terms-of-.htmlThis question I am asking right now comes from the Khan Academy practice task entitled 'Solve quadratic equations by using structure', so the credit goes to them. So, if $m = 6x + 5$, then what ...Mon, 07 Sep 2026 07:06:17 -0400https://track.liberty.io/what-is-the-difference-between-deviation-and-standard-deviation.htmlhttps://track.liberty.io/what-is-the-difference-between-deviation-and-standard-deviation.htmlIn my textbook, it describes the standard deviation "as a number that measures how far data values are from their mean". On the other hand, it says this about deviation: "if x is a number, then the ...Mon, 07 Sep 2026 07:03:19 -0400https://track.liberty.io/how-to-check-this-number-sqrt-47-is-irrational-duplicate.htmlhttps://track.liberty.io/how-to-check-this-number-sqrt-47-is-irrational-duplicate.htmlProve that $\sqrt{47}$ is irrational number. I know that a rational number is written as $\frac{p}{q}$ where $p$ & $q$ are co-prime numbers. But I do not have any idea to prove it irrational ......Mon, 07 Sep 2026 06:49:53 -0400https://track.liberty.io/solving-a-linear-system-of-differential-equations.htmlhttps://track.liberty.io/solving-a-linear-system-of-differential-equations.htmlGiven that $v_1 = \begin{bmatrix}1&1\end{bmatrix}$ and $v_2 = \begin{bmatrix}2 &1\end{bmatrix}$ are eigenvectors of the matrix $$ \begin{bmatrix}-1&-2\\1&-4\end{bmatrix} $$ which is......Mon, 07 Sep 2026 06:49:23 -0400https://track.liberty.io/can-quicksilver-sash-remove-airborne.htmlhttps://track.liberty.io/can-quicksilver-sash-remove-airborne.htmlIs this item able to remove airborne? To be more specific, during Yasuo's ult, can this item or Mercurial Scimitar dismiss the effect of Yasuo's ult?...Mon, 07 Sep 2026 06:44:27 -0400https://track.liberty.io/a-dot-with-custom-position-on-screen.htmlhttps://track.liberty.io/a-dot-with-custom-position-on-screen.htmlSo if you know about 3rd-person shooters, some of them don't have a cross and you have to predict where you shoot. Some people use a transparent tape with a marker dot to aim and I do that too, its......Mon, 07 Sep 2026 06:39:36 -0400https://track.liberty.io/how-can-i-raise-a-soldiers-hacking-ability.htmlhttps://track.liberty.io/how-can-i-raise-a-soldiers-hacking-ability.htmlMy main specialist seems to have a hard time hacking stuff. How can I make him better at it?...Mon, 07 Sep 2026 06:38:51 -0400https://track.liberty.io/circle-and-a-line-that-passes-through-it.htmlhttps://track.liberty.io/circle-and-a-line-that-passes-through-it.htmlGiven a line with equation: $y=ax-3$ that passes through a circle with equation $(x-1)^2+(y-1)^2= 1$. Find the range of values of $a$. I tried graphing and got: $0<x<2$ and $0<y<2$. ......Mon, 07 Sep 2026 06:29:50 -0400https://track.liberty.io/what-is-an-nonlinear-ordinary-differential-equation-and-give-an-exampl.htmlhttps://track.liberty.io/what-is-an-nonlinear-ordinary-differential-equation-and-give-an-exampl.htmlWhat is an nonlinear ordinary differential equation and give an example? And what is the difference between an linear ordinary differential equation and non-linear ordinary differential equation in ...Mon, 07 Sep 2026 06:28:38 -0400https://track.liberty.io/when-i-try-to-open-nexus-mod-manager-it-gives-me-a-message-saying-unre.htmlhttps://track.liberty.io/when-i-try-to-open-nexus-mod-manager-it-gives-me-a-message-saying-unre.htmlThe title explains the problem. Getting message of "Unrecognized Game Mode : Skyrim" before opening up, after clicking on icon ( after giving the admin. ok). Don't want to Uninstall because I don't......Mon, 07 Sep 2026 06:28:33 -0400https://track.liberty.io/use-of-either-or-in-maths-closed.htmlhttps://track.liberty.io/use-of-either-or-in-maths-closed.htmlI have been using these two words for a long time, especially when representing the solutions to quadratic equations. But I am little confused. These terms are often used simultaneously, but it seems ...Mon, 07 Sep 2026 06:24:33 -0400https://track.liberty.io/what-are-the-pre-requisites-required-to-learn-real-analysis.htmlhttps://track.liberty.io/what-are-the-pre-requisites-required-to-learn-real-analysis.htmlI already have quite a solid foundation in Single and Multivariable calculus. But how do I know if I'm prepared to tackle real analysis? Before I get into Real Analysis, I want to know everything t......Mon, 07 Sep 2026 06:23:22 -0400https://track.liberty.io/integration-methods-euler-039-s-substitution.htmlhttps://track.liberty.io/integration-methods-euler-039-s-substitution.htmlI've looked it up on the internet but I'm having trouble as to how to proceed using Euler's substitution. For example, how does one solve the following integrals using Euler's substitution: $\int......Mon, 07 Sep 2026 06:22:03 -0400https://track.liberty.io/extrinsics-vs-intrinsics-geometry-intuitive-explanation.htmlhttps://track.liberty.io/extrinsics-vs-intrinsics-geometry-intuitive-explanation.htmlI was wondering if anyone can give me an insight of what is meant with "Intrinsics Geometry" and "Extrinsics Geometry". At the beginning I thought this was like a distinction between differentiatio......Mon, 07 Sep 2026 06:17:04 -0400https://track.liberty.io/how-do-i-spawn-the-truffle.htmlhttps://track.liberty.io/how-do-i-spawn-the-truffle.htmlI don't know how to spawn him. How do I do it?...Mon, 07 Sep 2026 06:16:08 -0400https://track.liberty.io/how-to-sketch-the-graph-of-sin-x-2.htmlhttps://track.liberty.io/how-to-sketch-the-graph-of-sin-x-2.htmlClearly, we see that $y = \sin(x^2)$ is not periodic as $0$, $\sqrt{\pi}$, $\sqrt{2\pi}$, etc. are not equally spaced and for each of these values, $y=0$. Also $x^2$ changes much faster than $x$ do......Mon, 07 Sep 2026 06:13:45 -0400https://track.liberty.io/finding-the-integral-of-x-sec-2x-using-integration-by-parts.htmlhttps://track.liberty.io/finding-the-integral-of-x-sec-2x-using-integration-by-parts.htmlI need to find the integral of $\int x\sec(2x)dx $, but if I use integration by parts, I get an answer of $\int x\sec(2x)dx =0 $, which I know isn't correct. First I let $u=\sec(2x)$ and $v'=x$. ......Mon, 07 Sep 2026 06:12:24 -0400https://track.liberty.io/polynomial-root-finding.htmlhttps://track.liberty.io/polynomial-root-finding.htmlI have an univariate polynomial of some degree - how do I numerically find all of its real roots? I never thought I would ask this question - everyone knows how to find polynomial roots, right..? ......Mon, 07 Sep 2026 06:10:38 -0400https://track.liberty.io/value-of-cos-1-angle-is-in-radians.htmlhttps://track.liberty.io/value-of-cos-1-angle-is-in-radians.htmlHow can we calculate the value of $\cos 1$ where the angle is in radians (and not degrees). If this isn't possible, can we somehow find whether this value would be rational or irrational? P.S: I k......Mon, 07 Sep 2026 06:04:00 -0400https://track.liberty.io/how-to-see-whole-answers-for-long-floats-on-ti-83.htmlhttps://track.liberty.io/how-to-see-whole-answers-for-long-floats-on-ti-83.htmlDisclaimer: I guess answers on calculators are on topic for this SE site, tried searching and found alot of non-closed/moved questions. If not, please say so and i'll be happy to move the post ...Mon, 07 Sep 2026 06:03:12 -0400https://track.liberty.io/prove-that-every-bounded-sequence-in-bbb-r-has-a-convergent-subsequenc.htmlhttps://track.liberty.io/prove-that-every-bounded-sequence-in-bbb-r-has-a-convergent-subsequenc.htmlI am to prove that every bounded sequence in $\Bbb{R}$ has a convergent subsequence. I am stuck not knowing how and where to start....Mon, 07 Sep 2026 05:59:08 -0400https://track.liberty.io/question-on-ap-stats-variance-and-standard-deviation-closed.htmlhttps://track.liberty.io/question-on-ap-stats-variance-and-standard-deviation-closed.htmlThis was a question from the 2018 EXAM: A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and Western Farm. Let the random variable $X$ represent the weight of ...Mon, 07 Sep 2026 05:58:15 -0400https://track.liberty.io/understanding-the-least-squares-regression-formula.htmlhttps://track.liberty.io/understanding-the-least-squares-regression-formula.htmlI've seen the following tutorial on it, but the formula itself had not been explained (https://www.youtube.com/watch?v=Qa2APhWjQPc). I understanding the intuition behind finding a line that "best ......Mon, 07 Sep 2026 05:53:27 -0400https://track.liberty.io/expressing-the-minimum-function-in-terms-of-the-absolute-value-in-a-sy.htmlhttps://track.liberty.io/expressing-the-minimum-function-in-terms-of-the-absolute-value-in-a-sy.htmlIt is well known that: $$\max(a,b) = \frac12(a+b)+\frac12|a-b|$$ and similarly: $$\min(a,b) = \frac12(a+b)-\frac12|a-b|.$$ In fact, they are equivalent since $\max(a,b) = -\min(-a,-b)$. We can try ...Mon, 07 Sep 2026 05:30:32 -0400https://track.liberty.io/issue-with-modelling-word-problems-as-cubic-equations.htmlhttps://track.liberty.io/issue-with-modelling-word-problems-as-cubic-equations.htmlI am having problems with a specific set of word problems, which are meant to be modeled as cubic equations in order to be solved. I will give some examples to specify where I can't solve it. The......Mon, 07 Sep 2026 05:27:49 -0400https://track.liberty.io/examples-based-on-a-2-connected-graph.htmlhttps://track.liberty.io/examples-based-on-a-2-connected-graph.htmlAccording to Scott Smith 1984 Conjecture: In a $k$-connected graph, where $k \ge 2$, any two longest cycles have at least $k$ vertices in common. A 2-connected graph: every pair of longest cycles h......Mon, 07 Sep 2026 05:14:02 -0400https://track.liberty.io/prove-that-between-two-unequal-rational-numbers-there-is-another-ratio.htmlhttps://track.liberty.io/prove-that-between-two-unequal-rational-numbers-there-is-another-ratio.htmlI understand that I probably asked a question that the users of this site would view as elementary, but I have only just dipped my feet into the waters of proof solving. Can somebody please tell me......Mon, 07 Sep 2026 05:13:00 -0400https://track.liberty.io/why-is-039-abuse-of-notation-039-tolerated.htmlhttps://track.liberty.io/why-is-039-abuse-of-notation-039-tolerated.htmlI've personally tripped up on a few concepts that came down to an abuse of notation, and I've read of plenty more on stack exchange. It seems to all be forgiven with a wave of the hand. Why do we ...Mon, 07 Sep 2026 05:12:45 -0400https://track.liberty.io/how-do-i-calculate-generalized-eigenvectors.htmlhttps://track.liberty.io/how-do-i-calculate-generalized-eigenvectors.htmlI have the matrix $$A=\begin{pmatrix} 5 & 1 & 0\\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{pmatrix}$$ and I should determine generalised eigenvectors, if they exist. I found one ...Mon, 07 Sep 2026 04:50:52 -0400https://track.liberty.io/binomial-distribution-to-approximate-90-successes.htmlhttps://track.liberty.io/binomial-distribution-to-approximate-90-successes.htmlA student is taking a multiple choice test where each question has four options for an answer. The student mastered mastered 70% of the material. Assume this means that the student has a 0.7 chance......Mon, 07 Sep 2026 04:49:31 -0400https://track.liberty.io/is-it-possible-to-check-current-online-players-in-the-realm.htmlhttps://track.liberty.io/is-it-possible-to-check-current-online-players-in-the-realm.htmlIs there any way (macro, script, addon, command, API method?) to check how many online players are in the realm you're connected to?...Mon, 07 Sep 2026 04:45:57 -0400https://track.liberty.io/where-can-the-security-rooms-spawn-on-the-diamond-heist.htmlhttps://track.liberty.io/where-can-the-security-rooms-spawn-on-the-diamond-heist.htmlWhere are the possible spawn locations for the Security (ie Camera) room in The Diamond. I've seen in the maintenance rooms in the Lower Hall (see image below). Can the Security Room be in any of......Mon, 07 Sep 2026 04:43:41 -0400https://track.liberty.io/how-do-i-associate-my-xbox-360-copy-of-mass-effect-3-with-my-ea-origin.htmlhttps://track.liberty.io/how-do-i-associate-my-xbox-360-copy-of-mass-effect-3-with-my-ea-origin.htmlMass Effect 3 on Xbox logs into Origin every time I start the game up, but I never actually gave it my Origin credentials, and (understandably) it does not seem to be associated with my Origin acco......Mon, 07 Sep 2026 04:33:24 -0400https://track.liberty.io/how-to-find-the-vertex-of-a-triangle.htmlhttps://track.liberty.io/how-to-find-the-vertex-of-a-triangle.htmlI was given two coordinates of vertex - A(1,2) and B(5,-4) and also a circumcentre O(6,1). Is it possible to find out the 3rd vertex? My try is first find the midpoint of AC , which is D[(1+x)/2,(......Mon, 07 Sep 2026 04:33:03 -0400https://track.liberty.io/how-to-verify-a-solution-to-the-wave-equation.htmlhttps://track.liberty.io/how-to-verify-a-solution-to-the-wave-equation.htmlI have a wave equation: $$\frac{\partial^2u}{\partial t^2} = a^2 \frac{\partial^2u}{\partial x^2}.$$ How would I verify that the function $u(x,t)=\sin(x-at)$ satisfies the aforementioned wave equ......Mon, 07 Sep 2026 04:26:51 -0400https://track.liberty.io/how-do-you-do-a-cross-product-of-two-3-times-3-boolean-matrices.htmlhttps://track.liberty.io/how-do-you-do-a-cross-product-of-two-3-times-3-boolean-matrices.htmlI have two boolean matrices: A = |1 1 0| |0 1 0| |0 0 1| and B = |1 0 0| |1 1 1| |0 0 1| What is the result of A x B and what are the steps needed to attain the result? Note: My ...Mon, 07 Sep 2026 04:25:22 -0400https://track.liberty.io/how-does-xy-039-x-039-y-039-simplify-to-xy-x-039-y-039.htmlhttps://track.liberty.io/how-does-xy-039-x-039-y-039-simplify-to-xy-x-039-y-039.htmlHow does $$(xy' + x'y)'$$ simplify to $$(xy + x'y')$$...Mon, 07 Sep 2026 04:20:40 -0400https://track.liberty.io/how-do-i-know-if-peace-is-possible-between-the-geth-and-the-quarians.htmlhttps://track.liberty.io/how-do-i-know-if-peace-is-possible-between-the-geth-and-the-quarians.htmlI'm basically trying to make peace between the Geth and the Quarians in ME3. I have imported save files all the way from ME1 and ME2. My problem is that I couldn't select the peaceful option on Ra......Mon, 07 Sep 2026 04:10:35 -0400https://track.liberty.io/how-do-i-encounter-the-last-monster-in-the-core-hotland.htmlhttps://track.liberty.io/how-do-i-encounter-the-last-monster-in-the-core-hotland.htmlI’m doing the genocide route on my PS4, and I’ve cleared both hotland and the CORE, however there is one more monster left and I can’t find them, I’ve backtracked through the entire map (Hotland an......Mon, 07 Sep 2026 04:00:56 -0400https://track.liberty.io/using-the-washer-method-to-find-the-volume-of-an-object.htmlhttps://track.liberty.io/using-the-washer-method-to-find-the-volume-of-an-object.htmlWhen finding the volume of a solid generated by revolving $y=2x+8$ and $y=2x^2+1$, about the $x$ axis, I will first set them equal to each other to find the bounds for my integral. Doing this I get......Mon, 07 Sep 2026 03:53:19 -0400https://track.liberty.io/how-to-turn-sand-into-grass-in-minecraft-duplicate.htmlhttps://track.liberty.io/how-to-turn-sand-into-grass-in-minecraft-duplicate.htmlHow would I turn sand blocks into the grass block on Minecraft? Please help....Mon, 07 Sep 2026 03:51:32 -0400https://track.liberty.io/motivation-for-quasi-coherent-sheaf.htmlhttps://track.liberty.io/motivation-for-quasi-coherent-sheaf.htmlI have some background in vector bundles in the context of differential geometry and I have seen how vector fields form a module over smooth functions on a smooth manifold. Recently I came across ......Mon, 07 Sep 2026 03:44:42 -0400https://track.liberty.io/finding-the-angle-between-two-line-equations.htmlhttps://track.liberty.io/finding-the-angle-between-two-line-equations.htmlI need to find the angle between two lines in $y = mx + b$ form and they are: \begin{equation*} y = 4x + 2~\text{and}~y = -x + 3 \end{equation*} I have no idea how to solve this and if you could ......Mon, 07 Sep 2026 03:42:12 -0400https://track.liberty.io/derivative-of-sqrt-xy.htmlhttps://track.liberty.io/derivative-of-sqrt-xy.html$\sqrt{|xy|} = 1$ Attempting to find the derivative gives me $$\frac12(xy)^{-1/2}\left(x\frac{dy}{dx} + y\right) = 0$$ But I haven't figured out how to simplify this further. My teacher says that......Mon, 07 Sep 2026 03:41:32 -0400https://track.liberty.io/is-there-a-way-to-summon-dogmeat-to-you.htmlhttps://track.liberty.io/is-there-a-way-to-summon-dogmeat-to-you.htmlI've recently started playing Fallout 4, and I've acquired Dogmeat. Long story short, I told him to stay in a small building so I could down a few raiders quietly but I forgot about him and I can't......Mon, 07 Sep 2026 03:37:34 -0400https://track.liberty.io/determine-whether-the-set-spans-r-2.htmlhttps://track.liberty.io/determine-whether-the-set-spans-r-2.htmlSo I'm told to determine whether a set spans $R^2$ and if it doesn't then give a geometric description of the subspace that it does span. $S=\{\left(-1,4\right),\left(4,-1\right),\left(1,1\right)\......Mon, 07 Sep 2026 03:30:15 -0400https://track.liberty.io/variance-of-the-mle-for-a-geometric-distribution.htmlhttps://track.liberty.io/variance-of-the-mle-for-a-geometric-distribution.htmlI have derived the MLE for $p$ in the geometric distribution, $p=1/\overline X$. I now need to find its asymptotic variance. Trying to take the variance of $1/\overline X$ directly seems intracta......Mon, 07 Sep 2026 03:29:00 -0400https://track.liberty.io/transpose-of-conjugate-transpose.htmlhttps://track.liberty.io/transpose-of-conjugate-transpose.htmlWhat is the transpose of a conjugate transpose? Let's say we have a matrix $A$ and its conjugate transpose $A^{*}$, would the transpose of the conjugate transpose be the conjugate of $A$, i.e. $\ba......Mon, 07 Sep 2026 03:28:15 -0400https://track.liberty.io/prove-that-the-following-two-definitions-of-the-convex-hull-are-equiva.htmlhttps://track.liberty.io/prove-that-the-following-two-definitions-of-the-convex-hull-are-equiva.htmlI was wondering if a topology expert could help me solve this proof, as I have no idea but want to understand these concepts. This is not for homework. Let X be a point set, not necessarily finit......Mon, 07 Sep 2026 03:24:53 -0400https://track.liberty.io/non-ambiguous-description-of-pasta-property.htmlhttps://track.liberty.io/non-ambiguous-description-of-pasta-property.htmlI find the word "see" as in PASTA (Poisson Arrivals See Time Averages) to be a bit ambiguous and thus wanted some clarification in what it means (see http://pages.cs.wisc.edu/~dsmyers/cs547/...Mon, 07 Sep 2026 03:19:50 -0400https://track.liberty.io/learning-trigonometry-on-my-own.htmlhttps://track.liberty.io/learning-trigonometry-on-my-own.htmlI have been self teaching myself math beginning with a grade 10 level for a while now and need learn trigonometry from near scratch. I am seeking both books and perhaps lectures on trigonometry and ...Mon, 07 Sep 2026 03:19:20 -0400https://track.liberty.io/solving-a-logarithmic-polynomial.htmlhttps://track.liberty.io/solving-a-logarithmic-polynomial.htmlI want to solve this equation for $x$: $${\frac{1}{\sqrt{2 \pi x}} \left(\frac{e z}{2x}\right)^x} = \epsilon$$ Is there a closed form for it, or does it have to be solved numerically? I can turn......Mon, 07 Sep 2026 03:18:16 -0400https://track.liberty.io/derivative-of-sec-1-x.htmlhttps://track.liberty.io/derivative-of-sec-1-x.htmlI'm struggling with problem below which I eagerly want to solve. Let me know from where this problem is, if possible (the origin source of textbook). your answers might really helpful to get throug......Mon, 07 Sep 2026 03:14:18 -0400https://track.liberty.io/how-to-demolish-skyscraper.htmlhttps://track.liberty.io/how-to-demolish-skyscraper.htmlIn Battlefield 4 on map "Siege of Shanghai" there is skyscraper in center. By the end of "Conquest" round it usually destroyed. But every time I miss that moment. What trigger destruction of this ...Mon, 07 Sep 2026 03:06:45 -0400https://track.liberty.io/how-do-you-hide-command-blocks.htmlhttps://track.liberty.io/how-do-you-hide-command-blocks.htmlI am making a server, and I want to teleport the closest player to a certain area. But I don't know how to make the command blocks invisible, so the players don't see them. Does anyone know how?...Mon, 07 Sep 2026 02:55:37 -0400https://track.liberty.io/further-factorisation-of-a-difference-of-cubes.htmlhttps://track.liberty.io/further-factorisation-of-a-difference-of-cubes.htmlWe know that a difference of cubes can be factored using $a^3-b^3=(a-b)(a^2+ab+b^2)$. How do we know that the quadratic can't be factored further. For example, $$ 27x^3-(x+3)^3=((3x-(x+3))(9x^2+3......Mon, 07 Sep 2026 02:49:14 -0400https://track.liberty.io/what-is-48-div2-9-3-duplicate.htmlhttps://track.liberty.io/what-is-48-div2-9-3-duplicate.htmlThere is a huge debate on the internet on the value of $48\div2(9+3)$. I believe the answer $2$ as I believe it is part of the bracket operation in BEDMAS. Mathway yields the same answer. I also be......Mon, 07 Sep 2026 02:27:45 -0400https://track.liberty.io/convolution-of-a-step-function-with-itself.htmlhttps://track.liberty.io/convolution-of-a-step-function-with-itself.htmlI have a step function that states $f(x) = 1$ for $|x| < 1$ and 0 everywhere else. So far I've found this to be $$\int_{-\infty}^{\infty}\, dy\, f(y)\,f(x-y)$$ and from boundaries, $$-1 < y &......Mon, 07 Sep 2026 02:27:20 -0400https://track.liberty.io/how-to-get-the-i-like-it-hot-achievement-in-tsw-l-how-to-make-a-flamin.htmlhttps://track.liberty.io/how-to-get-the-i-like-it-hot-achievement-in-tsw-l-how-to-make-a-flamin.htmlThere is an Regional Achievement (hubs) called "I like it hot" in Secret World: Legends. To get it, you need to eat a "Flamin' Hot Taco". How do you get one?...Mon, 07 Sep 2026 02:13:05 -0400https://track.liberty.io/how-to-find-the-multiplicity-of-eigenvalues.htmlhttps://track.liberty.io/how-to-find-the-multiplicity-of-eigenvalues.htmlI don't understand how to find the multiplicity for an eigenvalue. To be honest, I am not sure what the books means by multiplicity. For instance, finding the multiplicty of each eigenvalue for the ...Mon, 07 Sep 2026 02:08:37 -0400https://track.liberty.io/can-039-t-seem-to-get-a-minecart-to-move.htmlhttps://track.liberty.io/can-039-t-seem-to-get-a-minecart-to-move.htmlI have Minecraft 1.8. I placed a powered rail on the floor of a room in my basement and a button to activate it. I place the minecart, press the button and the cart doesn't move. If I do the same ...Mon, 07 Sep 2026 02:06:53 -0400https://track.liberty.io/cauchy-integral-formula.htmlhttps://track.liberty.io/cauchy-integral-formula.htmlCan someone please help me answer this question as I cannot seem to get to the answer. Please note that the Cauchy integral formula must be used in order to solve it. Many thanks in advance! \begin{...Mon, 07 Sep 2026 02:06:17 -0400https://track.liberty.io/i-can-039-t-craft-a-silver-watch-terarria.htmlhttps://track.liberty.io/i-can-039-t-craft-a-silver-watch-terarria.htmlI have all the materials needed for a Silver Watch. I have 9 chains and 22 Silver. (I know you need 10 silver and 1 chain) But I can't craft it? I try a Crafting Table, Furnace, Anvil, Advanced Cra......Mon, 07 Sep 2026 02:05:20 -0400https://track.liberty.io/questions-tagged-world-of-warcraft.htmlhttps://track.liberty.io/questions-tagged-world-of-warcraft.htmlQ&A for passionate videogamers on all platforms...Mon, 07 Sep 2026 01:59:00 -0400https://track.liberty.io/fallout-4-do-i-really-need-the-institute-to-continue-and-complete-fall.htmlhttps://track.liberty.io/fallout-4-do-i-really-need-the-institute-to-continue-and-complete-fall.htmlI don't think I'm going to move forward anymore with the Institute, as a glitch has occurred in my previous question! But is it worth actually trying to fix this? Do I really need the Institute or ......Mon, 07 Sep 2026 01:51:17 -0400https://track.liberty.io/where-can-i-get-something-better-than-a-bronze-edge-for-frog.htmlhttps://track.liberty.io/where-can-i-get-something-better-than-a-bronze-edge-for-frog.htmlI've finally managed to rescue Frog from his sulking with a really expensive gift. However, he can't use that gift. For that matter, I'm having trouble finding something he can use. I travelled all......Mon, 07 Sep 2026 01:50:34 -0400https://track.liberty.io/can-you-easily-find-friends-039-ghosts.htmlhttps://track.liberty.io/can-you-easily-find-friends-039-ghosts.htmlI don't currently have Mario Kart 8 Deluxe, only the Wii U version. I'm trying to assess whether the deluxe version has some functionality I've been really wanting. On the Wii U, my friends and I ......Mon, 07 Sep 2026 01:30:24 -0400https://track.liberty.io/what-do-you-get-as-a-member-in-runescape.htmlhttps://track.liberty.io/what-do-you-get-as-a-member-in-runescape.htmlI thought of becoming a paid Runescape member, but I'm not sure the expense is worth it. Therefore I'm wondering what are the advantages of becoming a member? What more could I do? I'm already a l......Mon, 07 Sep 2026 01:28:06 -0400https://track.liberty.io/the-nth-order-linear-differential-equation-with-the-constant-coefficie.htmlhttps://track.liberty.io/the-nth-order-linear-differential-equation-with-the-constant-coefficie.htmlWe have the nth order linear differential equation with the constant coefficients such that $a_ny^n + a_{n-1}y^{n-1}+...+ a_1y' + a_0y= 0$. What would be the properties of the solution if the time ......Mon, 07 Sep 2026 01:23:56 -0400https://track.liberty.io/square-root-of-2-is-irrational.htmlhttps://track.liberty.io/square-root-of-2-is-irrational.htmlI am studying the proof that $\sqrt 2$ is an irrational number. Now I understand most of the proof, but I lack an understanding of the main idea which is: We assume $\frac{m^2}{n^2} = 2$. Then ......Mon, 07 Sep 2026 01:23:56 -0400https://track.liberty.io/what-is-a-dual-space.htmlhttps://track.liberty.io/what-is-a-dual-space.htmlI've started studying differential geometry by myself and I ran into dual spaces in a section on 1-forms. I'm not very well versed in linear algebra so any help is much appreciated....Mon, 07 Sep 2026 01:21:38 -0400https://track.liberty.io/macro-to-interact-with-target.htmlhttps://track.liberty.io/macro-to-interact-with-target.htmlIn World of Warcraft, is there an equivalent that you can use in a macro to 'Interact With Target' so that I can create a macro that interacts with specific NPCs with a single keypress?...Mon, 07 Sep 2026 01:11:55 -0400