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

Expert Solution

milcah answered 1 year ago

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.

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

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 H be the hemisphere x2 + y2 + z2 = 66, z ≥ 0, and...

Let H be the hemisphere x2 + y2 + z2 = 66, z ≥ 0, and suppose f is a continuous function with f(4, 5, 5) = 5, f(4, −5, 5) = 11, f(−4, 5, 5) = 12, and f(−4, −5, 5) = 15. By dividing H into four patches, estimate the value below. (Round your answer to the nearest whole number.) H f(x, y, z) dS

Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j...

Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j + (3 + x) k . Let a > 0 and let S be part of the spherical surface x2 + y2 + z2 = 2az + 15a2 that is above the x-y plane and the disk formed in the x-y plane by the circular intersection between the sphere and the plane. Find the flux of F outward across S.

Question

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

Solutions

Expert Solution

Related Solutions

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

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

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

Let H be the hemisphere x2 + y2 + z2 = 66, z ≥ 0, and...

Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j...

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