Recent content by slr77

I finally realized how to do it and it was a case of severe tunnel vision as I suspected. I just have to take the gradient of the two level surfaces at the specified point and cross them in order to get the tangent vector. Parameterizing the curve of intersection and computing the tangent vector...

sorry double post

The full problem requires me to compute r'(t) = <x'(t), y'(t),z'(t)> (well actually I just need a tangent vector to the curve of intersection at a certain point but this is the only way I can think of to compute it) so this parameterization seems too complicated. the closest I was able to get...

The first one is a sphere of radius sqrt(14) and and the second is a hyperbolic paraboloid. I even grahed both surfaces before posting this question and am looking at the curve of intersection right now. But I can't figure out what the parameterization should be. I tried look at the intersection...

Homework Statement Parameterize the curve of intersection of the two surfaces: x^2+y^2+z^2=14 z=y^2-x^2 Homework EquationsThe Attempt at a Solution I tried manipulating the equations above but can't seem to get a nice parameterization which I can use to do the rest of the (calculus) problem.

Oh of course, I remember how to do this now. ∂z/∂u is a function of (u,v) which are functions of (x,y) so I just apply the chain rule like usual. I made some really bad mistakes here (especially applying Clairaut's theorem so incorrectly) but at least the problem now looks pretty...

Homework Statement Homework EquationsThe Attempt at a Solution I have the solution to this problem and the issue I'm having is that I don't understand this step: Maybe I'm overlooking something simple but, for the red circled part, it seems to say that ∂/∂x(∂z/∂u) =...

Hmm, ok. I think I should have posted the full problem because I think it's more open ended than what my original post conveys: I'm just treating w as the variable and going from there but maybe that's not the right definition? So is there some way to do this problem that makes sense?

When I watched them, these were about the best quality I could find: http://cosmolearning.org/courses/802-physics-ii-electricity-and-magnetism/ http://cosmolearning.org/courses/801-physics-i-classical-mechanics/

I think this is the chain rule but we haven't learned that yet. I'll read ahead and come back to this and make sense of it but apparently there should be a way to do this without directly making use of the chain rule.

But w depends implicitly on y so can I really take y as constant? If I get y in terms w (y = w-x) and continue this way (so 1 + ∂y/∂w = 1 + ∂(w-x)/∂w). I just get an endless chain of 1+1+1+1+1... That's why I think what I'm doing is not right.

Homework Statement Define f(x,y) = x+2y, w = x+y. What is ∂f / ∂w? Homework EquationsThe Attempt at a Solution f = w+y so: ∂f/∂w = ∂(w+y)/∂w = ∂w/∂w + ∂y/∂w = 1 + ∂y/∂w. But I'm really not sure if this is right and if it right so far, I can't figure out what ∂y/∂w should be...

Hey gneill, The solution listed d (19) as the correct answer so I guess it's mistaken. This has uncovered some confusion about this topic though. I thought a thin-walled spherical shell had all it's mass distributed a distance r from the center. A thin-walled how cylinder has I = MR^2 (which...

Homework Statement [/B] A thin spherical shell of radius R = 0.50 m and mass 15 kg rotates about the z-axis through its center and parallel to its axis. When the angular velocity is 5.0 rad/s, its angular momentum (in kg ⋅ m2/s) is approximately: a . 15 b. 9.0 c. 12 d. 19 e. 25 Homework...