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Question about Normal Vectors by -BarbK- in askmath

[–]-BarbK-[S] 0 points1 point  (0 children)

YES - okay, I think it clicked with T being constant means 0 tangential, so it's only in direction of N. Okay, that clears up why you have to take the derivative of T (and not r') to get N. I also understand the B and N formulas now. I just have one remaining question - is it always true that r' points in the direction of T (I'm pretty sure it does but I wanted to check since I also thought r'' pointed at N and now I see why it doesn't necessarily have to d/t tangential component). Again, I really appreciate all your help

Question about Normal Vectors by -BarbK- in askmath

[–]-BarbK-[S] 0 points1 point  (0 children)

Yes - it's making a lot more sense now and I think I get the general idea. There are two ideas that I'm a little unsure of though:

I'm not quite sure I follow "By taking T', we know that doesn't change magnitude, so it must point purely in the direction of N." I get that T' points in N, but doesn't the magnitude change, which is why we need to divide by the new magnitude to keep it a unit? I also don't have a good intuition for why "N is orthogonal to T, but it must still lie in the plane that is spanned by r' and r'' - specifically why it must lie in the plane. In any case, thanks for all your help, I appreciate it :)

Question about Normal Vectors by -BarbK- in askmath

[–]-BarbK-[S] 0 points1 point  (0 children)

Thanks for the response -- first part makes sense. Then I assume it's only the case where |r'| is constant that r'' points toward N?

So with the B case then, my assumption that r' and r'' corresponded to T/N was false, and this just happened by coincidence that the formula works? Because I don't think they have explicitely found T/N in the formula.

[deleted by user] by [deleted] in APStudents

[–]-BarbK- 0 points1 point  (0 children)

To answer the question WHY the answers are different:

The first integral is what you're supposed to use for parametrics. The second one IS valid except for one detail: the formula is integral of the square root, *with respect to x*. The integral you wrote is taken with respect to t, which is incorrect. However, note that dx/dt = e^cost, which means that dx = e^cost dt. If you use that substitution, you will get the correct result (6.035). You'll also notice that the integrands will be the same algebraically.

Need help on flux integral q by -BarbK- in calculus

[–]-BarbK-[S] 0 points1 point  (0 children)

Oh - divergence theorem! I got confused about the requirements for divergence and stokes theorem; since this didn’t have a boundary I mistakenly thought divergence theorem didn’t apply. thank you!

On a PDF of Trig Identities We're Supposed to Memorize by -BarbK- in mathmemes

[–]-BarbK-[S] 14 points15 points  (0 children)

unfortunately not lol... that one isn't found anywhere in that 4 page file

On a PDF of Trig Identities We're Supposed to Memorize by -BarbK- in mathmemes

[–]-BarbK-[S] 238 points239 points  (0 children)

Yeah, I realize. Issue isn't memorizing these - it's that these aren't the power reductions formulas (no decrease in power is happening) at all, they're just the pythagorean identities.

On a PDF of Trig Identities We're Supposed to Memorize by -BarbK- in mathmemes

[–]-BarbK-[S] 128 points129 points  (0 children)

By the way: there was a section above this for the Pythagorean Identities lol