Recent content by clairez93

I could not get LaTex to format properly, so I typed out the question and my work using Microsoft Word's equation editor. Please see the attached document, apologies for any inconvenience! These problems involve the techniques for the method of undetermined coefficients and variation of parameters.

Homework Statement A series of true/false questions. I guess I don't understand the concepts of this very well: 1. If you know the directional derivative of f(x,y) in two different directions at a point P, we can find the derivative with respect to the x and y axes and thus we can...

Homework Statement 1. Evaluate \int_{S}\int curl F \cdot N dS where S is the closed surface of the solid bounded by the graphs of x = 4, z = 9 - y^2, and the coordinate planes. F(x,y,z) = (4xy + z^2)i + (2x^2 + 6y)j + 2xzk 2. Use Stokes's Theorem to evaluate \int_{C}F\cdot T dS...

Yes, sorry, typo. Sorry, typo, I meant spherical coordinates. I checked and dV should be \rho^2\sin^2(\phi)d\rho*d\varphi*d\theta So that should change the integral to: I_{z} = k \int^{2\pi}_{0}\int^{\pi/2}_{\pi/4}\int^{1}_{0}(\rho^2 sin^{2}\varphi)^{2}*d\rho*d\varphi*d\theta...

Homework Statement Use spherical coordinates to find the moment of inertia about the z-axis of a solid of uniform density bounded by the hemisphere \rho=cos\varphi, \pi/4\leq\varphi\leq\pi/2, and the cone \varphi=4. Homework Equations I_{z} = \int\int\int(x^{2}+y^{2})\rho(x, y, z) dV...

Does this mean I have to add another double integral with the equation of -5/sqrt 25-r^2 to get the right answer?

Once I have solved for x, would I plug this back into the original z bound? That's the only way I get the book answer. Why does that work? Also, I'm not quite sure I can "see" that the y goes up to the plane exactly?

Well for x, I think it would go from 0 to something like z = -3/4x+3? And wrt z, 0 to 3? But it still doesn't quite explain the dy?

Homework Statement \int^{4}_{0}\int^{(4-x)/2}_{0}\int^{(12-3x-6y)/4}_{0}dz*dy*dx Rewrite using the order dy dx dz. Homework Equations The Attempt at a Solution I have it graphed, but from here, I am having a hard time visualizing the bounds of all these dimensions to reorder the integral...

Homework Statement 1. Verify the given moments of inertia and find the center of mass. Assume each lamina has a density of p=1. The problem gives a circle with a radius a. 2. Find the area of the surface of the portion of the sphere x^2 + y^2 + z^2 = 25 inside the cylinder x^2 + y^2 = 9...

So I'm guessing this will involve an integral of sorts. Would I integrate the little bits of potential energy? So like the integral of V * q?

Homework Statement 2. The potential at the center of a circle of radius 90 cm with three charges of +1 nC, -2 nC, and +2 nC placed 120 degrees apart on the circumference is: a) 8.0 V b) 12 c) 16 d) 9 Answer: d 6. The electrostatic energy stored in the electric field around a conducting...

I think so; they are the questions that I got wrong on my last test for electrostatics. But it may be that the test bank is wrong, that has happened before. I'll have to speak with my teacher.

Please, I know there's a lot, but my exam is coming up and I would really appreciate if someone could show me what I'm doing wrong.

Homework Statement 1. A thin rod bent in the shape of a semicircle of radius 20 cm is uniformly charged along its length with a total charge of 8.0 microC. What is the electric field at the center of the semicircle? a. 7.3 x 10^4 N/C b. 8.4 x 10^4 c. 5.7 x 10^4 d. 3.9 x 10^4 e. None...