Seh-Kai Liao

What happens if you multiply all permutations in Sn for some n? I'm not sure where to start for this question, except to look at inverses. I tried breaking down a permutation and its inverse into transpositions by looking at examples in S5 but that didn't really lead me anywhere.

So f(x) = x^2. Using the standard procedure for finding the inverse of a function, where g = f^(-1), we have g = ±√x. Would I be correct in stating that g is neither a function nor an inverse (and that g = ±√x is called an "inverse" for convenience)?

I'm asking this because x^2 : R --> R isn't injective, so x^2 shouldn't have an inverse by definition, yet it "does." I understand that ln(x) and e^x aren't surjective if mapped from R --> R, but they can be made surjective via manipulation of codomains, but I don't see an injective analogue to that for x^2 (unless you were to restrict the domain to, say, x ≥ 0, but that sort of defeats the purpose of my question).

Is the flux integral of a vector field with constant divergence through some surface equal to the divergence multiplied by the area of the surface? That's what I'm seeing but I'm hesitant to take that shortcut if it's not true...

Thanks!

Find ∫∫s curl(F) dS

F = < 2cos(πy)e^(2x) + z^2 , x^2 cos(zπ/2) - πsin(πy)e^(2x) , 2xz >

curl(F) = < (1/2)πx^2 sin(πz/2) , 0 , 2xcos(πz/2) >

S is the surface parameterized by:

r(s,t) = < (1 - s^(1/3))cos(t) - 4s^2 , (1 - s^(1/3))sin(t), 5s >

0 ≤ t ≤ 2π

0 ≤ s ≤ 1

Oriented so that the normal vectors point to the outside of the thorn

If you could even point me in the right direction, that'd be great. I'm using Mathematica to calculate curl(F) · (r(s,t)s × r(s,t)t) * s dsdt, because it looks like it's in polar coordinates to me, but I get a ridiculous answer. Is there a way to do this using Stokes' Theorem?

Thanks!

I have here a question that's asking for the flux integral ∫∫s curl(F) dS where F = some ridiculous vector field and S is part of the ellipsoid x^2 + y^2 / 4 + (z+1)^2 = 2, z > 0. Now, normally I'd say that the flux integral of curl(F) over an ellipsoid is 0 by of the divergence theorem, but I'm wondering if the fact that the surface only includes the part of the ellipsoid where z > 0 affects anything.

How would you parameterize x^10 + y^10 = 1?

Is there a spending limit on the Chase debit card? I'm buying a laptop with the debit card.

More specifically, a point and the coordinate axes (without cross products or parametrics). For example, the point P = (5, 12, 0). Would that just be 12 away from the x-axis, 5 away from the y-axis, and 13 away from the z-axis?

Thanks!

Yay, please help me! :D

So I haven't been sick in years. About a week ago, I had to receive multiple vaccinations (6) for things like HPV and some other things (they were all different). A couple days later, I'm really sick, which is a huge issue for me during this time of year.

I'm just wondering, can multiple vaccinations overload the immune system and allow other things to enter? I feel like that's what happened.

Thanks!

Like, something that was commonly said out on the battlefield or among one another.

ex. "Semper Fidelis" - Marine Corps

Thanks! (Will pick a best answer.)

I never understood this. If this is meant to be an inconvenience or situational irony, then why aren't they directly proportional? As the itch's severity increases, it gets easier to reach (the reach gets shorter)? Shouldn't it be as the itch's severity increases, it gets harder to reach (the reach gets longer)? I don't get it.

I like clever ones, such as....

Ag N O S Ti C (Because it's chemistry...)

Am Er I C A / N

Stuff like that. I don't want really long words/phrases, they will do me no good. Thank you, I will choose a best answer!

A 0.1046 g sample of copper metal is dissolved in 56 mL of concentrated HNO3 to form Cu2+ ions and then water is added to make a total volume of 203.3 mL. (Calculate the molarity of Cu2+.)

0.1046g Cu = .001646 mol

.001646 mol / 0.056 L = 0.29 M

56 mL * 0.29 M = 203.3 mL * (M)

1.624 / 203.3 = M

M = 0.007988

I rounded when I found the first molarity, because if you don't you get 0.008096, which translates to 0.0081 M when you round with significant figures, and it says it's wrong. You don't need units by the way, it's included on the side. I don't know if it's 0.0080 or not; it's my last attempt at the question.

A 0.1046 g sample of copper metal is dissolved in 56 mL of concentrated HNO3 to form Cu2+ ions and then water is added to make a total volume of 203.3 mL. (Calculate the molarity of Cu2+.)

I used the equation M1V1 = M2V2, but the answer I got wasn't correct.

A square boat. Would it roll and turnover?

Would it?

If you're around an allergen for long enough, can your body adapt to it?

I'm really fond of cats and I want a cat, but I'm allergic to them. And hypoallergenic cats are ridiculously expensive.

I haven't taken it yet, and I want to. I heard it's mostly geometry, which I don't know.

If it is, are there any good review sites for geometry?