Find the volume of the solid that lies within the sphere x2+y2+z2=64, above the xy plane,...

Find the volume of the solid that lies within the sphere x2+y2+z2=64, above the xy plane, and outside the cone z=7sqrt(x2+y2)

Expert Solution

milcah answered 2 years ago

Use Polar coordinates to find the volume inside the sphere x2 + y2 + z2 =...

Use Polar coordinates to find the volume inside the sphere x2 + y2 + z2 = 16 and outside the cone z2 = 3x2 +3y2.

Let S be the surface with equation x2+y2-z2=1. (a) In a single xy-plane, sketch and label...

Let S be the surface with equation x2+y2-z2=1. (a) In a single xy-plane, sketch and label the trace curves z=k for k = -2,-1,0,1,2. In words describe what types of curves these are and how they change. (b) In a single yz-plane, sketch and label the trace curves x=k for k= -2,-1,0,1,2. In other words, describe what types of curves these are and how they change as k varies.

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2....

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2. Show that these surfaces are tangent where they intersect, that is, for a point on the intersection, these surfaces have the same tangent plane

Find the volume of the solid enclosed by the two paraboloids y=x2+z2y=x2+z2 and y=2−x2−z2y=2−x2−z2.

Consider the solid that lies above the rectangle (in the xy-plane) R=[−2,2]×[0,2], and below the surface...

Consider the solid that lies above the rectangle (in the xy-plane) R=[−2,2]×[0,2], and below the surface z=x2−4y+8. (A) Estimate the volume by dividing R into 4 rectangles of equal size, each twice as wide as high, and choosing the sample points to result in the largest possible Riemann sum. Riemann sum =? (B) Estimate the volume by dividing R into 4 rectangles of equal size, each twice as wide as high, and choosing the sample points to result in the...

Find the volume of the region that lies between the unit sphere and the sphere of...

Find the volume of the region that lies between the unit sphere and the sphere of radius 1 centered at (0,0,1) (ans is (5pi)/12 but I cant quite get it)

Find the volume of the solid in R^3 above the plane z = 0 and below...

Find the volume of the solid in R^3 above the plane z = 0 and below the surface z = 4 − x^2 − y^2.

The plane x+y+z= 24 intersects the cone x2+y2= z2 in an ellipse. The goal of this...

The plane x+y+z= 24 intersects the cone x2+y2= z2 in an ellipse. The goal of this exercise is to find the two points on this ellipse that are closest to and furthest away from the xy-plane. Thus, we want to optimize F(x,y,z)= z, subject to the two constraints G(x,y,z)= x+y+z= 24 and H(x,y,z)= x2+y2-z2= 0.

A solid S occupies the region of space located outside the sphere x2 + y2 +...

A solid S occupies the region of space located outside the sphere x2 + y2 + z2 = 8 and inside the sphere x2 + y2 + (z - 2)2 = 4. The density of this solid is proportional to the distance from the origin. Determine the center of mass of S. Is the center of mass located inside the solid S ? Carefully justify your answer.

Si U=(x2+y2+z2)-1/2 , demuestre que ∂2U/∂x2+∂2U/∂y2+∂2U/∂z2=0

Question