A. Let Q be a three dimensional solid and let F(x,y,z)
= (x and let S be the boundary of Q with outwardly pointing normal. The the volume so Q is given by
B.
Let
C. A new particle, the fluxon, has been discovered to be emitted from the sun. The particle emits a force field
where the origin represents the center of the sun. If the total flux through the earth's northern hemisphere has been calculated as 10,000, then the total flux through the earth's southern hemisphere must also be 10,000.
where t is measured in hours. However, at time t = 2, your engines fail and your ship begins drifting in deep space. There is a deep space station located at (6,2,38). A. Find the vector-valued function that describes the Potential's flight after the engines failed. Use t = 2 to represent the time at which your engines first shut down. (Hint: This should be a linear vector valued function.) B. Will your ship make it to the station, or will you float helplessly for eternity?
where
R is a positive constant, has the property that
where R is the square with vertices (4,0), (6,2), (4,4), and (2,2). A.
Use the appropriate change of variables (Jacobians) to find
B.
Find the probability that 0
A. The mass of the solid that lies inside the sphere
x and outside the cone
z that has density function
B. The surface area of the part of the paraboloid
z = x that lies inside the cylinder
x
as a particle moves counterclockwise around the rectangle with vertices (2,1), (5,1), (5,5), and (2,5).
Verify Stokes Theorem where
and S is part of the paraboloid
z = 9 - x that lies above the plane z = 8 oriented upward.
Use the transformations
and
To represent the volume of the solid inside of ( |