Recent content by dancingmonkey

Homework Statement Use Stokes' Theorem to evaluate ∫C F · dr. C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y^2) i + (y + z^2) j + (z + x^2) k C is the triangle with vertices (9, 0, 0), (0, 9, 0), and (0, 0, 9). Homework Equations Stokes' Theorem The...

Homework Statement The circuit parameters are: R = 60 Ohms, L = 5 mH, C = 40 microFarads, and e= 120 V. Initially the switch has been closed for a long time. At t=0 the switch is opened. What is t1, the first time greater than or equal to 0, that the current through the inductor is equal...

My question is how do I find the voltage across a capacitor? I have an RLC circuit with a switch and battery. It only gives me the values for the battery, L, C, and R. My main question is, is there an equation or something to find the voltage across a capacitor?

Homework Statement Find the area of the part of the plane 3x + 5y + z = 15 that lies inside the cylinder x^2 + y^2 = 25. Homework Equations A=∫∫(√1+(dz/dx)^2+(dz/dy)^2) dA The Attempt at a Solution my bounds were r=0 to 5 and theta=0 to 2pi ∫∫√1 + (-3)^2 + (-5)^2 dA =∫∫√35 dA...

Ah! Ok I got it now, thank you so much for helping!

So the equation of the sphere in spherical coordinates is ρ^2=x^2+y^2+z^2. So the integral should go from p=0 to 7, right?

So is ρ from 0 to cos(φ)? I'm still confused about this. And yes I understand that I still have to solve the integrals :)

Homework Statement Find the volume and the centroid of the solid E that lies above the cone z=√x^2+y^2 and below the sphere x^2+y^2+z^2=49. Homework Equations The Attempt at a Solution My bounds were: \theta=0 to 2\pi \varphi=0 to \pi/4 \rho=0 to 7cos(\varphi) So my integral...

Thank you so much! That was the problem. I missed the part where it said the first octant.

Homework Statement Evaluate the integral, where E is the solid in the first octant that lies beneath the paraboloid z = 9 - x2 - y2. ∫∫∫(2(x^3+xy^2))dV Homework Equations x=rcosθ y=rsinθ x^2+y^2=r^2 The Attempt at a Solution θ=0 to 2π, r=0 to 3, z=0 to (9-r^2)...

An infinitely long solid insulating cylinder of radius a = 5.3 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 45 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 14.2 cm, and...