Question

In: Advanced Math

h Consider a solid T enclosed by the paraboloid z = x^2 +y^2 and the plane...

h Consider a solid T enclosed by the paraboloid z = x^2 +y^2 and the plane z = 4 (the solid above the paraboloid and below the plane). Let M the (closed) surface representing the boundary surface of T. The surface M consists of two surfaces: the paraboloid M1 and the lid M2. Orient M by an outward normal. Let F=(z,2y,-2)

Compute the integral using the Divergence theorem. Carry out the computation of the triple integral using the spherical coordinates.

Solutions

Expert Solution

  • Had we proceeded using surface integrals, the process would have been tedious, thus, in such cases the divergence theorem helps a lot !!

Related Solutions

So we have a paraboloid x^2 + y^2 - 2 = z and the plane x...
So we have a paraboloid x^2 + y^2 - 2 = z and the plane x + y +z = 1 how do we find the center of mass? For some reason we have to assume the uniform density is 8? Seems complicated because I don't know where to start?
The plane x + y + 2z = 12 intersects the paraboloid z = x2 +...
The plane x + y + 2z = 12 intersects the paraboloid z = x2 + y2 in an ellipse. Find the points on the ellipse that are nearest to and farthest from the origin. nearest point      (x, y, z) =    farthest point      (x, y, z) =   
The paraboloid z = 8 − x − x2 − 2y2 intersects the plane x =...
The paraboloid z = 8 − x − x2 − 2y2 intersects the plane x = 4 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (4, 2, −20). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)
Find the surface area of the part of the paraboloid x = y^2 + z^2 that...
Find the surface area of the part of the paraboloid x = y^2 + z^2 that lies inside the cylinder y^2 + z^2 = 25
*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z):...
*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=c}. (b) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): x=a}. (c) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): y=b}. *(2) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=kx+b} assuming both b and k are positive. (a) For what value of...
find the surface area of the paraboloid z = 4−x^2 −y^2 in the first octant.
find the surface area of the paraboloid z = 4−x^2 −y^2 in the first octant.
The temperature at a point (x,y,z) is given by T(x,y,z)=200e^(-x^2-y^2/4-z^2/9) , where T is measured in...
The temperature at a point (x,y,z) is given by T(x,y,z)=200e^(-x^2-y^2/4-z^2/9) , where T is measured in degrees Celsius and x,y, and z in meters. just try to keep track of what needs to be a unit vector. a) Find the rate of change of the temperature at the point (1, 1, -1) in the direction toward the point (-5, -4, -3). b) In which direction (unit vector) does the temperature increase the fastest at (1, 1, -1)? c) What is...
Consider the scalar functions f(x,y,z)g(x,y,z)=x^2+y^2+z^2, g(x,y,z)=xy+xz+yz, and=h(x,y,z)=√xyz Which of the three vector fields ∇f∇f, ∇g∇g and...
Consider the scalar functions f(x,y,z)g(x,y,z)=x^2+y^2+z^2, g(x,y,z)=xy+xz+yz, and=h(x,y,z)=√xyz Which of the three vector fields ∇f∇f, ∇g∇g and ∇h∇h are conservative?
I'm stuck on this python exercise using plots Consider the hyperbolic paraboloid function: z=x^2−y^2 Create several...
I'm stuck on this python exercise using plots Consider the hyperbolic paraboloid function: z=x^2−y^2 Create several plots of the hyperbolic paraboloid function. Use true aspect ratio and label all axes. Any help would be appreciated!Matlab can be used as long as the code can be used in Python as well
F(x,y,z) = x^2z^2i + y^2z^2j + xyz k S is the part of the paraboloid z...
F(x,y,z) = x^2z^2i + y^2z^2j + xyz k S is the part of the paraboloid z = x^2+y^2that lies inside the cylinder x^2+y^2 = 16, oriented upward.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT