Recent content by zjmarlow

cos(u(x)) u'(x) and -sin(u(x)) u'(x).

So this should be sin(x^{5}) , correct?

Is this just 5x^4 sin(x^{5}) ?

Ok, I copied the example problem wrong. It should be \iiint\limits_B e^{(x^2 + y^2 + z^2)^{(3/2)}}dV which becomes \int_0^{2\pi} \int_0^\pi \int_0^1 e^{(\rho^2)^{(3/2)}} \cdot \rho^2 sin \phi d\rho d\phi d\theta = \int_0^{2\pi} \int_0^\pi \frac{e - 1}{3} sin \phi d\phi d\theta =...

Sorry, that should be f(x, y, z) (in general) or e^{x^2 + y^2 + z^2} (in this particular case).

Or is \frac{4\pi}{3}(e - 1) like a scalar field that says how much each position in the unit ball is "worth"?

Thank you for your reply. The solution is worked out: \frac{4\pi}{3}(e - 1) . My problem now is visualizing e^{x^2 + y^2 + z^2} . Could you explain what this would look like?

Homework Statement Evaluate \iiint\limits_B e^{x^2 + y^2 + z ^2}dV where B is the unit ball. Homework Equations See above. The Attempt at a Solution Does this evaluate the volume of f(x, y, z) within the unit ball (i.e. anything falling outside the unit ball is discarded)...

Hi Simon. The reflectivity is a dimensionless number in the book. I imagined it was like a coefficient of friction. Your suggestion that the reflectivity is rounded is interesting because the table with the coefficients only lists them to two significant figures. Still, it's hard to believe...

Thanks for your reply. You mentioned W/c ≈ .00576 but I get the wrong dimensions (pressure in Pascals) when I do that. Doing W\pi r^2 / c gets me .00581 which seems a bit too much error compared to the expected solution...

Homework Statement The intensity of the Sun's radiation just outside the Earth's atmosphere is approximately 8 \cdot 10^4 \frac {joules}{m^2 \cdot min} . Echo II is a spherical shell of radius r_0 = 20.4m. Its skin consists of a layer of Mylar plastic ... between two layers of aluminum. ...