4. Convert the following quadric surface into spherical coordinates. (x-3)²+y²+(z+1)² = 1

Consider two spheres, defined by x^2 + y^2 + z^2 = 1 and (x − 2)^2 + (y − 6)^2 + (z − 3)^2 = 16, respectively. How close are the spheres from touching?

If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the resulting surface.

Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein model, solve: to When X2+Y2<=1, find the point F(x,y) that is the intersection lxy with the sphere E

Sketch the solid that has the given description in spherical coordinates. 0 ≤ θ ≤ π 0 ≤ ϕ ≤ π/2 1 ≤ p ≤ 3

Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

find an equation of the form r = f (θ , z) in cylindrical coordinates for the following surfaces. x2 + y2 = 4

Identify this surface, φ = π/3 in spherical coordinates, and find its equation in x, y, z coordinates

Find an equation in rectangular coordinates for the surface represented by the cylindrical equation r = 2 cos , and sketch its graph.

Find an equation in spherical coordinates for the surface represented by the rectangular equation x2 + y2 + z2 − 9z = 0