Recent content by mcafej

Homework Statement Determine Equilibrium points, limiting cycles, and their stabilities for the following equations r'=r(r-1)(r-3) θ'=1 The Attempt at a Solution So I know one equilibrium point is going to be (0,0) because r=0 is a limiting cycle (I believe), and that is simply a...

Homework Statement 1. The sample space Ω of a certain experiment are the values 1, 2, 3, 4 and 5 and the probability assigned to a possible value w is proportional to w2. (a) What is the probability mass function p(w) for this probability space? (b) What probability does this mass...

Ok, so I know that the laws of physics say reaching absolute zero temperature is impossible, but suppose we took a box that was perfectly insulated in completely empy space, and I took all the particles out of it to create a vacuum. Now, since there are no particles in the box, then wouldn't...

Ok, so I was just thinking about einsteins famous equation E=mc^2, and I was just wondering, if I were to take, say a rock or piece of metal. If I were to weigh it, and get it's mass, I could compute how much energy it contains. However, if I were to add heat to the rock or piece of metal by...

Homework Statement A mass of 4 kg is stretches a spring by 1 m. An external force of cos (!t) N acts on the mass. Assume that the damping constant is nonzero and gravity is 10 ms^-2. Consider a spring mass system described by the following IVP. u''+yu'+u = cos(wt) u(0) = 0 u'(0) = 0 1) Find...

Ok, so I just watched the nova fabric of the cosmos (blew my mind). Anyways, suppose I jumped on top of a beam of light and road it as it traveled out into space. Now, suppose that as I was traveling out there, another person is coming at me in the exact opposite direction on another beam of...

I'm just checking my work on this. Given an 8x8 chessboard, you randomly place 8 rooks on the board. What is the probability that no rooks can capture another one. In other words, probability that no 2 rooks are in the same row or column. My solution is simply 8!/(64 choose 8), but that...

Ok, so this relates to my homework, but I really can't find an answer anywhere, so this is more of a general question. First off, what does a "chart" of a manifold look like? Is it a set, a function, a drawing, a table, what?! I have found so many things about charts, but nothing shows what...

Thank you, that makes a lot more sense. It also helps with part 2 of the problem (where you can take the limit as theta approaches 3π/2 for MS and you get x>1 or x<1, and you can do the same with MN, but instead have theta approach ∏/2 to get the same thing). I am a little confused on how to...

Homework Statement Take the unit circle in the x-y plane with center at (0, 0), bisected by the x-axis. Take two maps, the first MS from the circle minus the south pole S to the x-axis that take a point P on the circle to the intersection of the line from the south pole (0, −1) through P with...

Ok, so I was just thinking about this today. First off, I was thinking about absolute zero, and how they say it's impossible, but then I thought about what the average temp. of the universe is. According to several internet sources, the current average temp is about 2.73 kelvin. I was...

Ok, so I just looked up the formula for the radii of a torus, and I just explained how I got 1 as the radius of the circle of the tube, and 3 as the radius of the torus itself. As for the Area of coverage, I was able to simplify it down and for the Area you end up just getting the double...

Homework Statement Consider the parametrization of the torus given by: x = x(s, t) = (3 + cos(s)) cos(t) y = y(s, t) = (3 + cos(s)) sin(t) z = z(s, t) = sin(s), for 0 ≤ s, t ≤ 2π. (a). What is the radius of the circle that runs though the center of the tube, and what is the radius of the tube...

Wow...yea, i got a sign mixed up and ended up with .75-.75 instead of .75+.75. I got 1.5 as an answer, which sounds much more reasonable, thanks.

Homework Statement Consider the change of variables x = x(u, v) = uv and y = y(u, v) =u^3+v^3 Compute the area of the part of the x-y plane that is the transform of the unit square in the 2nd quadrant of the u-v plane, which has one corner at the origin. (Since the transformation is 1:1...