https://track.liberty.ioFresh celebrity buzz with instant attention value.en-usMon, 07 Sep 2026 02:26:00 -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 -0400https://track.liberty.io/how-do-i-downgrade-xbox-360-dashboard.htmlhttps://track.liberty.io/how-do-i-downgrade-xbox-360-dashboard.htmlI have an Xbox 360 Elite and I want to downgrade the dashboard version from 2.x to 9199. I tried putting $SystemUpdate (from the official $SystemUpdate9199.zip) folder into a FAT32 formatted USB and ...Mon, 07 Sep 2026 01:07:44 -0400https://track.liberty.io/quadratic-formula-with-negative-square-root.htmlhttps://track.liberty.io/quadratic-formula-with-negative-square-root.htmlI encountered this while doing a very basic physics question (so I hope you don't mind if I post it, the problem lies within my math anyways): A stunt vehicle leaves an inclined slope of 28 degrees......Mon, 07 Sep 2026 00:57:57 -0400https://track.liberty.io/how-do-you-find-a-multiplicative-inverse-in-modulo-arithmetic.htmlhttps://track.liberty.io/how-do-you-find-a-multiplicative-inverse-in-modulo-arithmetic.htmlIn one of my lectures I have been given this example: When Googling 'multiplicative inverse' most of the tutorials seem to indicate it's as easy as just multiplying a number by the number divided ......Mon, 07 Sep 2026 00:27:53 -0400https://track.liberty.io/how-many-players-can-play-splitscreen-in-cod-wwii.htmlhttps://track.liberty.io/how-many-players-can-play-splitscreen-in-cod-wwii.htmlHow many players can play split-screen, and what game modes are (or aren't) available? How many players can play local co-op? How many players can play local multiplayer? How many players can play ...Mon, 07 Sep 2026 00:16:21 -0400https://track.liberty.io/executing-a-command-for-an-entity-in-front-of-me.htmlhttps://track.liberty.io/executing-a-command-for-an-entity-in-front-of-me.htmlI'd like to know if there is a command for detecting an entity in front of me, that upon detection can execute a command for that entity. The command would be like: There's a cow in front the p......Mon, 07 Sep 2026 00:11:20 -0400https://track.liberty.io/subgroups-of-the-klein-4-group.htmlhttps://track.liberty.io/subgroups-of-the-klein-4-group.htmlCan anyone explain to me the subgroups of the Klein-4 group? I'm trying to view it this way: I want some groups that are not empty and $ab^{-1} \in H$, where $H$ denotes the subgroups I am looking......Mon, 07 Sep 2026 00:09:48 -0400https://track.liberty.io/do-normal-region-restrictions-apply-when-playing-ps1-games-on-ps3.htmlhttps://track.liberty.io/do-normal-region-restrictions-apply-when-playing-ps1-games-on-ps3.htmlI got my PS1 while living in the US and I live in EU now. Will my US PS1 games work on a PAL PS3 or do normal region restrictions apply?...Mon, 07 Sep 2026 00:03:57 -0400https://track.liberty.io/derivation-of-chi-squared-pdf-with-one-degree-of-freedom-from-normal-d.htmlhttps://track.liberty.io/derivation-of-chi-squared-pdf-with-one-degree-of-freedom-from-normal-d.htmlHow can we derive the chi-squared probability density function (pdf) using the pdf of normal distribution? I mean, I need to show that $$f(x)=\frac{1}{2^{r/2}\Gamma(r/2)}x^{r/2-1}e^{-x/2} \>, \...Sun, 06 Sep 2026 23:59:01 -0400https://track.liberty.io/what-is-complex-analysis-why-is-it-accompanied-by-linear-algebra.htmlhttps://track.liberty.io/what-is-complex-analysis-why-is-it-accompanied-by-linear-algebra.htmlI hope this doesn't extend to a lengthy question. I studied Linear Algebra recently in my first term at university. I came to the realization however that some institutions would teach that course ......Sun, 06 Sep 2026 23:58:36 -0400https://track.liberty.io/is-there-a-strategy-to-win-this-move-color-game.htmlhttps://track.liberty.io/is-there-a-strategy-to-win-this-move-color-game.htmlMy girlfriend has been playing a game on her smartphone for a while. The rules are: there are $n+2$ tubes (with $n\ge 1$) and $n$ colored liquids. Two tubes are left empty and the others are fille......Sun, 06 Sep 2026 23:41:40 -0400https://track.liberty.io/plot-y-range-on-mathematica.htmlhttps://track.liberty.io/plot-y-range-on-mathematica.htmlI have a plot that I would like to slightly manipulate in Mathematica. Here is the code I am entering: Plot[{x, 2^x, log_2(x)}, {x, -1, 3}] As you can see $x$, $2^x$, and $log_2(x)$ are all plo......Sun, 06 Sep 2026 23:40:49 -0400https://track.liberty.io/fubini-study-metric-on-the-complex-projective-space-mathbb-pc-m.htmlhttps://track.liberty.io/fubini-study-metric-on-the-complex-projective-space-mathbb-pc-m.htmlI study Andrei Moroianu's Lectures on Kähler Geometry and have some troubles to understand the proof of Lemma 7.1. The claim is that the tensor $h$ that gives some called Fubini–Study metric on the ...Sun, 06 Sep 2026 23:30:14 -0400https://track.liberty.io/is-equilateral-trapezium-possible.htmlhttps://track.liberty.io/is-equilateral-trapezium-possible.htmlQ.Is equilateral Trapezium possible? The defination of Trapezium :A quadrilateral with one pair of parallel sides. If we have a trapezium that have equal sides,it becomes a rhombus (& contrad......Sun, 06 Sep 2026 23:28:19 -0400https://track.liberty.io/intuitive-understanding-of-the-constant-e.htmlhttps://track.liberty.io/intuitive-understanding-of-the-constant-e.htmlPotentially related-questions, shown before posting, didn't have anything like this, so I apologize in advance if this is a duplicate. I know there are many ways of calculating (or should I say "e......Sun, 06 Sep 2026 23:26:22 -0400https://track.liberty.io/average-length-of-chord-of-circle-definite-integral.htmlhttps://track.liberty.io/average-length-of-chord-of-circle-definite-integral.htmlGiven a circle C of radius a, and a diameter AB of C. Chords are drawn perpendicular to AB, intercepting equal arcs along the circumference of C. Find the limit of the average of the lengths of t......Sun, 06 Sep 2026 23:19:28 -0400https://track.liberty.io/pairs-of-trig-functions-pythagorean-identities-and-derivatives.htmlhttps://track.liberty.io/pairs-of-trig-functions-pythagorean-identities-and-derivatives.htmlOr, "Why do the six trig functions split up into three pairs of best friends?" There are three Pythagorean identities: $$ \begin{align*} \sin^2 x + \cos^2 x &= 1\\ \tan^2 x + 1 &= \sec^2 ......Sun, 06 Sep 2026 23:05:40 -0400https://track.liberty.io/finding-the-angular-size-of-a-minor-arc.htmlhttps://track.liberty.io/finding-the-angular-size-of-a-minor-arc.htmlThe question is as follows: A 20-inch chord is drawn in a circle with a 12-inch radius. What is the angular size of the minor arc of the chord? What is the length of the arc, to the nearest tent......Sun, 06 Sep 2026 23:01:26 -0400https://track.liberty.io/do-79-42-in-binary-using-2-039-s-complement.htmlhttps://track.liberty.io/do-79-42-in-binary-using-2-039-s-complement.htmlI did: 79_10 = 1001111 42_2 = 101010 I took 2's Complement of 42 and got 010110. Then I did 1001111 + 010110 and got 1100101 but this is 101. If I remove the leftmost one it becomes 37 which is ...Sun, 06 Sep 2026 23:00:54 -0400https://track.liberty.io/when-is-the-frobenius-endomorphism-an-automorphism.htmlhttps://track.liberty.io/when-is-the-frobenius-endomorphism-an-automorphism.htmlI was thinking about some problem: Lef $F$ be a finite field with the characteristic $p$. Then a map $x\mapsto x^p$ is an automorphism. I figured out that this map is called the Frobenius ...Sun, 06 Sep 2026 23:00:18 -0400https://track.liberty.io/showing-whether-a-sequence-is-bounded-above-or-not.htmlhttps://track.liberty.io/showing-whether-a-sequence-is-bounded-above-or-not.htmlI am trying to solve the following problem about a sequence: Consider the sequence ${a_n}$ where $a_n = 1 + \frac{1}{1 \cdot 3} + \frac {1}{1 \cdot 3 \cdot 5} + \frac {1}{1 \cdot 3 \cdot 5 \cdot 7}......Sun, 06 Sep 2026 22:49:01 -0400https://track.liberty.io/what-does-a-mod-2-pi-function-mean.htmlhttps://track.liberty.io/what-does-a-mod-2-pi-function-mean.htmlI read somewhere that cosine is a "$\bmod 2 \pi$ function". I think it means that it repeats every $2\pi$, but what is this "mod"?...Sun, 06 Sep 2026 22:44:08 -0400https://track.liberty.io/what-is-a-series.htmlhttps://track.liberty.io/what-is-a-series.htmlThis question is rather pedantic, but it is something that has been bothering me for some time. Summing up infinitely many terms of a sequence is something that is done in pretty much every subfie......Sun, 06 Sep 2026 22:37:13 -0400https://track.liberty.io/next-book-in-learning-differential-geometry.htmlhttps://track.liberty.io/next-book-in-learning-differential-geometry.htmlI have just finished the book "Manfredo P. do Carmo - Differential Geometry of Curves and Surfaces". My aim is to reach to graduate level to do research, but articles are not only too advanced to ......Sun, 06 Sep 2026 22:31:44 -0400https://track.liberty.io/find-the-solution-to-the-initial-value-problem.htmlhttps://track.liberty.io/find-the-solution-to-the-initial-value-problem.htmlFind the solution of the initial value problem $$ \frac{dy}{dt}=1-y^2,\;y(0)=y_0 $$ (i) in the case $y_0=1$; (ii) $y_0=-1$; (iii) in all other cases. Are there any $y_0$ such that the sol......Sun, 06 Sep 2026 22:22:57 -0400https://track.liberty.io/proof-c-n-r-c-n-n-r.htmlhttps://track.liberty.io/proof-c-n-r-c-n-n-r.htmlHello just want to see if my proof is right, and if not could someone please guide me because I am not clearly seeing the steps to this proof. I don't know if I correctly solve the proof in the sec......Sun, 06 Sep 2026 22:15:22 -0400https://track.liberty.io/how-to-factor-x-5-x-1.htmlhttps://track.liberty.io/how-to-factor-x-5-x-1.htmlI put $x^5 + x + 1$ into Wolfram and my TI-89 to factor it and they both arrived at the same factored answer: $$(x^2+x+1)(x^3-x^2+1)$$ I've tried to expand this out to reverse engineer it: $$\be......Sun, 06 Sep 2026 21:37:36 -0400https://track.liberty.io/why-is-it-wrong-to-take-the-cube-root-of-both-sides-z-1-3-z-3.htmlhttps://track.liberty.io/why-is-it-wrong-to-take-the-cube-root-of-both-sides-z-1-3-z-3.htmlif i take square root of both sides of the equation then the z cancel each other: $ \sqrt[3] {(z+1)^3 }=\sqrt[3]{z^3} $ $ z+1 =z $ $ z-z+1=0$ $ 1=0 $ I thought this complex equation had no solution......Sun, 06 Sep 2026 21:35:12 -0400https://track.liberty.io/how-many-numbers-between-1-10000-can-be-divided-by-2-and-5-but-are-not.htmlhttps://track.liberty.io/how-many-numbers-between-1-10000-can-be-divided-by-2-and-5-but-are-not.htmlFirst i calculated how many numbers are divisible by 2 and 5 $\frac{10000}{2}+\frac{10000}{5}-\frac{10000}{2*5}=6000$ Then i calculated how many numbers are not divisible by 3 or 4 $10000-(\frac{10......Sun, 06 Sep 2026 21:34:01 -0400https://track.liberty.io/finding-center-of-tessellating-hexagons.htmlhttps://track.liberty.io/finding-center-of-tessellating-hexagons.htmlGiven a hexagon such that opposite angles and radii are equal, how can I find the center point of any number of other hexagons (of the same dimensions) that form a tessellation? In this (very ug......Sun, 06 Sep 2026 21:32:07 -0400https://track.liberty.io/what-does-adding-sin-theta-cos-theta-make-my-graph-a-linear-relationsh.htmlhttps://track.liberty.io/what-does-adding-sin-theta-cos-theta-make-my-graph-a-linear-relationsh.htmlWhat is the point of adding sin n cos of theta when graphing range? e.g. I see on hyperphysics a graph of range vs sin n cos of theta and it makes the experimental data embody a linear relationshi......Sun, 06 Sep 2026 21:30:33 -0400https://track.liberty.io/what-is-the-point-of-countable-vs-uncountable-sets.htmlhttps://track.liberty.io/what-is-the-point-of-countable-vs-uncountable-sets.htmlI understand how to use these concepts and how to prove certain sets are countable or uncountable. However I don't get the point of it. What difference does it make whether a set is countable? Peop......Sun, 06 Sep 2026 21:22:40 -0400https://track.liberty.io/cross-product-equation-with-sine-i-don-039-t-understand-the-unit-vecto.htmlhttps://track.liberty.io/cross-product-equation-with-sine-i-don-039-t-understand-the-unit-vecto.html$\vec{a} \times \vec{b}=\mid \vec{a} \mid \mid \vec{b} \mid \sin(\theta)\, \vec{n}$ I know this is probably an incredibly simple question, and I know that "n" is the unit vector at right angles to......Sun, 06 Sep 2026 21:22:22 -0400https://track.liberty.io/rules-of-inference-is-my-application-of-simplification-in-this-proof-c.htmlhttps://track.liberty.io/rules-of-inference-is-my-application-of-simplification-in-this-proof-c.htmlCould someone verify that my proof is valid as the question did not have a solution? $(\lnot R \lor \lnot F) \to (S \land L)$ $(S \to T)$ $(\lnot T)$ $(\lnot S)$ 2,3 Modus tollens $\lnot (\l......Sun, 06 Sep 2026 21:09:44 -0400https://track.liberty.io/is-there-any-commonality-between-math-induction-and-logic-induction.htmlhttps://track.liberty.io/is-there-any-commonality-between-math-induction-and-logic-induction.htmlLogic induction is reasoning by probability. Math induction seems to be related to just Natural numbers and used to prove a statement for every natural number. From these definitions there is no ...Sun, 06 Sep 2026 20:45:09 -0400https://track.liberty.io/expand-function-in-legendre-polynomials-on-the-interval-1-1.htmlhttps://track.liberty.io/expand-function-in-legendre-polynomials-on-the-interval-1-1.htmlExpand the following function in Legendre polynomials on the interval [-1,1] : $$f(x) = |x|$$ The Legendre polynomials $p_n (x)$ are defined by the formula : $$p_n (x) = \frac {1}{2^n n!} \frac{......Sun, 06 Sep 2026 20:42:56 -0400https://track.liberty.io/simplifying-large-exponents-in-modular-arithmetic-like-1007-in-4-1007-.htmlhttps://track.liberty.io/simplifying-large-exponents-in-modular-arithmetic-like-1007-in-4-1007-.htmlHow would I rigorously prove that $4^{1007} \pmod{5} = 4$ and $4^{1008} \pmod{5} = 1$? I was simplifying a larger modular arithmetic problem ($2013^{2014} \pmod{5}$) and got it down to $4^{1007} \......Sun, 06 Sep 2026 20:33:47 -0400https://track.liberty.io/intersection-of-normal-extensions-is-a-normal-extension.htmlhttps://track.liberty.io/intersection-of-normal-extensions-is-a-normal-extension.htmlLet's assume that we have two normal extensions $L_1$ and $L_2$ which means that $L_1=K(A_1)$ and $L_2=K(A_2)$, where $A_1$ and $A_2$ are sets of roots of proper polynomials. How can I show that ...Sun, 06 Sep 2026 20:16:56 -0400https://track.liberty.io/formula-for-infinite-sum-of-a-geometric-series-with-increasing-term.htmlhttps://track.liberty.io/formula-for-infinite-sum-of-a-geometric-series-with-increasing-term.htmlI'm looking for the Expectation of the discrete random variable X, E[X], with pmf: $$p(x)=(\frac 16)^{x+1}, x=0,1,2,3...$$ so what I tried is as follows... $$E[X]= \sum_{0}^\infty xp(x) =$$ so t......Sun, 06 Sep 2026 20:13:01 -0400