Posts from Quiz Auto-translated

I will try to figure it out further.

By the way, I'm a fan of "What? Where? When?" trivia game, and I can share some of the most interesting questions here...

I'm increasingly inclined to believe that I was once related to Tox.
Perhaps, in a past life, we were crocodiles from the same clutch.

I'll try to figure it out further.

I messed up, and you have to sort it out... That's the essence of teaching.

Uranium, bro, where have you been? =(
Without you, no one tested my setting in the Mafia game, and as a result, many questions arose among the players during the game...

I looked up the answer in Wolfram, but it refuses to provide a step-by-step solution, the jerk.

Oh, damn, I forgot to mention one thing about the third game. Let me add it now.

mg=integrate (h from 0 to H) ρg(H-h)*sin(α)*dS(h) ----------- (1) It seems like there should be a "-" sign here. Because the direction is upwards, not downwards, and because I need to adjust the answer. integrate (h from 0 to H) ρgHsin(α)*dS(h) = integrate (α from 0 to arcsin(H/R)) ρgH*2π(Rcos(α))sin(α)*Rdα = πρgHR^2 integrate (α from 0 to arcsin(H/R)) sin(2α)dα = -0.5 πρgHR^2 cos(2α) dα (α from 0 to arcsin(H/R)) = -0.5 πρgHR^2 (cos(2arcsin(H/R))-1) = -0.5 πρgHR^2 (1-2(H/R)^2-1) = πρgH^3 -------------- (2) integrate (h from 0 to H) ρghsin(α)*dS(h) = integrate (α from 0 to arcsin(H/R)) ρgRsin(α)sin(α)*2π(Rcos(α))*Rdα = integrate (α from 0 to arcsin(H/R)) ρgsin(α)sin(2α)*πR^3 dα = ... Let's recall the formula: sinx siny = 1/2 (-cos(x+y)+cos(x-y)) and continue: ... = integrate (α from 0 to arcsin(H/R)) ρg((cos(α)-cos(3α))/2)*πR^3 dα = 0.5 πρgR^3 (sin(α) - (1/3)sin(3α)) (α from 0 to arcsin(H/R)) = 0.5 πρgR^3 (H/R - (1/3)sin(3arcsin(H/R))) = ... The sine of a triple angle sin(3x) = 3 sin x - 4 sin^3 x ... = 0.5 πρgR^3 *(4/3) (H/R)^3 = 2/3 πρgH^3 ----------------- (3) (1), (2), (3): m = (1/3)πρH^3 H=(3m/πρ)^(1/3)

It would have been better to post it in the Quenta expansion forum.

To solve integrals, you don't need inspiration; you just calculate and that's it... And then you simply correct the errors, and then again, but that's not important.

I messed up, you figure it out...

ok

0.5 πρgR^3 (H/R - (1/3)sin(3arcsin(H/R))) = ...
Triple angle sine sin(3x) = 3 sin x - 4 sin^3 x
... = 0.5 πρgR^3 * 4 (H/R)^3 = 2 πρgH^3 ----------------- (3)

There seems to be an error here.
Here is the expression in the last parentheses
H/R - (1/3)sin(3arcsin(H/R)) = H/R - (1/3)*(3(H/R) - 4(H/R)^3) = H/R - H/R + (4/3)(H/R)^3 = (4/3)(H/R)^3

Then it will not be

2 πρgH^3

It’s as if you don’t need inspiration for a quest. You just write, and that’s it.

It would have been better to post this in the Quenta expansion thread.

What if I were to visit your expansion with our integrals and derivatives combined?:smile04::smile04::smile04: Not just for fun, of course, but with the goal of calculating character stats...:D

It's as if inspiration isn't needed for a quest. You just write, and that's it.

It's not working.

What if I were to visit your expansion and bring along our integrals and derivatives? Not just for fun, of course, but to calculate character stats...

Sure, go ahead. Although there isn't much to calculate there.

ok

I think I've improved, but thanks for figuring everything out in this chaos.)

Have a cup of tea, and everything will be alright.

I think I've improved, but respect for figuring everything out in this chaos.

Apparently, it took me a while to figure it out. Now the answer is exactly like mine!!!

Added 1 minute ago
Ment figured everything out correctly!