Cross section of two figure:
Ellipsoid: blue color
Sphere: red color
3. Does the ellipsoid 4. surrounding the sphere + v +2? = 1 or is it...
At what points the normal line that passes by the point (-1,-2,1) above the ellipsoid 2x2 + y"2+2°2+7intersects with the sphere x^2+ y 2 zA2 100? (Post all the procedure, not only the answer, please) At what points the normal line that passes by the point (-1,-2,1) above the ellipsoid 2x2 + y"2+2°2+7intersects with the sphere x^2+ y 2 zA2 100? (Post all the procedure, not only the answer, please)
Only need prob 4 3. Geodesics on the sphere. Consider the 2-sphere with coordinates (0,0) and metric dsa = aʼ(do? + sin? 0d$2) Note that a is the constant radius of the sphere. (a) Show that lines of constant longitude (ø = po = constant) are geodesics. (b) Show that the only line of constant latitude (0 = 0o = constant) that is a geodesic is the equator (@0 = 7/2). 4. Parallel transport on the sphere. Consider the 2-sphere...
Calculate the volume of the section of the ellipsoid x^2 ?+ y^2/9 + z^2/4 =? 1 corresponding to −1 ≤ and ≤ 1.
A sphere of radius r has surface area A = 4πr2 and volume V = (4/3) πr3. The radius of sphere 2 is double the radius of sphere 1. (a)What is the ratio of the areas, A2/A1? (b)What is the ratio of the volumes, V2/V1?
(1 pt) Consider the sphere (x - 4)2 + (y - 3)2 + (z - 5)2 25 (a) Does the sphere intersect each of the following planes at zero points, at one point, at two points, in a line, or in a circle? The sphere intersects the xy-plane ? The sphere intersects the xz-plane ? The sphere intersects the yz-plane ? (b) Does the sphere intersect each of the following coordinate axes at zero points, at one point, at two...
2. Consider the line (t) = (4t + 1,3,2-t) and the ellipsoid + + z2 = 1. What is the distance from the point (-3,3,3) on the line to the point where the line intersects the ellipsoid? a) 8/5 b) (2+ 89)/10 c) (2 - 89)/10 d) 62/V10 e) It makes no sense, the line does not intersect the ellipsoid. 3. Suppose f(x,y) is a function such that f.(0,1) = -3 and f(0, 1) = 8. What is the rate...
2 x-I 3. Find the volume of solids enclosed by a paraboloid z x2+ y2 and an x2y2+z2 =6 ellipsoid 4 Sud, a. 2 x-I 3. Find the volume of solids enclosed by a paraboloid z x2+ y2 and an x2y2+z2 =6 ellipsoid 4 Sud, a.
The volume of a sphere is given by V = (4/3)πrr3 , where r is the radius. Compute the volume of a sphere with a radius of 673 pm. State your answer in units of m^3
9. The upper half of the ellipsoid tr + ty? + Z2-1 intersects the cylinder x2 + y2-y 0 in a curves C. Calculate tfe circulation of v y'i+y+3i k around C by using Stokes Theorem. x2 + y2 intersec ts the plane z y in a curve C. Calculate the circulation 10. The paraboloid z of v 2zi+ x j + y k around C by using Stokes Theorem. 9. The upper half of the ellipsoid tr + ty?...
the volume of a sphere is given by v The volume of a sphere is given by V = (4/3)pi r^3, where r is the radius. Compute the volume of a sphere with a radius of 925 pm. State your answer in units of m^3.