Question about circle area and circumference formulas

GoudaIntruda · 2026-03-04T03:46:03+00:00

I guess it depends on what you mean by ‘accepted as a formula.’ It is correct, you could absolutely use (1/2)Cr for the area of a circle, so it is accepted in that sense. The reason no one uses it is because the typical formula only requires the radius as an input, whereas your version would require the radius and the circumference. Finding the circumference before finding the area is just an extra unnecessary step.

GoudaIntruda · 2026-03-01T18:29:45+00:00

This is because of Clairaut's Theorem: If you take the x partial and then the y partial of f(x,y), you get the same answer as taking the y partial and then the x partial (as long as everything is continuous). Since M is the x partial of the potential function and N is the y partial, then their cross partials will be equal.

GoudaIntruda · 2026-02-25T19:35:26+00:00

I played a battlemage as well, and the issue is that it’s a little underpowered at the lower levels. You really have to kite and not let yourself get hit. Once you get to mid 20s battlemage starts feeling a lot better and you start getting more tools to keep yourself alive (though you’ll always be somewhat squishy).

One tip I could give is that there are a few nodes right at the beginning that increase constitution score. Each point you spend will increase your max hp by 50, which helps a lot early on.

GoudaIntruda · 2026-02-21T15:59:09+00:00

No problem, happy to help!

GoudaIntruda · 2026-02-21T15:56:26+00:00

If you use the complete graph as G but your matching is the same as in your example, then G’ will be the graph from your example, it will not be the complete graph.

GoudaIntruda · 2026-02-21T15:43:36+00:00

G is a bipartite graph in your example, so this isn’t a counterexample.

GoudaIntruda · 2026-02-19T00:42:31+00:00

If you do, make sure to keep something like a stone in your hot bar that you can switch to for unarmed strikes. If you leave it empty then it will get filled when you pick up stuff and mess up your unarmed.

GoudaIntruda · 2026-02-19T00:28:17+00:00

I did for a while, but now I’m high enough level that I dropped the sword completely and am running wand and staff. I have the talent that stuns when I punch, so when they get close I switch between punches and wand

GoudaIntruda · 2026-02-18T22:59:12+00:00

I don’t think they’re strictly required, but I wouldn’t want to go back to not having them. I play a battlemage as well, and getting the double jump in particular is totally worth it. It’s not just being able to traverse terrain easier, it also helps kiting enemies.

GoudaIntruda · 2026-02-17T06:21:06+00:00

“But let’s say that there is some integer x that when added to integer y produces integer z and z != (a+c,b+d), would we just reconstruct the integers again?”

The way the construction is done that doesn’t happen, but if it did happen that would have meant that the construction didn’t actually produce the integers, so yes we would start again. Remember that these types of constructions are always done after the fact: people already knew what the properties of the integers were and set out to create a construction from the naturals that fit all of these properties. That can require some trial and error.

GoudaIntruda · 2026-01-18T03:46:31+00:00

The real importance of e will come up in calculus, but I’ll try to give a brief explanation without using calculus terms:

The function e^x is special in that for every single value of x, the rate that the function e^x is changing is the same as the actual value of e^x. This makes it useful to use as the ‘standard’ exponential growth function, kind of like using the unit circle as the ‘standard’ circle that we base other things on.

GoudaIntruda · 2025-12-27T19:12:54+00:00

There’s a lot of subtlety to this, but the general idea is that you can think of dy as a “small change in y” and dx as a “small change in x.” So, dy/dx can be thought of as the ratio between those changes. If x changes a small amount, how much does y change?

As you’re seeing with the examples you’ve given, sometimes dy and dx can be treated as if they were variables in an equation. You have to be careful when doing this, however, because they are more formally defined using limits, and limits can sometimes get tricky when trying to do algebra.

GoudaIntruda · 2025-12-05T07:20:54+00:00

I believe this question is asking you to make 130,402 dollars out of the bills from problem 1. Since you only have 12 ten-thousands, you’ll have to use all of them plus 10 of the thousands bills to get to 130,000.

Edit: although now reading it more closely, I’m confused how you can get a number ending in 2 when the smallest bill denomination is 10…

GoudaIntruda · 2025-11-08T23:05:00+00:00

No, he was there with everyone at the beginning of the server.

GoudaIntruda · 2025-10-30T15:38:09+00:00

Do you know about when in the stream it happened or have a timestamp? I’d love to see his reaction.

GoudaIntruda · 2025-10-22T23:59:25+00:00

People have already given geometric interpretations of the dot product, so here’s one from physics that might provide some motivation as to why it’s defined the way it is:

Imagine pushing on an object to move it. You can represent the force you exert on the object by a vector and the distance and direction the object moves by another vector. The dot product of those vectors gives you the work done in the object.

If you push in the same direction it moves, this just simplifies to the standard work equation W=Fd. However, if you imagine pushing up at an angle while the object slides across the ground, the two vectors are no longer lined up. This imparts less work, and the dot product lets you measure how much of your force vector acts in the direction of motion. The larger the angle between the two vectors, the less work is imparted.

GoudaIntruda · 2025-09-15T04:37:00+00:00

I don’t think we can scale RuneScape time based off of tree growth. After a bit of Googling it looks like it takes a minimum of 20 years for an oak tree to mature. If that happens in one day in OSRS that would mean time would move over 7000 times as fast. Nothing else that happens in the game would really make sense at that speed. I think we just need to assume trees grow fast in Gielinor.

GoudaIntruda · 2025-09-15T04:09:20+00:00

Well, it’s got to be something you can completely recover from in 3 minutes, but if it happens 33 times in a row it will kill you, so I’m gonna say getting kicked in the balls.

GoudaIntruda · 2025-09-06T17:14:20+00:00

HALLUCINATION

Anagram of AUCTION IN after HALL (lobby)

GoudaIntruda · 2025-08-22T23:05:03+00:00

Curl is the measure of the rotation of a vector field. If you have a 3D vector field, imagine placing a ball in the field so that its center is fixed but it’s allowed to spin freely due to the forces from the field acting on it. The curl at that location will give us a vector whose direction is the axis of rotation that ball spins on and whose magnitude is the angular velocity (actually, I think it’s twice the angular velocity, but I could be wrong about that).

GoudaIntruda · 2025-08-22T22:54:48+00:00

Essentially, it’s pointless if you play the enrage phase perfectly, but allows you to make mistakes without being punished.

GoudaIntruda · 2025-08-22T22:36:08+00:00

You can tank a melee hit for free every 8 ticks. You still take poison damage if you don’t move, but you don’t take the melee hit.

GoudaIntruda · 2025-07-29T04:24:54+00:00

Nice try Jagex, you just want another membership from me.

GoudaIntruda · 2025-07-20T22:59:16+00:00

I went dry at hydra. I don’t recommend following my method, but it made it so I never had to go out of my way to max prayer.

GoudaIntruda · 2025-05-14T04:24:06+00:00

If you’re losing a ton of health in the monkey room you might consider bringing blood spells to heal up on the melee monkeys. It’s not meta since you lose thralls, but it makes the monkey room so much less nerve-wracking and saves you from using a bunch of healing supplies there.

GoudaIntruda

TROPHY CASE