Recent content by wilcofan3

Homework Statement A 700 g block is released from rest at height h0 above a vertical spring with spring constant k = 445 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 20.5 cm. (a) How much work is done by the block on the...

Homework Statement Find the centroid of the solid bounded below by the cone z = \sqrt{3(x^2+y^2)} and bounded above the sphere x^2+y^2+z^2=36. Homework Equations Let G be the given solid and denote its volume by V_{G}=\int \int \int_{G} 1 dV. \frac{\bar{x}= \int \int \int_{G} x...

I don't know what I was thinking with those bounds I guessed. After looking at the graph more, I see that the base is an ellipse and that the major axis is 4 and minor is 2. This leaves me to believe the bounds for dx would be from -2 to 1 (because of the line x=1 if we do not ignore it)...

I looked at the region. Would the bounds for dx be from 0 to 1, dy from 0 to 16, and dz from 0 to 1 as well?

Homework Statement Find \int \int \int_{D} xydV, where D is the solid bounded by the coordinate planes, the plane x = 1 and the surface z = 16 - 4x^2 - y^2. Homework Equations The Attempt at a Solution I have no problem with actually performing the integration, but I'm lost on...

Thank you very much! I am pretty sure I understand it now!

I was referring to the constant when I integrate with respect to x. Sorry, I was a little vague. Thank you, though, I just was a little unsure on whether having a "u" substitution would change things up, but I should just treat it as a constant. I ended up with the result 2e^3 - 2e^2.

Homework Statement Find the center of mass of the triangle with vertices at (0,0), (6,6) and (-6,6) if the density at (x,y) is equal to y. Homework Equations The Attempt at a Solution I am having trouble with these centroid/center of mass problems, and I can't even figure out the...

Homework Statement Evaluate the double integral \int \int_{R} ln(xy) dA where R is the rectangle bounded by x=e, x=e^2,y=1,y=e. Homework Equations ln (xy) = ln x + ln y The Attempt at a Solution I was just wondering, do I need to do anything other than take the integral with respect to x...

I feel so stupid, I'm failing at solving this simple system, yet I am pretty sure I know what I'm going to end up with. I'm sure it will be something like x+y=-z that I end up with, because than that would say x+y+z=0 which isn't true, which proves that x=y. EDIT: Nevermind, it's solved. I...

Homework Statement Consider the problem of finding the points on the surface xy+yz+zx=3 that are closest to the origin. 1) Use the identity (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx) to prove that x+y+z is not equal to 0 for any point on the given surface. 2) Use the method of Lagrange...

Not quite. I understand what you are doing with the bottom, the equation is that of a sphere, and therefore you are using another equation to show the bottom is going to 0. But how exactly does that prove the numerator is going to 0 as well?

Homework Statement \lim_{(x,y,z) \to (0,0,0)} \frac {x^3 + y^3 + z^3} {x^2 + y^2 + z^2} Homework Equations The Attempt at a Solution I believe the limit is going to 0, but I have yet to find a way to prove this is the case.

Homework Statement Let u= (x^2 + y^2 + z^2)^\frac {-1} {2} Find \frac {\partial^2 u} {\partial x^2} + \frac {\partial^2 u} {\partial y^2} + \frac {\partial^2 u} {\partial z^2} Homework Equations The Attempt at a Solution \frac {\partial^2 u} {\partial x^2} = -(x^2 + y^2...

Thanks! Hopefully this is all that's required.