Find a parametric representation for the surface. the part of the sphere x² + y² + z² = 16 that lies between the planes z = 0 and z = 2√3. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of u and/or v.) TT where 0 ≤ u≤ 2π, I SUST 6 2

Q: Identify the equation associated with each graphed surface. (a) O 22 = - x? – y? + 1 O22 – 1 = y + x…

A: Given graph is  (a)                                                      from graph we observe that…

Q: Project: S is a surface in R° with equation x² +y² – z² = 1. The point P (2,1,2) lies on this…

A: Clearly : x-z = 0 and y+1 = 2. So, we can write: 1.(x-z) = 0.(y+1). So, L1 can be written…

Q: Give a geometric description of the set of points in space whose coordinates satisfy the given pairs…

A: Give a geometric description of the set of points in space whose coordinates satisfy the given pairs…

Q: I. Use the Divergence Theorem: (² F. ds = Ifv. Fav SSS E = to calculate the flux of the field F…

A: Divergence theorem uses  Double integration converts into triple integration.

Q: Find the distnace between the point and the plane. (2,8,4) 2x + y + z = 5

A: We know, The distance from (p,q,r) to the plane ax+by+cz+d=0 is  a.p+b.q+c.r+da2+b2+c2

Q: Identify and sketch the quadric surface. Use a computer algebra system to confirm your sketch. 9x2 +…

A: Quadric surface: A quadric surface is a graph in the three dimensional space with the equation z=fx,…

Q: Find the perpendicular distance from the point P(9,11,−8) ft to a plane

A:

Q: Find the point on the sphere x +y +z = 4 farthest from the point (1, – 1,1). The point is ( ID:…

A:

Q: Find the standard equation of the sphere. (Let r = 5 and C = (9, 7, 5).)

A: Standard equation of a sphere with radius r and centre at c=(h,k,l) is  (x-h)2+(y-k)2+(z-l)2=r2