https://pop.com.sgExplosive pop stories with broad entertainment appeal.en-usMon, 07 Sep 2026 19:26:01 -0400https://pop.com.sg/the-cos-alpha-beta-formula-always-need-alpha-beta-or-not.htmlhttps://pop.com.sg/the-cos-alpha-beta-formula-always-need-alpha-beta-or-not.htmlI'm a beginner student study the proof of sum and difference trigonometry formula. There is a formula that: $$\cos(\alpha-\beta) = \cos(\alpha)\cos(\beta)+\sin(\alpha)\sin(\beta)$$ In the tutori......Mon, 07 Sep 2026 23:23:14 -0400https://pop.com.sg/how-can-i-delete-the-ps-plus-games-of-the-month-after-my-ps-plus-subsc.htmlhttps://pop.com.sg/how-can-i-delete-the-ps-plus-games-of-the-month-after-my-ps-plus-subsc.htmlI subscribed to PS Plus for two months and decided it was not for me. I downloaded all the games of the month then realized I don't want to actually play them anymore. Whenever I try downloading a ......Mon, 07 Sep 2026 23:14:00 -0400https://pop.com.sg/undo-command-in-minecraft.htmlhttps://pop.com.sg/undo-command-in-minecraft.htmlI would want to know if there is a sort of "undo" command in Minecraft (no mods) that undo one action at the time. For example, the player pressed a button that started a huge redstone system or he ...Mon, 07 Sep 2026 22:49:05 -0400https://pop.com.sg/when-does-a-rational-function-pass-through-the-horizontal-asymptote-ho.htmlhttps://pop.com.sg/when-does-a-rational-function-pass-through-the-horizontal-asymptote-ho.htmlSorry if this is a bit simple compared to everything here, but I can't really seem to find an answer. If I have $$f(x) = \frac{(x-2)(x-4)}{x(x-1)}$$ 1) When is the horizontal asymptote is crossed? ...Mon, 07 Sep 2026 22:46:28 -0400https://pop.com.sg/what-is-the-extraneous-solution-of-sqrt-a-a-6.htmlhttps://pop.com.sg/what-is-the-extraneous-solution-of-sqrt-a-a-6.htmlWhat is the extraneous solution of $$\sqrt a=a-6$$ The roots are $9$ and $4$. So I'm assuming that $4$ is the extraneous solution because when you plug it in to the equation you wind up with $2=-2$. ...Mon, 07 Sep 2026 22:37:01 -0400https://pop.com.sg/proving-directly-trace-matrix.htmlhttps://pop.com.sg/proving-directly-trace-matrix.htmlI am having difficulties in proving directly the following statement: I know that similar matrices have the same eigenvalues and that implies that their traces are the equal (if eigenvalues exist......Mon, 07 Sep 2026 22:33:29 -0400https://pop.com.sg/graph-theory-adjacency-vs-incident.htmlhttps://pop.com.sg/graph-theory-adjacency-vs-incident.htmlOkay, so I think if 2 vertices are adjacent to each other, they are incident to each other....or do I have it wrong? Is this just different terminology. I thought I was totally clear on this for my......Mon, 07 Sep 2026 22:25:24 -0400https://pop.com.sg/how-do-we-know-all-numbers-alternate-between-odd-and-even-numbers.htmlhttps://pop.com.sg/how-do-we-know-all-numbers-alternate-between-odd-and-even-numbers.htmlBasically, I tried proving that multiplying an odd and even number together gives you an even number to a friend of mine. This is what I said. Let's first take a random number $k$. It doesn't matt......Mon, 07 Sep 2026 22:22:40 -0400https://pop.com.sg/unkill-mettaton-neo-undertale-genocide.htmlhttps://pop.com.sg/unkill-mettaton-neo-undertale-genocide.htmlI killed mettaton neo when I hadn't gotten the required kills for Hotland... and I saved it how do I de kill her? I tried the time-travel thing and it did not work....Mon, 07 Sep 2026 22:21:09 -0400https://pop.com.sg/formula-for-a-very-steep-exponential-interpolation.htmlhttps://pop.com.sg/formula-for-a-very-steep-exponential-interpolation.htmlI have two points in the 2D space, e.g. point A is (3, 2) and point B is (30, 20) I want to get some points in between, aka, interpolating between A and B. But I don't want linear interpolation, I......Mon, 07 Sep 2026 22:12:18 -0400https://pop.com.sg/definite-integral-of-sine-squared-over-one-period.htmlhttps://pop.com.sg/definite-integral-of-sine-squared-over-one-period.htmlI'm working through a textbook on Fourier series ("The Intuitive Guide to Fourier Analysis and Spectral Estimation: with Matlab", by Langton and Levin), and I'm a bit stuck on the derivat......Mon, 07 Sep 2026 22:06:43 -0400https://pop.com.sg/do-specific-creatures-types-of-creatures-have-weaknesses-to-specific-t.htmlhttps://pop.com.sg/do-specific-creatures-types-of-creatures-have-weaknesses-to-specific-t.htmlDo specific creatures have weaknesses to specific types of attack, e.g. I have both a fire and shock based destruction spells. Would one work better on some creatures, and the other better on other......Mon, 07 Sep 2026 22:05:44 -0400https://pop.com.sg/calculate-radius-of-circle-that-by-given-length-of-square-that-is-insi.htmlhttps://pop.com.sg/calculate-radius-of-circle-that-by-given-length-of-square-that-is-insi.htmlin this picture a length of square edge is 8 cm. I want to calculate the radius of circle. i try to calculate it, but i don't know how. I calculate this:...Mon, 07 Sep 2026 22:01:40 -0400https://pop.com.sg/solve-the-equation-sqrt-cos-x-2-cos-x-1.htmlhttps://pop.com.sg/solve-the-equation-sqrt-cos-x-2-cos-x-1.htmlSolve this. Show work as detailed as possible. $$\sqrt{\cos x} = 2\cos x-1$$ My work: \begin{align*} 2\cos x & = \sqrt{\cos x}+1\\ \cos x & = \frac{\sqrt{\cos x}+1}{2}\\ x & = \c......Mon, 07 Sep 2026 21:59:21 -0400https://pop.com.sg/how-to-draw-greek-letters-on-paper-blackboard.htmlhttps://pop.com.sg/how-to-draw-greek-letters-on-paper-blackboard.htmlFor $\gamma$ (gamma), I've noticed people doing a sort of $\alpha$ (alpha) rotated by ninety degrees, which seems to be the standard on-paper-or-blackboard equivalent of $\gamma$. But for letters ......Mon, 07 Sep 2026 21:57:35 -0400https://pop.com.sg/in-dead-money-how-do-i-trap-father-elijah-in-the-vault.htmlhttps://pop.com.sg/in-dead-money-how-do-i-trap-father-elijah-in-the-vault.htmlThere's an achievement for trapping Father Elijah in the vault, but he has a knack for seeing right through stealth regardless of your preparations. Other guides suggest you should be able to just ......Mon, 07 Sep 2026 21:56:28 -0400https://pop.com.sg/why-normal-approximation-to-binomial-distribution-uses-np-5-as-a-condi.htmlhttps://pop.com.sg/why-normal-approximation-to-binomial-distribution-uses-np-5-as-a-condi.htmlI was reading about normal approximation to binomial distribution and I dunno how it works for cases when you say for example p is equal to 0.3 where p is probability of success. On most websites ......Mon, 07 Sep 2026 21:51:35 -0400https://pop.com.sg/is-there-a-way-to-calculate-lg-on-a-scientific-calculator.htmlhttps://pop.com.sg/is-there-a-way-to-calculate-lg-on-a-scientific-calculator.htmlTaking introduction to algorithms for computer science this semester and wanted to know if there is a way to calculate lg on scientific calculator? Thank you....Mon, 07 Sep 2026 21:50:37 -0400https://pop.com.sg/why-polynomial-functions-f-x-g-x-f-g-x.htmlhttps://pop.com.sg/why-polynomial-functions-f-x-g-x-f-g-x.htmlWhy polynomial functions f(x)+g(x) is the same notation as (f+g)(x)? I've seen the sum of polynomials as f(x)+g(x) before, but never seen a notation as with a operator in a prenthesis as (f+g)(x).......Mon, 07 Sep 2026 21:45:32 -0400https://pop.com.sg/distance-in-the-metric-induced-by-the-fisher-information-matrix.htmlhttps://pop.com.sg/distance-in-the-metric-induced-by-the-fisher-information-matrix.htmlFrom this (Section 2.1.2) paper I quote: "The Fisher information matrix defines a (Riemannian) metric on $\Theta$: the distance in this metric, between two very close values of $\theta$ is given b......Mon, 07 Sep 2026 21:44:41 -0400https://pop.com.sg/is-there-a-shortcut-for-raising-2-to-the-power-of-a-number-e-g-2-27.htmlhttps://pop.com.sg/is-there-a-shortcut-for-raising-2-to-the-power-of-a-number-e-g-2-27.htmlIn networking, when dealing with subnetting, you convert the net mask to binary and count the number of ones (for the example in the question there would be $27$ $1$'s) and to figure out how many s......Mon, 07 Sep 2026 21:32:16 -0400https://pop.com.sg/how-do-the-aiming-options-work-when-in-a-vehicle-in-grand-theft-auto-v.htmlhttps://pop.com.sg/how-do-the-aiming-options-work-when-in-a-vehicle-in-grand-theft-auto-v.htmlWhen in a vehicle, there are two aiming options - aim, and aim + fire. From testing, it seems like when "aim + fire" is chosen, holding down R1 on my PS4 controller automatically shoots - whereas w......Mon, 07 Sep 2026 21:25:01 -0400https://pop.com.sg/relations-between-optimization-versions-of-k-coloring-and-max-k-colora.htmlhttps://pop.com.sg/relations-between-optimization-versions-of-k-coloring-and-max-k-colora.htmlI am a tourist of Graph theory but I have this problem I am trying to solve, part of a research objective connected to quantum computing. I am trying to understand the relationship between: the ...Mon, 07 Sep 2026 21:23:26 -0400https://pop.com.sg/how-to-find-limits-involving-trigonometric-functions-as-x-to-0.htmlhttps://pop.com.sg/how-to-find-limits-involving-trigonometric-functions-as-x-to-0.htmlProblem: find the limit $lim _{x\rightarrow 0}\dfrac{\tan(3x)}{\sin(2x)}$ $lim _{x\rightarrow 0}\dfrac{(\sin(2x) + 3)}{(\cos(7x)-8)}$ Note I am able to solve the first one using l'Hopitals, but I ...Mon, 07 Sep 2026 21:16:38 -0400https://pop.com.sg/what-039-s-the-difference-between-a-roguelike-and-a-roguelite-game.htmlhttps://pop.com.sg/what-039-s-the-difference-between-a-roguelike-and-a-roguelite-game.htmlWhat exactly defines a Roguelike game and what is the difference between them and Roguelite games?...Mon, 07 Sep 2026 21:14:12 -0400https://pop.com.sg/is-my-answer-for-this-truth-table-boolean-expression-correct.htmlhttps://pop.com.sg/is-my-answer-for-this-truth-table-boolean-expression-correct.htmlI was given the following boolean diagram: I had to come out with the truth table and the simplified expression. I need help to check if my answers are correct below....Mon, 07 Sep 2026 21:11:21 -0400https://pop.com.sg/what-does-this-definition-of-permutation-mean.htmlhttps://pop.com.sg/what-does-this-definition-of-permutation-mean.htmlA simple question. They give the definition of permutation as "a one to one mapping of the set onto the set of positive integers $\{1, 2,3,4, \ldots n\}$." What does this definition exactly m......Mon, 07 Sep 2026 21:08:17 -0400https://pop.com.sg/which-type-of-followers-still-benefit-from-garrison-mission-xp.htmlhttps://pop.com.sg/which-type-of-followers-still-benefit-from-garrison-mission-xp.htmlMost of my followers are now level 100. I've currently got a mix of green, blue (rare), and purple (epic) followers. My question is: do they still benefit from Base XP or Bonus XP? I've tried answ......Mon, 07 Sep 2026 21:05:54 -0400https://pop.com.sg/why-are-my-npcs-disappearing-and-chest-loot-too.htmlhttps://pop.com.sg/why-are-my-npcs-disappearing-and-chest-loot-too.htmlI Received a Dryad after killing the Eye of Cthulhu, but it's now gone. There's still proof that I killed the Eye of Cthulu. The chair that made the Dryad's house is gone too! Also, my Goblin Tinke......Mon, 07 Sep 2026 21:05:09 -0400https://pop.com.sg/basis-of-a-subspace-meaning-of-the-term-039-unique-039.htmlhttps://pop.com.sg/basis-of-a-subspace-meaning-of-the-term-039-unique-039.htmlFollowing on from a previous question - Definition for Basis of a Subspace; it is often said that a basis of a subspace is a set of vectors that can be used to uniquely represent any vector in the ...Mon, 07 Sep 2026 20:38:38 -0400https://pop.com.sg/can-i-turn-off-my-ps4-with-my-vita-using-remote-play.htmlhttps://pop.com.sg/can-i-turn-off-my-ps4-with-my-vita-using-remote-play.htmlI've been using my Vita for Remote Play recently to the point that I haven't turned on my TV for days (go figure). However, despite how much I've been using it, while I know how to turn the PS4 on ......Mon, 07 Sep 2026 20:38:10 -0400https://pop.com.sg/help-setting-up-a-differential-equation-with-rate-in-rate-out.htmlhttps://pop.com.sg/help-setting-up-a-differential-equation-with-rate-in-rate-out.htmlI'm in a differential equations class and I am not getting it. It's been over a year since any calculus classes and I am struggling to set up the following problem. If some one can explain to me the ...Mon, 07 Sep 2026 20:36:48 -0400https://pop.com.sg/are-there-any-benefits-for-going-after-non-lethal-takedowns-in-cyberpu.htmlhttps://pop.com.sg/are-there-any-benefits-for-going-after-non-lethal-takedowns-in-cyberpu.htmlFor my first playthrough, I'm planning to play stealthily. I won't run and gun cause mayhem, but sneak around and take people down without alerting anyone. I've noticed when grabbing people, I have......Mon, 07 Sep 2026 20:36:42 -0400https://pop.com.sg/prove-that-a-horizontal-asymptote-can-never-be-crossed.htmlhttps://pop.com.sg/prove-that-a-horizontal-asymptote-can-never-be-crossed.htmlThis is a lot simpler of a problem than others posted here, but I was bored in class and decided to work out why a horizontal asymptote exists. Bear in mind that I am still fairly low on the “math ......Mon, 07 Sep 2026 20:34:40 -0400https://pop.com.sg/getting-delphine-esbern-039-unstuck-039.htmlhttps://pop.com.sg/getting-delphine-esbern-039-unstuck-039.htmlSo I've gotten myself into the documented bug with Delphine & Esbern getting stuck @ the Karthspire. I used the PC console code of setstage MQ203 280 as I COULDN'T get them to get passed the f......Mon, 07 Sep 2026 20:31:16 -0400https://pop.com.sg/pokestops-not-working.htmlhttps://pop.com.sg/pokestops-not-working.htmlPokestops aren't working for me. Every time I spin it, it just says "Try again later". Even when I wait for a few seconds to spin it, I get the same results. I don't have any connectivity problems,......Mon, 07 Sep 2026 20:28:34 -0400https://pop.com.sg/how-to-find-3-1000-bmod-7.htmlhttps://pop.com.sg/how-to-find-3-1000-bmod-7.htmlSorry this is a really simple problem but I couldnt figure it out. I'm trying to find the value of $3^{1000}\bmod 7$. I know the actual value is 4, but I used a calculator. How would I simplify this ...Mon, 07 Sep 2026 20:26:26 -0400https://pop.com.sg/example-of-a-covariance-matrix.htmlhttps://pop.com.sg/example-of-a-covariance-matrix.htmlCan someone provide an example of a covariance matrix for any set of data? For example, if given: 2 3 4 5 1 8 9 7 6 how would I take this 3x3 matrix and convert it to the covariance matrix? I s......Mon, 07 Sep 2026 20:23:25 -0400https://pop.com.sg/what-are-the-possible-mann-manor-gifts-spawn-places.htmlhttps://pop.com.sg/what-are-the-possible-mann-manor-gifts-spawn-places.htmlSo I've been playing on a couple 24/7 Mann Manor servers (I know!) to get some of the ghostchievements and scarechievements I missed from previous years. I got the pumpkin hat, the paper mask, the ...Mon, 07 Sep 2026 20:20:09 -0400https://pop.com.sg/integrate-sec-4x.htmlhttps://pop.com.sg/integrate-sec-4x.htmlHow do I go about doing this? I try doing it by parts, but it seems to work out wrong: $\eqalign{ & \int {\sec 4xdx} \cr & u = \sec 4x \cr & {{du} \over {dx}} = 4\sec 4x\tan......Mon, 07 Sep 2026 20:10:48 -0400https://pop.com.sg/examples-of-infinite-boolean-rings.htmlhttps://pop.com.sg/examples-of-infinite-boolean-rings.htmlI'm attempting to list examples of infinite boolean rings and I need some clarification. Firstly, is it possible to take an infinite direct product of the integers mod $2$ to get a boolean ring? ......Mon, 07 Sep 2026 20:01:11 -0400https://pop.com.sg/formula-for-sequence-0-0-0-0-1-0-0-0-0-1-ldots.htmlhttps://pop.com.sg/formula-for-sequence-0-0-0-0-1-0-0-0-0-1-ldots.htmlThere is a sequence with the values $0, 0, 0, 0, 1, 0, 0, 0, 0, 1, \ldots$ (basically there are always four 0s followed by a 1, then it repeats). Is there a function for this sequence? Here are two ...Mon, 07 Sep 2026 19:48:33 -0400https://pop.com.sg/domain-and-range-of-composite-functions.htmlhttps://pop.com.sg/domain-and-range-of-composite-functions.htmlWould I be correct in assuming that the domain of the composite function $(f∘g)(x)$ is the intersection of the range of $g$ and the domain of $x$? If not, how do I find the domain of a composite fu......Mon, 07 Sep 2026 19:40:20 -0400https://pop.com.sg/how-do-i-give-players-already-enchanted-tools-armour-weapons.htmlhttps://pop.com.sg/how-do-i-give-players-already-enchanted-tools-armour-weapons.htmlI'm making a map where I want players to be able to choose there kits/classes. The problem I'm having with it though is giving players already enchanted Tools/Armour/Weapons. I'm not sure if you c......Mon, 07 Sep 2026 19:39:06 -0400https://pop.com.sg/help-me-find-a-good-potions-calculator-closed.htmlhttps://pop.com.sg/help-me-find-a-good-potions-calculator-closed.htmlTrying to find a good potions calculator. I used to have one but lost it when my comp crashed, it had a list of the reagents and you input the number you had and it gave a readout of craftable poti......Mon, 07 Sep 2026 19:34:26 -0400https://pop.com.sg/proof-of-the-polynomial-remainder-theorem.htmlhttps://pop.com.sg/proof-of-the-polynomial-remainder-theorem.htmlMy textbook states that $f(x)$ can always be written as $$f(x) = q(x)g(x) + r(x)$$ but it doesn't provide any proof of this and I cannot seem to find it anywhere. And what does it actually say, t......Mon, 07 Sep 2026 19:18:20 -0400https://pop.com.sg/poisson-distribution-lambda-or-mu.htmlhttps://pop.com.sg/poisson-distribution-lambda-or-mu.htmlThe number of goals in a hockey game is modelled using a Poisson process with rate 1.5 per minute. (a) What is the distribution for the number of goals in the first quarter (12 minutes)? Write dow......Mon, 07 Sep 2026 19:11:59 -0400https://pop.com.sg/what-are-the-applications-of-the-mean-value-theorem.htmlhttps://pop.com.sg/what-are-the-applications-of-the-mean-value-theorem.htmlI'm going through my first year of teaching AP Calculus. One of the things I like to do is to impress upon my students why the topics I introduce are interesting and relevant to the big picture of ...Mon, 07 Sep 2026 19:07:10 -0400https://pop.com.sg/why-is-the-set-of-all-sets-a-paradox-in-layman-039-s-terms.htmlhttps://pop.com.sg/why-is-the-set-of-all-sets-a-paradox-in-layman-039-s-terms.htmlI've heard of some other paradoxes involving sets (i.e., "the set of all sets that do not contain themselves") and I understand how paradoxes arise from them. But this one I do not under......Mon, 07 Sep 2026 19:02:49 -0400https://pop.com.sg/how-can-i-find-out-what-missions-are-available-in-borderlands.htmlhttps://pop.com.sg/how-can-i-find-out-what-missions-are-available-in-borderlands.htmlAs I make my way through the main storyline, Claptrap will randomly appear in the top-right and say something like: Greetings, Person X has more jobs for you at Place Y. Or similar to that. ...Mon, 07 Sep 2026 18:59:53 -0400https://pop.com.sg/drawing-direction-fields-online.htmlhttps://pop.com.sg/drawing-direction-fields-online.htmlI am looking for a convenient and free online tool for plotting Direction Fields and Solution Curves of Ordinary Differential Equations. I tried the "Slope Field Plotter" on Geogebra; it worked tol......Mon, 07 Sep 2026 18:47:57 -0400https://pop.com.sg/multiplying-a-matrix-by-a-row-vector.htmlhttps://pop.com.sg/multiplying-a-matrix-by-a-row-vector.htmlIs multiplying a matrix by a row vector the same as multiplying it by a column vector? Or are there any differences between the two?...Mon, 07 Sep 2026 18:46:28 -0400https://pop.com.sg/how-do-you-jungle-in-smite.htmlhttps://pop.com.sg/how-do-you-jungle-in-smite.htmlI'm not very familiar with jungling in Smite. Assuming that you've picked an appropriate jungler, what does the jungler do during the course of the game? Some information I'm looking for is: Star......Mon, 07 Sep 2026 18:33:10 -0400https://pop.com.sg/solving-lyapunov-equation-matlab-has-different-solution-why.htmlhttps://pop.com.sg/solving-lyapunov-equation-matlab-has-different-solution-why.htmlI need to solve the lyapunov equation i.e. $A^TP + PA = -Q$. With $A = \begin{bmatrix} -2 & 1 \\ -1 & 0 \end{bmatrix}$ and $Q = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$. Hence.......Mon, 07 Sep 2026 18:23:01 -0400https://pop.com.sg/how-do-i-read-strawberry-facts.htmlhttps://pop.com.sg/how-do-i-read-strawberry-facts.htmlIn Fruit Ninja, to unlock one of the achievements, you have to "Read three strawberry facts". What does that mean? Somehow, I got that achievement; how did I do it?...Mon, 07 Sep 2026 18:10:35 -0400https://pop.com.sg/getting-the-sequence-1-0-1-0-1-0-1-0-ldots-without-trig.htmlhttps://pop.com.sg/getting-the-sequence-1-0-1-0-1-0-1-0-ldots-without-trig.htmlWhat's the simplest way to write a function that outputs the sequence: {1, 0, -1, 0, 1, 0, -1, 0, ...} ... without using any trig functions? I was able to come up with a very complex sequence ...Mon, 07 Sep 2026 17:58:55 -0400https://pop.com.sg/the-two-definitions-of-a-compact-set.htmlhttps://pop.com.sg/the-two-definitions-of-a-compact-set.htmlIn general, $A$ is compact if every open cover of $A$ contains a finite subcover of $A$. In $R$, $A$ is compact if it is closed and bounded. The second is very easy to understand because I can ea......Mon, 07 Sep 2026 17:51:45 -0400https://pop.com.sg/what-should-the-width-of-the-border-be-closed.htmlhttps://pop.com.sg/what-should-the-width-of-the-border-be-closed.htmlYou have made a rectangular stained glass window that is $2$ feet by $4$ feet. You have 7 square feet of clear glass to create a border of uniform width around the window. What should the width of ......Mon, 07 Sep 2026 17:49:44 -0400https://pop.com.sg/find-the-function-arcsin-cos-x.htmlhttps://pop.com.sg/find-the-function-arcsin-cos-x.htmlQuestion is from Spivak's Calculus 15-18. It asks to find the function $\arcsin(\cos x)$. Answer below: I have problem with the highlighted part. If that is true, then why is it our answer for ......Mon, 07 Sep 2026 17:48:29 -0400https://pop.com.sg/how-do-the-new-missions-work-in-cs-go.htmlhttps://pop.com.sg/how-do-the-new-missions-work-in-cs-go.htmlWith the latest Patch and Operation Breakthrough Valve has introduced Missions to the game. As far as I can see you get 2 objectives with 1 Mission. My question is, do the missions cycle over tim......Mon, 07 Sep 2026 17:45:15 -0400https://pop.com.sg/derivative-of-the-2-norm-of-a-multivariate-function.htmlhttps://pop.com.sg/derivative-of-the-2-norm-of-a-multivariate-function.htmlI've got a function $$g(x,y) = \| f(x,y) \|_2$$ and I want to calculate its derivatives with respect to $x$ and $y$. Using Mathematica, differentiating w.r.t. $x$ gives me $ f'_x(x,y) \text{Norm}'(......Mon, 07 Sep 2026 17:42:02 -0400https://pop.com.sg/eigenvalues-of-tensor-product-of-matrices-question-about-general-prope.htmlhttps://pop.com.sg/eigenvalues-of-tensor-product-of-matrices-question-about-general-prope.htmlI would like to refresh my mind on eigenvalues/eigenvector of tensor product of operator (for Quantum Mechanics purposes). Consider two hermitic matrices $A$ and $B$ living in Hilbert spaces of fi......Mon, 07 Sep 2026 17:32:04 -0400https://pop.com.sg/find-the-point-normal-form-for-this-line-passing-through-point-p.htmlhttps://pop.com.sg/find-the-point-normal-form-for-this-line-passing-through-point-p.htmlGive the point-normal form for the following 2D line with the following description: - Through P(-2,5) and perpendicular to the line x + 2y = 5 I know that the point-normal form is n * (x - p) = 0......Mon, 07 Sep 2026 17:12:18 -0400https://pop.com.sg/what-does-the-notation-0-1-mean.htmlhttps://pop.com.sg/what-does-the-notation-0-1-mean.htmlI am studying the procedure for bucket sort from Introduction To Algorithms by Cormen et al, which assumes that the input is generated by a random process that distributes the elements uniformly and ...Mon, 07 Sep 2026 17:03:22 -0400https://pop.com.sg/skyrim-potions-for-boosting-alchemy-skill.htmlhttps://pop.com.sg/skyrim-potions-for-boosting-alchemy-skill.htmlI'd like to know what ingredients (if any) will make a potion of fortify alchemy in skyrim...Mon, 07 Sep 2026 17:00:50 -0400https://pop.com.sg/how-to-befriend-a-dog.htmlhttps://pop.com.sg/how-to-befriend-a-dog.htmlA loading screen tip told me that by befriending a dog, it could show me some interesting things. How do I do that? If I shove myself into the dog for a while, hearts will show up, be it will stay ...Mon, 07 Sep 2026 17:00:32 -0400https://pop.com.sg/how-can-i-gain-curie-039-s-approval-quickly.htmlhttps://pop.com.sg/how-can-i-gain-curie-039-s-approval-quickly.htmlI went with Nick Valentine as companion for most of the time, but now that I completed his quest I switched to Curie. Valentine was easy to please, but I'm having a much harder time rising Curie's ...Mon, 07 Sep 2026 16:55:23 -0400https://pop.com.sg/how-do-you-apply-potion-effects-to-players.htmlhttps://pop.com.sg/how-do-you-apply-potion-effects-to-players.htmlI'm developing a minigame server. I just need to know what commands to use, via command block, to give players special effects infinitely such as: speed boost, regeneration, or jump boost. I know i......Mon, 07 Sep 2026 16:48:29 -0400https://pop.com.sg/does-rainbow-six-siege-lag-a-lot-if-you-play-on-windows-via-virtualbox.htmlhttps://pop.com.sg/does-rainbow-six-siege-lag-a-lot-if-you-play-on-windows-via-virtualbox.htmlI'm curious to know as I have a Mac and I want to play Rainbow Six Siege via VirtualBox but I don't want it to be a waste if it lags too much....Mon, 07 Sep 2026 16:46:10 -0400https://pop.com.sg/how-do-i-hook-up-my-gamecube-to-my-desktop.htmlhttps://pop.com.sg/how-do-i-hook-up-my-gamecube-to-my-desktop.htmlSo I bought an PC/LAPTOP VGA SVGA TO S-Video 3 RCA Composite AV TV Out Converter Adapter Cable to play my GameCube on my Monitor but I can figure out how to Switch it? This is where I got the Cable......Mon, 07 Sep 2026 16:41:45 -0400https://pop.com.sg/integral-of-e-x-3-x-2-1-3x-4-2x-3-2x.htmlhttps://pop.com.sg/integral-of-e-x-3-x-2-1-3x-4-2x-3-2x.htmlI understand that this looks exactly like a "Do my Homework" kinda question but trust me, I've spent hours(I won't go into detail as it's off topic). Note: I'm a High School student, our teacher gave ...Mon, 07 Sep 2026 16:41:39 -0400https://pop.com.sg/greatest-number-of-regions-we-can-get-when-dividing-with-lines-and-cir.htmlhttps://pop.com.sg/greatest-number-of-regions-we-can-get-when-dividing-with-lines-and-cir.htmlWhat is the greatest number of regions a plane can be divided into using $n$ straight lines? What about $n$ circles? Can you generalize this into 3-dimensional space, planes and spheres? For line......Mon, 07 Sep 2026 16:38:08 -0400https://pop.com.sg/how-do-i-reset-npcs-in-skyrim.htmlhttps://pop.com.sg/how-do-i-reset-npcs-in-skyrim.htmlI have been trying to play the Mage's College quest, but Mirabelle Ervine is frozen in place and can't go anywhere. I can still talk to her, but that's about all I can do. How can I reset her or re......Mon, 07 Sep 2026 16:23:56 -0400https://pop.com.sg/how-many-bit-strings-of-length-5-do-not-have-consecutive-1-039-s.htmlhttps://pop.com.sg/how-many-bit-strings-of-length-5-do-not-have-consecutive-1-039-s.htmlHow many bit strings of length 5 do not have consecutive 1's? I'm trying to think of a way to calculate how many ways we can arrange a string of length 5 starting with the first position (or index......Mon, 07 Sep 2026 16:05:51 -0400https://pop.com.sg/what-counters-ap-kog-039-maw-in-mid.htmlhttps://pop.com.sg/what-counters-ap-kog-039-maw-in-mid.htmlI played a few games over the weekend and I kept seeing a bunch of AP Kog'maw players and they were giving me a really hard time in mid. What are some solid counter picks or strategies I could use ...Mon, 07 Sep 2026 16:04:18 -0400https://pop.com.sg/how-is-the-damage-for-reverse-slash-calculated.htmlhttps://pop.com.sg/how-is-the-damage-for-reverse-slash-calculated.htmlI have a question regarding ESO skill reverse slash. In the skill description it says: "Gives up to 300% more damage against enemies under 50%". The thing is, how is that up to computed? Is it ran......Mon, 07 Sep 2026 16:02:37 -0400https://pop.com.sg/lim-sup-and-lim-inf-of-sequence-of-sets.htmlhttps://pop.com.sg/lim-sup-and-lim-inf-of-sequence-of-sets.htmlI was wondering if someone would be so kind to provide a very simple explanation of lim sup and lim inf of s sequence of sets. For a sequence of subsets $A_n$ of a set $X$, the $\limsup A_n= \bigc......Mon, 07 Sep 2026 15:59:48 -0400https://pop.com.sg/what-is-the-complexity-of-complex-matrix-multiplication-closed.htmlhttps://pop.com.sg/what-is-the-complexity-of-complex-matrix-multiplication-closed.htmlI want to calculate the complexity of an algorithm in MATLAB (not the time complexity), however, all the matrices are complex ones. I guess that the complexity of complex matrix multiplication is h......Mon, 07 Sep 2026 15:42:37 -0400https://pop.com.sg/why-particular-integral-gives-two-different-values-in-two-different-me.htmlhttps://pop.com.sg/why-particular-integral-gives-two-different-values-in-two-different-me.htmlI would like to find out the particular integral (P.I.) of the differential equation : $$(D^2-5D+6)y=e^{2x}$$ Result: P.I. of the D.E., $F(D)y=X$ is (i) $\dfrac{1}{F(D)}e^{ax}=\dfrac{1}{F(a)}e^{a......Mon, 07 Sep 2026 15:37:06 -0400https://pop.com.sg/lost-all-buddies-in-metal-gear-solid-v.htmlhttps://pop.com.sg/lost-all-buddies-in-metal-gear-solid-v.htmlI am going through all of the side ops in MGSV and on one of the ops eliminating a tank unit Quiet took a lot of fire and was extracted. Now I have no buddies at all available for missions. How do......Mon, 07 Sep 2026 15:35:22 -0400https://pop.com.sg/finding-coefficients-of-legendre-polynomials.htmlhttps://pop.com.sg/finding-coefficients-of-legendre-polynomials.htmlBy considering the 2-norm(least squares) approximation of $f(x)=e^x$ for $-1\le x\le 1$ by a polynomial of degree $N$ which is expanded into a series of Legendre polynomials $P_j(x):$ $$Q_N(x)=\su......Mon, 07 Sep 2026 15:34:39 -0400https://pop.com.sg/how-to-use-custom-names-and-lores-in-minecraft-1-14-2-duplicate.htmlhttps://pop.com.sg/how-to-use-custom-names-and-lores-in-minecraft-1-14-2-duplicate.htmlHow can I give myself an item with a custom name, and how can I search for a player holding an item with a certain name. This is what I tried: /give @p minecraft:acacia_button{display:{Name:"ieat",...Mon, 07 Sep 2026 15:25:10 -0400https://pop.com.sg/where-can-i-find-a-new-place-to-live.htmlhttps://pop.com.sg/where-can-i-find-a-new-place-to-live.htmlWhen I first, let's say arrived, in Fallen London, real estate opportunities were scarce for someone of my... standing. I certainly wasn't too choosy back then, but now that I feel a little more s......Mon, 07 Sep 2026 15:21:39 -0400https://pop.com.sg/solutions-of-sixth-order-polynomial-equations.htmlhttps://pop.com.sg/solutions-of-sixth-order-polynomial-equations.htmlDo you know a way to solve exactly a general sixth order polynomial equation: $x^{6}+a_{5}x^{5}+a_{4}x^{4}+a_{3}x^{3}+a_{2}x^{2}+a_{1}x+a_{0}=0$ ? According to this link, it is possible to solve ......Mon, 07 Sep 2026 15:11:34 -0400https://pop.com.sg/solution-verification-exercise-1-4-in-brezis-039-s-functional-analysis.htmlhttps://pop.com.sg/solution-verification-exercise-1-4-in-brezis-039-s-functional-analysis.htmlExercise 1.4 in Brezis's Functional Analysis, Sobolev Spaces and partial Differential Equations reads as follows: Let $E = c_0$ be the space of real sequences tending to $0$ with norm $||u|| = \......Mon, 07 Sep 2026 15:07:07 -0400https://pop.com.sg/what-does-r-rightarrow-r-means-in-functions.htmlhttps://pop.com.sg/what-does-r-rightarrow-r-means-in-functions.htmlI have a function. The function is: $$ f:R \rightarrow R $$ $$ f(x) = x^3$$ What does $R \rightarrow R$ means? I don't know what types of questions should I ask here. If it is not ok, the I will ...Mon, 07 Sep 2026 15:03:30 -0400https://pop.com.sg/what-is-the-purpose-of-those-friendly-big-plant-looking-creatures.htmlhttps://pop.com.sg/what-is-the-purpose-of-those-friendly-big-plant-looking-creatures.htmlNot sure how best to describe them. There is a big momma type one and 2-3 baby ones. They look like big fat plants and they have a creepy love towards me. If you hit them they say something like "o......Mon, 07 Sep 2026 15:02:50 -0400https://pop.com.sg/learning-arcsin-arccos-arctan-how-to.htmlhttps://pop.com.sg/learning-arcsin-arccos-arctan-how-to.htmlSorry for asking such question. I have a very basic understanding of $\arcsin, \arccos, \arctan$ functions. I do know how their graph looks like and not much more beyond that. Calculate: Which ...Mon, 07 Sep 2026 14:47:08 -0400https://pop.com.sg/is-it-possible-to-sell-stolen-items.htmlhttps://pop.com.sg/is-it-possible-to-sell-stolen-items.htmlI recently discovered the average shopkeeper is unwilling to buy stolen goods (how they know they are stolen, I do not know). Is there anyway for me to sell stolen items, without making use of the ...Mon, 07 Sep 2026 14:46:03 -0400https://pop.com.sg/evaluate-the-triple-integral-using-spherical-coordinates.htmlhttps://pop.com.sg/evaluate-the-triple-integral-using-spherical-coordinates.htmlUse spherical coordinates to evaluate the triple integral: $$\iiint_{E}{(x^2+y^2+z^2)dV}$$ Where E is the ball: $E=\left\{(x,y,z)\in \mathbb{R}^3 \mid x^2+y^2+z^2≤49\right\}$....Mon, 07 Sep 2026 14:45:22 -0400https://pop.com.sg/kayle-as-a-support-or-solo-top.htmlhttps://pop.com.sg/kayle-as-a-support-or-solo-top.htmlSo I've played League of Legends since season 1, and after the season ended, we got our Kayle+skin. Ever since than, I haven't seen her being played by anyone. Is there a reason behind that? I thin......Mon, 07 Sep 2026 14:31:39 -0400https://pop.com.sg/why-are-invertible-matrices-called-039-non-singular-039.htmlhttps://pop.com.sg/why-are-invertible-matrices-called-039-non-singular-039.htmlWhere in the history of linear algebra did we pick up on referring to invertible matrices as 'non-singular'? In fact, since the null space of an invertible matrix has a single vector an inverti......Mon, 07 Sep 2026 14:27:02 -0400https://pop.com.sg/is-there-a-game-called-sonic-the-next-level.htmlhttps://pop.com.sg/is-there-a-game-called-sonic-the-next-level.htmlI've been watching the docuseries "High Score" on Netflix, and in episode 4, the Sega episode, there are several clips that refer to something called "Sonic: The Next Level" and a ...Mon, 07 Sep 2026 14:24:02 -0400https://pop.com.sg/division-isn-039-t-associative.htmlhttps://pop.com.sg/division-isn-039-t-associative.htmlConsider the following fraction: $$\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://pop.com.sg/is-it-possible-to-get-the-horadric-cube-with-a-level-lower-than-70.htmlhttps://pop.com.sg/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://pop.com.sg/why-does-it-make-no-sense-to-define-addition-on-points-in-geometry.htmlhttps://pop.com.sg/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://pop.com.sg/is-it-possible-to-respec-all-skill-points-duplicate.htmlhttps://pop.com.sg/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://pop.com.sg/what-would-be-the-most-significant-way-to-farm-neural-sensors-in-warfr.htmlhttps://pop.com.sg/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://pop.com.sg/how-do-i-kill-the-crab-boss.htmlhttps://pop.com.sg/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://pop.com.sg/how-to-test-weapons-in-battlefield-3-without-affecting-accuracy-score.htmlhttps://pop.com.sg/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 -0400