Ok, I know this is not too much of a teaser but maybe you guys could come up with something cool and original. I'm getting a tattoo and part of it has my birthdate in it. Except I don't want it to be obvious...I want some type of complicated equation with lots of mathmatical symbols etc so if...
If S is part of the plane z = y - 2 that lies inside the elliptic cylinder x^2 + 4y^2 = 4 and I want to parametrize S I will let
x = 2sin(t)
y = cos(t)
z = cos(t) - 2
I assume this is right but let me know if not. My question is are there any other ways of parametizing S?
Well, we are working on Green's Theorem right now but i don't remember it incorporating the area of a rectangle. So, to answer your question...no, i don't even know where to begin.
Anyone know how to do this question?
Let C be the boundary of any rectangular region in R2. Show that the value of the line integral
\oint (x^2 y^3 -3y)dx + x^3 y^2 dy
depends only on the area of the rectangle and not on its placement in R2.
a good job?
chronos...you and everyone else should read this http://www.disclosureproject.org/Transcripts/TranscriptCharlesGoyetteRadioShowInterview-DrStevenGreer-Feb252005.htm
Ok, but then that gives me
T(t) = \frac{(1 + sin(t))i + (cos(t))j + k} {\sqrt{2sin(t) + 3}}
Now for T'(t) I don't ever remember taking derivatives of vectors this complicated. Do I use the quotient rule?
I need to calculate the Frenet apparatus for the space curve defined by
\overrightarrow{r} (t) = \langle t - cos (t), sin(t), t \rangle
so for T I did
\overrightarrow{r} \prime (t) = \langle 1 + sin(t), cos(t), 1 \rangle
then I got |r'(t)| = \sqrt{2sin(t) + 3
which I'm pretty sure...
If you drilled a hole exactly in the center of a container there would be no swirl no matter what the shape and size of the container as long as the top is open to the atmosphere. There is never a swirl in a seperatory funnel...the level of the liquid lowers evenly on a horizontal plane unless...
"Anyway, a stove puts out 10s of kilowatts of energy. The subsequent sound waves constitute maybe 1 milliwatt of energy. That's a ratio of over 10,000,000, so it's no use relating the two. "
If there's no relation(indirectly or directly) then why would the ticking start when the stove is...