Recent content by dylanhouse

Homework Statement I am having trouble setting up the bounds on the following two integrals: (a) The region E bounded by the paraboloid y=x2+z2 and the plane y=4. (b) The region bounded by the cylinder x2+y2=1, z=4, and the paraboloid z=1-x2-y2. Homework EquationsThe Attempt at a Solution I...

Homework Statement Find the tangent vector and unit tangent vector for the curve: r=sint, theta=t/3 for 0<=t<=6pi. Homework Equations If the tangent vector is r'(t)e(hat)r + r*theta(t)e(hat)theta, how does the restriction on t affect the answer? The same for the unit tangent vector, they don't...

So F would be (2t^2)i + (t^2 - t)j. And dr is just <1, 2t>dt. But how would I integrate with respect to ds if I end up with a dt?

Homework Statement For F = (x^2+y)i + (y-x)j, calculate the integral over C of Fds for r = (t, t^2) where t goes from 0 to 1. Homework EquationsThe Attempt at a Solution I know the integral over C of fds is f*sqrt(r'(t)^2+r^2*theta'(t)^2) dt. But I have no theta in this question, is this the...

Perfect! I had converted x and y to polar coordinates but I was getting stuck with theta's and r's! I didn't realize that from how C was defined I could rewrite the r and theta's! Thanks a bunch.

Homework Statement I am asked to find the integral over C of fds given C={r=cos(2t), theta=2t, for 0<=t<=pi/2} and f=xy. Homework EquationsThe Attempt at a Solution I know the integral over C of fds is the integral over C of [fsqrt(r'^2+r^2(theta)'^2)]dt, but I don't know how to convert my...

Well, I converted the polynomials to a matrix, and tried to put it into RREF to prove they were linearly independent. But the first column is all 0's, so it was pointless to go any further as they were obviously linearly dependent and thus not a basis I assumed.

Well, it wouldn't be possible unless my scalar was the variable x, and not a real number.

I figured it out :) I was also wondering if I am given four polynomials, of which the highest degree is x^2, they cannot be a basis for the vector space P3(R)?

I have shown that they are linearly independent. But I also need to show that the Span(s)=V.

Homework Statement Letting u=[3, 0, -5], v=[2, 1, 5] and w=[-1, 3, 4], how would I show that a general vector can be written as a linear combination of this 'basis?' Without using an augmented matrix and getting a really messy result by using arbitrary a, b, and c values as the solutions...

Homework Statement Given W={A belonging to M2(ℂ) | A is symmetric} is a subspace of M2(ℂ) over ℂ, when showing it is closed under scalar multiplication, do I need to use a complex scalar as it is over the complex numbers, or will a real number be okay? Homework Equations The...

A 1.0 kg cart traveling at 1.0m/s right hits a 4.0kg cart at rest. After the collision, the lighter cart is observed to move to the left at 0.5m/s. What impulse did the interaction deliver to the massive cart (magnitude and direction)? What is the carts velocity after the collision? I...

I guess my question is how would I use that ratio to show that the atom is always 50,000 times larger than proton?

What is rx? I'd have (0.5x10^-10)/(10^-15)=rx/x? Assume the marble radius is x..