https://pop.com.sgExplosive pop stories with broad entertainment appeal.en-usMon, 07 Sep 2026 06:44:59 -0400https://pop.com.sg/is-the-thrill-digger-minigame-deterministic.htmlhttps://pop.com.sg/is-the-thrill-digger-minigame-deterministic.htmlIn Skyward Sword, in the Edlin Volcano area near the Bokoblin tower, there is a cave where one can play the game Thrill Digger. My question is: can one predict the layout of the board based on: ...Mon, 07 Sep 2026 10:37:20 -0400https://pop.com.sg/derivative-of-natural-log-vs-base-10-log.htmlhttps://pop.com.sg/derivative-of-natural-log-vs-base-10-log.htmlConsider the logarithmic function with base $10.$ $$ y=\log{\left(x\right)} $$ wherein the derivative with respect to $x$ is: $$ f'\left(x\right)=\frac{1}{x} $$ Now consider the natural logarith......Mon, 07 Sep 2026 10:26:43 -0400https://pop.com.sg/database-of-fol-statements-and-proofs.htmlhttps://pop.com.sg/database-of-fol-statements-and-proofs.htmlIs there a database somewhere of simple FOL statements, with their proofs written out in a Hilbert-style deduction system, or perhaps a tool to take such statements and produce proofs? While I see ...Mon, 07 Sep 2026 10:21:37 -0400https://pop.com.sg/the-final-state-of-1000-light-bulbs-switched-on-off-by-1000-people-pas.htmlhttps://pop.com.sg/the-final-state-of-1000-light-bulbs-switched-on-off-by-1000-people-pas.htmlThere are 1000 light bulbs and 1000 tutors. All light bulbs are off. Tutor 1 goes flipping light bulb 1,2,3,4... tutor 2 then flips 2,4,6,8... tutor 3 then 3,6,9...etc until all 1000 tutors have ......Mon, 07 Sep 2026 10:18:54 -0400https://pop.com.sg/user-calvin-lin-mathematics-stack-exchange.htmlhttps://pop.com.sg/user-calvin-lin-mathematics-stack-exchange.htmlQ&A for people studying math at any level and professionals in related fields...Mon, 07 Sep 2026 10:17:57 -0400https://pop.com.sg/proving-gradient-of-a-function-is-always-perpendicular-to-the-contour-.htmlhttps://pop.com.sg/proving-gradient-of-a-function-is-always-perpendicular-to-the-contour-.htmlCan someone give an explanation of how such a proof would go, given a function example: $y = f(x)$...Mon, 07 Sep 2026 10:14:54 -0400https://pop.com.sg/what-039-s-the-point-of-a-kingdom-past.htmlhttps://pop.com.sg/what-039-s-the-point-of-a-kingdom-past.htmlIt seems to indicate that you should replicate the Kingdom, based on this image, but nothing seems to happen when you do. What's the point of this image?...Mon, 07 Sep 2026 10:14:03 -0400https://pop.com.sg/what-is-the-relation-between-production-meals-and-total-export-price.htmlhttps://pop.com.sg/what-is-the-relation-between-production-meals-and-total-export-price.htmlI'm playing Tropico 4 right now, but I'm pretty sure it's the same for all Tropico games. I've finished the normal campain, but I'm still wondering what these numbers are about. So let's take an e......Mon, 07 Sep 2026 10:05:07 -0400https://pop.com.sg/why-dominated-convergence-theorem-is-related-to-the-superiority-of-leb.htmlhttps://pop.com.sg/why-dominated-convergence-theorem-is-related-to-the-superiority-of-leb.htmlI read the following paragraph from wikipedia: In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which almost everywhere convergence of a sequence of ...Mon, 07 Sep 2026 09:59:19 -0400https://pop.com.sg/how-to-enable-steam-overlay-while-playing-dungeons-of-dredmor.htmlhttps://pop.com.sg/how-to-enable-steam-overlay-while-playing-dungeons-of-dredmor.htmlFor some reasons I cannot access to Steam overlay and other Steam features (F12->screenshot) while playing Dungeons of Dredmor. Do you know how to fix it? Just to be precise the in-game option in ......Mon, 07 Sep 2026 09:52:45 -0400https://pop.com.sg/for-numbers-divisible-by-three-why-is-the-sum-of-their-digits-able-to-.htmlhttps://pop.com.sg/for-numbers-divisible-by-three-why-is-the-sum-of-their-digits-able-to-.htmlWhen you add the digits of any number that is divisible by three, that sum of those digits also appears to be divisible by three (with no remainder). For example a number (which I randomly grab fr......Mon, 07 Sep 2026 09:48:20 -0400https://pop.com.sg/darboux-theorem.htmlhttps://pop.com.sg/darboux-theorem.htmlDarboux's Theorem states that" If $f$ is differentiable on $[a,b]$ and if $k$ is a number between $f^{\prime}(a)$ and $f^{\prime}(b)$, then there is at least one point $c\in (a,b)$ such that $f^{\p......Mon, 07 Sep 2026 09:27:24 -0400https://pop.com.sg/properties-of-dictionary-order-topology.htmlhttps://pop.com.sg/properties-of-dictionary-order-topology.htmlProperties of dictionary order topology Choose the correct option My attempt : According to Munkres the order topology on $\mathbb{R} \times \mathbb{R}$ has as basis the collection of all ......Mon, 07 Sep 2026 09:24:48 -0400https://pop.com.sg/getting-attributes-bonuses-5-5-5-in-elder-scrolls-oblivion.htmlhttps://pop.com.sg/getting-attributes-bonuses-5-5-5-in-elder-scrolls-oblivion.htmlI have just completed the recommended quests for the Mages Guild to get accepted into the Arcane University. Now, I think it's time to work on leveling up the mage class character that I have. I'm ...Mon, 07 Sep 2026 09:16:41 -0400https://pop.com.sg/how-to-prove-that-mathbb-z-2z-times-z-2z-is-not-cyclic.htmlhttps://pop.com.sg/how-to-prove-that-mathbb-z-2z-times-z-2z-is-not-cyclic.htmlHow to prove that $\mathbb{Z/2Z\times Z/2Z}$ is not cyclic? Here is what I did, what is wrong with it if anything and is there a better way to prove it? A group $G$ is cyclic if $\exists\ a \in G$ ......Mon, 07 Sep 2026 08:44:47 -0400https://pop.com.sg/steam-purchase-issue.htmlhttps://pop.com.sg/steam-purchase-issue.htmlWhen you attempt to purchase Realm of the Mad God's "Beginner's Package", it lists the purchase as buying "2600 Gold". The package contains more than just gold, so what does this mean?...Mon, 07 Sep 2026 08:42:36 -0400https://pop.com.sg/finding-the-measure-of-an-angle-given-area-and-diameter.htmlhttps://pop.com.sg/finding-the-measure-of-an-angle-given-area-and-diameter.htmlAlright, so i've been trying to tackle this problem. The answer to this problem is 40 degrees (3). Now i'm trying to figure out how. I decided to start with finding the area of the whole circle wh......Mon, 07 Sep 2026 08:33:44 -0400https://pop.com.sg/how-do-i-set-a-kill-command-on-a-block.htmlhttps://pop.com.sg/how-do-i-set-a-kill-command-on-a-block.htmlYou can set a /kill command on a command block, I know that, but how do I do it? I am making a map, so please help!...Mon, 07 Sep 2026 08:28:24 -0400https://pop.com.sg/area-enclosed-between-3-curves.htmlhttps://pop.com.sg/area-enclosed-between-3-curves.htmlQuestion: What is the area of the region enclosed by the curves: $$2y = 4\sqrt{x},\quad y = 3,\quad \text{and} \quad 2y + 2x = 6. $$ I have tried calculate all the definite integrals but I am not ......Mon, 07 Sep 2026 08:16:18 -0400https://pop.com.sg/why-do-some-players-play-league-of-legends-in-window-mode.htmlhttps://pop.com.sg/why-do-some-players-play-league-of-legends-in-window-mode.htmlWhile watching this current LoL live world championship (Intel extreme masters), I noticed some players play in window mode. Why is that? What are the benefits of playing LoL in window mode?...Mon, 07 Sep 2026 08:07:51 -0400https://pop.com.sg/what-is-the-solution-of-a-2-b-2-closed.htmlhttps://pop.com.sg/what-is-the-solution-of-a-2-b-2-closed.htmlHow to solve $a^2=b^2$? Should I consider if the number is negative or positive?...Mon, 07 Sep 2026 08:02:27 -0400https://pop.com.sg/when-does-order-of-partial-derivatives-matter.htmlhttps://pop.com.sg/when-does-order-of-partial-derivatives-matter.htmlI've taken multivariate calculus and am wondering if I can see a specific function where the order of taking the partial derivative matters. I've been told that there are some exceptions where $ \d......Mon, 07 Sep 2026 08:01:33 -0400https://pop.com.sg/when-do-people-use-nydus-worm.htmlhttps://pop.com.sg/when-do-people-use-nydus-worm.htmlI'm not a Zerg player, but I've never seen Nydus worm used against me either. When do people actually use it?...Mon, 07 Sep 2026 08:00:11 -0400https://pop.com.sg/using-dimensional-analysis-to-convert-oz-to-l.htmlhttps://pop.com.sg/using-dimensional-analysis-to-convert-oz-to-l.htmlI'm having trouble deciding whether this table has enough information to convert between fluid $oz$ and $L$. I'm inclined to say it doesn't, but my homework problem has me considering otherwise....Mon, 07 Sep 2026 07:31:00 -0400https://pop.com.sg/recommended-free-software-to-draw-both-histogram-and-graph-paper-grid.htmlhttps://pop.com.sg/recommended-free-software-to-draw-both-histogram-and-graph-paper-grid.htmlIs there any software for drawing both the graph (histogram, ogive or other statistical graphs) and the graph paper grid behind it? I want to draw graph that look like image below. Thanks!...Mon, 07 Sep 2026 07:29:28 -0400https://pop.com.sg/what-is-the-value-of-6.htmlhttps://pop.com.sg/what-is-the-value-of-6.htmlI know this is not absolute value, so what do the parentheses mean? If it was absolute value, it would have lines so I can rule that out. And I guess I should mention, the question I was asked is ......Mon, 07 Sep 2026 07:27:12 -0400https://pop.com.sg/even-function-divided-by-odd-function-is-an-odd-function-proof.htmlhttps://pop.com.sg/even-function-divided-by-odd-function-is-an-odd-function-proof.htmlAn Even function divided by Odd function is an Odd function,that is a fact. However is there a means to prove this?...Mon, 07 Sep 2026 07:17:44 -0400https://pop.com.sg/moving-minecart-once-hopper-has-items-and-then-becomes-empty.htmlhttps://pop.com.sg/moving-minecart-once-hopper-has-items-and-then-becomes-empty.htmlHere's a rough outline of what I want Empty cart stays still under an empty hopper Hopper gets x items in it, the cart stays still Once the hopper has emptied all its items into the cart, the c......Mon, 07 Sep 2026 07:15:53 -0400https://pop.com.sg/why-was-the-inverse-sine-ratio-used-and-not-sine.htmlhttps://pop.com.sg/why-was-the-inverse-sine-ratio-used-and-not-sine.htmlFrom what point should I look when determining what trig ratio to use? If they can use hypotenuse over opposite, they can also use opposite over hypotenuse. Were should I look to determine the corr......Mon, 07 Sep 2026 07:11:40 -0400https://pop.com.sg/how-many-diamonds-can-a-diamond-ore-drop-in-minecraft.htmlhttps://pop.com.sg/how-many-diamonds-can-a-diamond-ore-drop-in-minecraft.htmlMy friends and I are having an argument on how many diamonds a Diamond Ore can drop (on avg. or maximum) without any fortune levels on a pickaxe. My friend says there will always drop only one, but......Mon, 07 Sep 2026 07:09:00 -0400https://pop.com.sg/why-is-there-no-product-quotient-rule-for-integration.htmlhttps://pop.com.sg/why-is-there-no-product-quotient-rule-for-integration.htmlSo it's known that there's no product rule and quotient rule for integration. But is there a reason why they don't exist, and the rules exist for differentiation?...Mon, 07 Sep 2026 07:07:36 -0400https://pop.com.sg/if-i-buy-a-ubisoft-game-on-steam-can-i-play-the-game-through-uplay-clo.htmlhttps://pop.com.sg/if-i-buy-a-ubisoft-game-on-steam-can-i-play-the-game-through-uplay-clo.htmlI just bought Assassin's Creed Unity on Steam, but the place I was playing can't install the game on Steam but the game is already installed in Uplay, can I play the game from Uplay instead of from......Mon, 07 Sep 2026 07:05:42 -0400https://pop.com.sg/which-diy-recipes-can-you-self-learn.htmlhttps://pop.com.sg/which-diy-recipes-can-you-self-learn.htmlAn overwhelmingly vast majority of DIY recipes in the game can be found by buying them from Nook's Cranny, finding them in the balloon presents or beach bottles, or getting them from crafting villa......Mon, 07 Sep 2026 06:57:38 -0400https://pop.com.sg/is-it-possible-to-switch-sides-in-ingress.htmlhttps://pop.com.sg/is-it-possible-to-switch-sides-in-ingress.htmlI chose to play as Enlightened, but it appears that nearly all of the portals in a nearby city are already controlled by Enlightened. In order to get experience I need to hack enemy portals, not fr......Mon, 07 Sep 2026 06:49:47 -0400https://pop.com.sg/an-extension-of-the-four-4-039-s-game.htmlhttps://pop.com.sg/an-extension-of-the-four-4-039-s-game.htmlWhen I was in lower school I remember playing the Four $4$'s game and we got to around $10$. For those of you who don't know the Four $4$'s game is one where you have to use four $4$'s and you have......Mon, 07 Sep 2026 06:46:17 -0400https://pop.com.sg/what-is-a-good-estimate-of-total-play-time-for-zelda-skyward-sword-dup.htmlhttps://pop.com.sg/what-is-a-good-estimate-of-total-play-time-for-zelda-skyward-sword-dup.htmlI want to complete Skyward Sword before Christmas, I'm trying to get a good grasp on how much time I need to finish it off. At the very least, I want to beat the game, but I tend to get most of the......Mon, 07 Sep 2026 06:45:39 -0400https://pop.com.sg/represent-f-x-1-x-as-a-power-series-around-x-1.htmlhttps://pop.com.sg/represent-f-x-1-x-as-a-power-series-around-x-1.htmlAs stated on the title, my question is: (a) represent the function $ f(x) = 1/x $ as a power series around $ x = 1 $. (b) represent the function $ f(x) = \ln (x) $ as a power series around $ x = 1 ......Mon, 07 Sep 2026 06:42:56 -0400https://pop.com.sg/stole-the-temptress-how-can-i-upgrade-it.htmlhttps://pop.com.sg/stole-the-temptress-how-can-i-upgrade-it.htmlI just stole the Temptress, looks like a cross between a Porsche and a Lamborghini I think. This is the car I would like to keep with as much damage resistance I can buy. I am trying to upgrade it. I ...Mon, 07 Sep 2026 06:42:07 -0400https://pop.com.sg/how-long-does-original-game-boy-battery-backed-memory-last.htmlhttps://pop.com.sg/how-long-does-original-game-boy-battery-backed-memory-last.htmlI have a Nintendo Game Boy Pocket (which plays original monochrome Game Boy games and is probably not capable of playing Game Boy Advance or similar "advanced" cartridges.) At any rate it is the or......Mon, 07 Sep 2026 06:41:47 -0400https://pop.com.sg/what-specific-bonus-loyalty-powers-are-available.htmlhttps://pop.com.sg/what-specific-bonus-loyalty-powers-are-available.htmlI know that the concept of Bonus Powers earned from loyal squadmates to enhance Shepards abilities has been retained. But what I can't find any information on is what specific powers are availiable......Mon, 07 Sep 2026 06:38:30 -0400https://pop.com.sg/an-introduction-to-tensors.htmlhttps://pop.com.sg/an-introduction-to-tensors.htmlAs a physics student, I've come across mathematical objects called tensors in several different contexts. Perhaps confusingly, I've also been given both the mathematician's and physicist's definiti......Mon, 07 Sep 2026 06:37:42 -0400https://pop.com.sg/can-the-value-of-9-be-found-duplicate.htmlhttps://pop.com.sg/can-the-value-of-9-be-found-duplicate.htmlI saw this question on an fb page and I couldn't solve it. Question: What is the value of $(-9!)$? a)$362800$ b)$-362800$ c) Can not be calculated The first options seems to be incorrect,which ...Mon, 07 Sep 2026 06:37:19 -0400https://pop.com.sg/what-do-you-call-numbers-such-as-100-200-500-1000-10000-50000-as-oppos.htmlhttps://pop.com.sg/what-do-you-call-numbers-such-as-100-200-500-1000-10000-50000-as-oppos.htmlThere are different categories of numbers that we use every day. Integers that written in decimal notation have $1, 2$ or $5$ as the leading figure, followed by none, one or more zeros. These are ......Mon, 07 Sep 2026 06:34:31 -0400https://pop.com.sg/permutations-with-forbidden-positions-sit-n-students-in-a-row.htmlhttps://pop.com.sg/permutations-with-forbidden-positions-sit-n-students-in-a-row.htmlSuppose we have $N$ students $(N>20)$ that should be seated in a row. ($1-n$ seats) $1.$ In how many ways can we arrange such that student number $2$ won't sit on chair number $1,3$ or $7......Mon, 07 Sep 2026 06:31:54 -0400https://pop.com.sg/how-can-you-give-a-player-a-speed-boost-when-they-are-sprinting-in-min.htmlhttps://pop.com.sg/how-can-you-give-a-player-a-speed-boost-when-they-are-sprinting-in-min.htmlI'm trying to make a vanilla KitPvP server, and I want to make a kit that gives you normal walking speed, but when you are sprinting, you have a speed boost. Is that possible? If so, then how?...Mon, 07 Sep 2026 06:30:28 -0400https://pop.com.sg/where-can-i-find-a-large-number-of-fish.htmlhttps://pop.com.sg/where-can-i-find-a-large-number-of-fish.htmlNearly every crafting/carry capacity upgrade needs fish bones/skin for the final, end-game items. I want to stop carrying animal bits as soon as possible, since my inventory is full of stuff I may ......Mon, 07 Sep 2026 06:29:04 -0400https://pop.com.sg/cdf-of-pareto-distribution.htmlhttps://pop.com.sg/cdf-of-pareto-distribution.htmlI want to compute the CDF of a Pareto distribution In particular, I have a Pareto distribution with p.d.f. $$f(x) = \lambda x^{-(\lambda + 1)},$$ and I want to find the CDF of $f$. When I perform ...Mon, 07 Sep 2026 06:24:58 -0400https://pop.com.sg/radians-negative-and-positive-values.htmlhttps://pop.com.sg/radians-negative-and-positive-values.htmlRecently I have been reading books on DSP where I came across Polar co-ordinates. I understand that on Polar graph (4 quadrants) we have $0, \frac{\pi}{2}, \pi, \frac{3}{2\pi}$ and $2 \pi$ radians ......Mon, 07 Sep 2026 06:23:31 -0400https://pop.com.sg/parametric-equation-of-a-circle-using-a-line.htmlhttps://pop.com.sg/parametric-equation-of-a-circle-using-a-line.htmlConsider the unit circle $$ x^2+y^2=1. $$ How can I parametrize it using the line $y=m(x+1)$, where $m$ is its slope?...Mon, 07 Sep 2026 06:08:08 -0400https://pop.com.sg/number-of-occurrences-in-contiguous-subarrays.htmlhttps://pop.com.sg/number-of-occurrences-in-contiguous-subarrays.htmlHow to count the number of occurrences of each element in all contiguous subarrays? For an array $[1,2,3]$, the contiguous subarrays are: $[1]$, $[2]$, $[3]$ $[1,2]$, $[2,3]$ $[1,2,3]$ $1$ occu......Mon, 07 Sep 2026 06:07:51 -0400https://pop.com.sg/what-are-the-domain-s-of-self-inverse-functions.htmlhttps://pop.com.sg/what-are-the-domain-s-of-self-inverse-functions.htmlA self inverse function is a function $f$, such that $y=f(x)$, with the special property that $ff(x)=x$, or written another way, $f(x) = f^-1(x)$ Example: Imagine there's a function $f$, such that......Mon, 07 Sep 2026 06:06:25 -0400https://pop.com.sg/give-a-serious-explanation-of-the-difference-between-an-equation-and-a.htmlhttps://pop.com.sg/give-a-serious-explanation-of-the-difference-between-an-equation-and-a.htmlWhat's the difference between an equation and a function? I mean, I am not seeking for a high school-like answer like "an equation has an equals sign". I want to know what is the fundamental differ......Mon, 07 Sep 2026 06:03:27 -0400https://pop.com.sg/what-do-you-get-for-tsanna-039-s-sacrificial-offering-in-chapter-7.htmlhttps://pop.com.sg/what-do-you-get-for-tsanna-039-s-sacrificial-offering-in-chapter-7.htmlIn Chapter 7 - Tsanna offers to sacrifice Evindra to give you the blessings of Lamashtu. If you do it, what benefit do you see for the final battle?...Mon, 07 Sep 2026 06:01:33 -0400https://pop.com.sg/infinite-sum-and-partial-sum-not-equal-in-wolframalpha.htmlhttps://pop.com.sg/infinite-sum-and-partial-sum-not-equal-in-wolframalpha.html$$\sum_{n=0}^{\infty} |(-0.8)^n \theta(n)-(-0.8)^{n-1} \theta(n-1)|$$ $\theta(n) = 1$ for $n \geq 0$ and 0 otherwise. My attempt to calculate this summation numerically with Python yielded 10. To ......Mon, 07 Sep 2026 05:57:56 -0400https://pop.com.sg/how-do-i-use-the-undermounted-shotgun-attachment-for-assault-rifles.htmlhttps://pop.com.sg/how-do-i-use-the-undermounted-shotgun-attachment-for-assault-rifles.htmlIn call of duty: modern warfare 3 (PC version) when playing multiplayer. You can select at weapon level 20 the shotgun attachment for the assault rifle. How do you fire it? Does it happen automati......Mon, 07 Sep 2026 05:56:05 -0400https://pop.com.sg/is-it-worth-it-to-upgrade-the-clan-castle.htmlhttps://pop.com.sg/is-it-worth-it-to-upgrade-the-clan-castle.htmlI was wondering if the clan castle building is worth the resources to upgrade it. I rarely attack getting all my resources from farming and use all them for upgrading defenses. I'm questioning th......Mon, 07 Sep 2026 05:53:21 -0400https://pop.com.sg/mega-stone-of-chosen-starter-pokemon-buyable.htmlhttps://pop.com.sg/mega-stone-of-chosen-starter-pokemon-buyable.htmlIf I am choosing Charmander as my starter, will I be able to buy the Charizardite Mega Stone again? So I could buy another one and trade it to someone else. Edit: I just found this site and it sa......Mon, 07 Sep 2026 05:49:33 -0400https://pop.com.sg/my-world-keeps-not-responding-correctly-how-do-i-fix-that.htmlhttps://pop.com.sg/my-world-keeps-not-responding-correctly-how-do-i-fix-that.htmlI was using a lan server on my favorite world and when i saved and exited the world everything worked fine. Then later i tried to enter the world and it glitched out a bit at the load screen and wh......Mon, 07 Sep 2026 05:45:41 -0400https://pop.com.sg/find-max-vertical-distance.htmlhttps://pop.com.sg/find-max-vertical-distance.htmlWhat is the maximum vertical distance between the line $y = x + 20$ and the parabola $y = x^2$ for $−4 ≤ x ≤ 5?$ What steps do I take to solve this? Do I have to use the distance formula and wh......Mon, 07 Sep 2026 05:37:02 -0400https://pop.com.sg/quote-from-mathematician-poet.htmlhttps://pop.com.sg/quote-from-mathematician-poet.htmlI read once a quote by a mathematician (or scientist) who was also a poet and it was something similar to: As a mathematician I try to make complicated things obvious, as a poet I try to make ob......Mon, 07 Sep 2026 05:23:40 -0400https://pop.com.sg/when-to-play-the-old-hunters-during-the-first-run-or-ng.htmlhttps://pop.com.sg/when-to-play-the-old-hunters-during-the-first-run-or-ng.htmlI'm doing my first Bloodborne run. I beat the boss of Byrgenwerth. Currently I have the option of playing the new DLC, The Old Hunters. If I waited until I finish my first run, it means I have to......Mon, 07 Sep 2026 05:21:14 -0400https://pop.com.sg/do-i-need-to-play-the-previous-games.htmlhttps://pop.com.sg/do-i-need-to-play-the-previous-games.htmlDarksiders II is out for free on XboxLive. Do I need to play Darksiders to understand whats going on? Or is the game completely different to the first?...Mon, 07 Sep 2026 05:14:34 -0400https://pop.com.sg/quick-way-of-selling-at-the-trading-post.htmlhttps://pop.com.sg/quick-way-of-selling-at-the-trading-post.htmlIs there a way to quickly sell goods at the trading post in GW2? I know there is the sell at trading post option by right clicking the desired item but that loads up the trading post every time and......Mon, 07 Sep 2026 04:59:15 -0400https://pop.com.sg/what-039-s-a-good-trophy-army-for-a-town-hall-8-closed.htmlhttps://pop.com.sg/what-039-s-a-good-trophy-army-for-a-town-hall-8-closed.htmlI've maxed out my troops for town hall 8 and I'm trying to do a big push, any suggestions?...Mon, 07 Sep 2026 04:56:49 -0400https://pop.com.sg/does-walking-fast-prevent-eggs-hatching.htmlhttps://pop.com.sg/does-walking-fast-prevent-eggs-hatching.htmlI have a couple of eggs that I've picked up from some Pokestops (I'm lucky enough to live above one). I walk a lot. I get to work through a 2 mile walk / train journey every day, so I should be p......Mon, 07 Sep 2026 04:55:22 -0400https://pop.com.sg/elementary-proof-of-multiplicative-property-of-determinant.htmlhttps://pop.com.sg/elementary-proof-of-multiplicative-property-of-determinant.htmlWhy LU decomposition is not used to give elementary proof of $\det (AB) = \det (A) \det (B) $ for square matrices? It seems for any square matrix $ A $, $ A = PLU$ P is permutation matrix, L lo......Mon, 07 Sep 2026 04:45:02 -0400https://pop.com.sg/tao-real-analysis-question-on-function-definition-should-it-be-an-axio.htmlhttps://pop.com.sg/tao-real-analysis-question-on-function-definition-should-it-be-an-axio.htmlIn Terence Tao's book "Analysis 1", in definition 3.3.1 (function definition), he says Let $X, Y$ be sets, and let $P(x, y)$ be a property pertaining to an object $x \in X$ and an object......Mon, 07 Sep 2026 04:18:17 -0400https://pop.com.sg/calculate-the-norm-of-a-polynomial-knowing-inner-product.htmlhttps://pop.com.sg/calculate-the-norm-of-a-polynomial-knowing-inner-product.htmlThe polynomial $p(x) = 3 - 2x$ is a polynomial in an inner product space with the inner product defined as $$ \langle p, q \rangle = \int_0^1 p(x)q(x) \, dx$$ on the interval $[0, 1]$ in the vec......Mon, 07 Sep 2026 03:52:23 -0400https://pop.com.sg/what-is-the-frobenius-map-really.htmlhttps://pop.com.sg/what-is-the-frobenius-map-really.htmlI know what the frobenius map is the naive sense, just the $p$th power map on an $\mathbb{F}_p$ algebra, and that this can be upgraded somewhat to the generator of the monoid of natural transformat......Mon, 07 Sep 2026 03:51:28 -0400https://pop.com.sg/how-do-you-get-back-from-z8n-tp.htmlhttps://pop.com.sg/how-do-you-get-back-from-z8n-tp.htmlI can get TO the CL4PTP unit in Tycho's Ribs for it's quest but when I try to use the jumppad to get back, it always tosses me into the rotating spire in the middle and instakills me. I have tried......Mon, 07 Sep 2026 03:51:25 -0400https://pop.com.sg/where-are-the-fairy-fountains.htmlhttps://pop.com.sg/where-are-the-fairy-fountains.htmlI am playing Ocarina of Time on the 3DS, and I vaguely recall there being a fairy fountain somewhat close to each dungeon/temple. Is that true? Where are the fairy fountains?...Mon, 07 Sep 2026 03:47:06 -0400https://pop.com.sg/definite-integration-having-d-dx-operator-inside-the-integral-sign-clo.htmlhttps://pop.com.sg/definite-integration-having-d-dx-operator-inside-the-integral-sign-clo.html$$\int_{-1}^1 \frac{d}{dx}\ \frac{1}{1 + 2^{1/x}}\ dx$$ How to approach this integral ? Should I differentiate the expression and then integrate ? I tried that but couldn't proceed Thank you....Mon, 07 Sep 2026 03:40:36 -0400https://pop.com.sg/every-superperfect-number-except-2-is-a-square-number.htmlhttps://pop.com.sg/every-superperfect-number-except-2-is-a-square-number.htmlI recently read about superperfect numbers: $σ^2(n) = 2n$, where $σ(n)$ is the divisor function. I saw that the first few numbers were: $2, 4, 16, 64, 4096, 65536, 262144$, which are all square-nu......Mon, 07 Sep 2026 03:30:00 -0400https://pop.com.sg/what-are-the-differences-in-ingress-portal-shield-types.htmlhttps://pop.com.sg/what-are-the-differences-in-ingress-portal-shield-types.htmlI have collected a few different types of shields, with different colours and of differing rarity. I assume the rarer shield types are more powerful in some way but I can't find any information o......Mon, 07 Sep 2026 03:26:50 -0400https://pop.com.sg/simplify-abc-a-039-bc-ab-039-c-a-039-b-039-c-039-to-logic-gates.htmlhttps://pop.com.sg/simplify-abc-a-039-bc-ab-039-c-a-039-b-039-c-039-to-logic-gates.htmlI've simplified $ABC+A'BC+AB'C+A'B'C'$ to $BC+AC+A'B'C'$. However, I want to go further to logic gates for which ICs are readily available. I would like to use at most three such ICs....Mon, 07 Sep 2026 03:20:18 -0400https://pop.com.sg/can-rotations-in-4d-be-given-an-explicit-matrix-form.htmlhttps://pop.com.sg/can-rotations-in-4d-be-given-an-explicit-matrix-form.htmlRotation in 2D by an angle $t$ can be performed using $$R=\begin{pmatrix}\cos(t) &-\sin(t) \\ \sin(t) & \cos(t)\end{pmatrix}$$ matrix. But, if I want to rotate a point or vector in 4D, is t......Mon, 07 Sep 2026 03:00:02 -0400https://pop.com.sg/is-it-possible-to-split-a-division-problem-into-parts-like-in-multipli.htmlhttps://pop.com.sg/is-it-possible-to-split-a-division-problem-into-parts-like-in-multipli.htmlIn multiplication we can mentally split a problem that is too big into multiple problems. For example: 26 * 40 = (20 * 40) + (6 * 40) = 800 + 240 = 1040 This is a very quick way to multiply other......Mon, 07 Sep 2026 02:56:47 -0400https://pop.com.sg/i-need-help-finding-the-mean-radius-of-a-cylinder.htmlhttps://pop.com.sg/i-need-help-finding-the-mean-radius-of-a-cylinder.htmlThe question is: What is the mean radius $\overline{r}$ from the midpoint of a cylinder of radius $a$ and height $h$ to its boundary surface? Evaluate $\overline{r}$ for $a = h/2 = 10~\mathrm{cm}$. ...Mon, 07 Sep 2026 02:51:56 -0400https://pop.com.sg/what-cosmetic-items-can-you-get-for-free.htmlhttps://pop.com.sg/what-cosmetic-items-can-you-get-for-free.htmlI recently completed a quest, The Death of Chivalry, and unlocked the cosmetic armors "Dulcin Armour" and "Templar Armour", which got me to wondering... What other cosmetic items can be unlocked th......Mon, 07 Sep 2026 02:49:16 -0400https://pop.com.sg/questions-tagged-group-theory.htmlhttps://pop.com.sg/questions-tagged-group-theory.htmlQ&A for people studying math at any level and professionals in related fields...Mon, 07 Sep 2026 02:41:16 -0400https://pop.com.sg/find-the-locus-of-centroid-of-right-angled-isoceles-triangle-for-the-f.htmlhttps://pop.com.sg/find-the-locus-of-centroid-of-right-angled-isoceles-triangle-for-the-f.htmlAn isosceles right angled triangle whose sides are $1, 1, \sqrt{2}$ lies entirely in the first quadrant with the ends of the hypotenuse on the coordinate axes. If it slides prove that the locus of......Mon, 07 Sep 2026 02:32:08 -0400https://pop.com.sg/about-math-notation-the-set-of-the-first-n-natural-numbers.htmlhttps://pop.com.sg/about-math-notation-the-set-of-the-first-n-natural-numbers.htmlIs it true that I can write the set of the the first $n$ natural numbers as $[ n] $? For example, $[10]= \{1,2,3,4,5,6,7,8,9,10 \}$. And in which math context this is used?...Mon, 07 Sep 2026 02:28:23 -0400https://pop.com.sg/3-2x-34-15-x-1-5-2x-0.htmlhttps://pop.com.sg/3-2x-34-15-x-1-5-2x-0.htmlI've never seen anything like this. Do somebody have a way to solve it? I've tried the basci exponential functions techniques but it does not work. Even substitution does not work... I'm really ...Mon, 07 Sep 2026 02:24:32 -0400https://pop.com.sg/conditions-for-a-quadratic-equation-to-be-positive.htmlhttps://pop.com.sg/conditions-for-a-quadratic-equation-to-be-positive.htmlI was solving a problem in physics when I encountered this problem. I wanted to find the condition where the value of a quadratic equation is positive. Suppose the function is : $f(x) = Ax^2+Bx+C$ ......Mon, 07 Sep 2026 02:23:05 -0400https://pop.com.sg/multiplying-3d-matrix.htmlhttps://pop.com.sg/multiplying-3d-matrix.htmlI was wondering if it is possible to multiply a 3D matrix (say a cube $n\times n\times n$) to a matrix of dimension $n\times 1$? If yes, then how. Maybe you can suggest some resources which I can r......Mon, 07 Sep 2026 02:14:05 -0400https://pop.com.sg/what-effects-do-the-sword-enchantments-have.htmlhttps://pop.com.sg/what-effects-do-the-sword-enchantments-have.htmlIn the forge, you can enchant the sword with different scrolls. What are the different enchantments I can get and what is the effect of each?...Mon, 07 Sep 2026 02:09:02 -0400https://pop.com.sg/is-there-a-difference-between-d-2x-and-dx-2.htmlhttps://pop.com.sg/is-there-a-difference-between-d-2x-and-dx-2.htmlI've just started reading through Calculus Made Easy by Silvanus Thompson and am trying to solidify the concept of differentials in my mind before progressing too far through the text. In Chapter 1 ...Mon, 07 Sep 2026 02:08:30 -0400https://pop.com.sg/question-regarding-horizontal-shrink-and-horizontal-stretch.htmlhttps://pop.com.sg/question-regarding-horizontal-shrink-and-horizontal-stretch.htmlI know the property of Horizontal shrink is $y=f(cx)$ where $ c>1$ and we need to divide the $x$ coordinates by the factor. Horizontal Stretch is $y=f(cx)$ where $0<c<1$ and we also need......Mon, 07 Sep 2026 02:07:09 -0400https://pop.com.sg/what-is-the-difference-between-frequency-and-density-in-a-histogram.htmlhttps://pop.com.sg/what-is-the-difference-between-frequency-and-density-in-a-histogram.htmlI know count is simply the amount of times the observations occur in a single bin width, but what is density?...Mon, 07 Sep 2026 02:02:28 -0400https://pop.com.sg/what-does-x2-mean-is-it-x-cdot-2-or-the-variable-x2.htmlhttps://pop.com.sg/what-does-x2-mean-is-it-x-cdot-2-or-the-variable-x2.htmlI'm working on a online mathematical learning environment. There is a mathematical editor where students can give their answers using a graphical interface: However, we have had the problem in the......Mon, 07 Sep 2026 01:59:07 -0400https://pop.com.sg/when-is-the-bipod-used-and-can-this-be-controlled.htmlhttps://pop.com.sg/when-is-the-bipod-used-and-can-this-be-controlled.htmlSometimes, either prone or crouched, my player will fold down the bipod, forcing the gun to move slightly and blinding my scope with leaves in the process. I've unlocked the bipod on a number of ...Mon, 07 Sep 2026 01:57:12 -0400https://pop.com.sg/finding-the-t-value-in-order-to-find-the-maximum-curvature-for-a-space.htmlhttps://pop.com.sg/finding-the-t-value-in-order-to-find-the-maximum-curvature-for-a-space.htmlEditted work. I am attempting to find the maximum curvature for the space curve mentioned below. space curve: $\vec{r}(t) = <3t, 4t, e^{2t}>$ From the space curve, I'm able to find that: ......Mon, 07 Sep 2026 01:44:10 -0400https://pop.com.sg/how-can-we-derive-the-interpolation-formula-for-higher-order.htmlhttps://pop.com.sg/how-can-we-derive-the-interpolation-formula-for-higher-order.htmlLet, $$y = mx + c \tag 1$$ is the equation of a straight line. Let, it passes through the point, $$(x_0, y_0)$$. So, from (1) we find, $$c = y_0 + mx_0 \tag 2$$ On the othet hand, from the form......Mon, 07 Sep 2026 01:40:40 -0400https://pop.com.sg/how-do-i-keep-my-animals-from-eating-my-people-food.htmlhttps://pop.com.sg/how-do-i-keep-my-animals-from-eating-my-people-food.htmlI've got a reasonably flourishing village with decent population and all the amenities. However, lately I've been having severe issues because my tame animals keep breaking into the food warehouse ......Mon, 07 Sep 2026 01:40:34 -0400https://pop.com.sg/partial-derivative-max-and-minimum.htmlhttps://pop.com.sg/partial-derivative-max-and-minimum.htmlI'm faced with the following problem, find the maximum and minimum value of the function: $$f(x,y)= x^{5}y^{7}e^{-2 x-2 y}$$ within the triangle with the corners (0,0), (3 ,0) and (0,3 ). My in......Mon, 07 Sep 2026 01:40:20 -0400https://pop.com.sg/calculate-which-of-the-four-fundamental-subspaces-a-vector-belongs-to.htmlhttps://pop.com.sg/calculate-which-of-the-four-fundamental-subspaces-a-vector-belongs-to.htmlAbove you have the question (b) and it's answer underneath. I am out of the blue as how they proved that it belongs to the nullspace of $A^{T}$?...Mon, 07 Sep 2026 01:35:49 -0400https://pop.com.sg/what-does-game-of-the-year-actually-mean.htmlhttps://pop.com.sg/what-does-game-of-the-year-actually-mean.htmlOften times, many games have an additional variant named "Game X: Game of the Year edition" or "Game X: GOTY edition". Within the same year, there are multiple games that seemingly have GOTY versio......Mon, 07 Sep 2026 01:35:33 -0400https://pop.com.sg/how-can-i-fix-pollution.htmlhttps://pop.com.sg/how-can-i-fix-pollution.htmlMy city has developed a bit of a ground pollution and a water pollution problem. In other similar games, you can mitigate the effects of pollution by planting trees, among other things. What can ......Mon, 07 Sep 2026 01:33:27 -0400https://pop.com.sg/frequency-of-the-golden-bowser-train.htmlhttps://pop.com.sg/frequency-of-the-golden-bowser-train.htmlDoes anyone happen to know how often you can go to the Golden Bowser Train? For those that don't yet know, it is a level with nothing but coins, and is a great way to bolster your extra lives....Mon, 07 Sep 2026 01:30:12 -0400https://pop.com.sg/is-there-a-way-to-get-ds-games-to-use-the-full-top-screen-on-a-3ds.htmlhttps://pop.com.sg/is-there-a-way-to-get-ds-games-to-use-the-full-top-screen-on-a-3ds.htmlI noticed that when I play DS games on my 3DS, the games don't fill the entirety of the top screen on the 3DS - there are black bars on either side of the image. Is there a way to get the game to ......Mon, 07 Sep 2026 01:23:03 -0400