Homework Statement
Verify Greens theorem for the line integral ∫c xydx + x^2 dy where C is the triangle with vertices (0,0) (1,1) (2,0). This means show both sides of the theorem are the same.
Homework Equations
∫c <P,Q> dr = ∫∫dQ/dx -dP/dy dA
∫c xydx + x^2dy
The Attempt at a...
Homework Statement
Find the parametric equations for the line of intersection of two planes
Homework Equations
Equations for the two planes...
z=x+y,-------(1)
2x-5y-z=1 -----(2)
The Attempt at a Solution
My answers are not correct so I guess I'm going about it the wrong way. Someone...
Homework Statement
Find the mass and the center of mass of the solid E with the given density function ρ(x,y,z). E is bounded by the parabolic cylinder z = 1 – y2 and the planes x + 4z = 4, x=0, and z=0; ρ(x,y,z) =6.
m=?
x=?
y=?
z=?
Homework Equations
z = 1 – y2 and the planes x...
Homework Statement
At what point do the curves r1(t) = (t, 4-t, 63+t^2) and r2(s)= (9-s, s-5, s^2) intersect?
Answer in the form: (x,y,z) = ____
Find the angle of intersection theta to the nearest degree.
Homework Equations
The Attempt at a Solution
i: t=9-s
j: 4-t=s-5...