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- If x and y are elements of an ordered integral domain D, prove the following inequalities. a. x22xy+y20 b. x2+y2xy c. x2+y2xyConsider 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?Determine the points on the following sphere: x2 + y2 + z2 = 16 where f(x, y, z) = 3x + 5y + 9z has its minimum and maximum values:
- Suppose S is a smooth surface parametrized by r(u, v) over D = [0, 1] x [0, 1] with ru = <1,2,3> and rv = <-1,0,2>. Find the area of SConsider the following geometry problems in 3-spaceEnter T or F depending on whether the statement is true or false. 1. Two lines either intersect or are parallel 2. A plane and a line either intersect or are parallel 3. Two planes orthogonal to a third plane are parallel 4. Two lines orthogonal to a third line are parallel 5. Two planes parallel to a line are parallel 6. Two lines parallel to a third line are parallel 7. Two lines parallel to a plane are parallel 8. Two lines orthogonal to a plane are parallel 9. Two planes orthogonal to a line are parallel 10. Two planes either intersect or are parallel 11. Two planes parallel to a third plane are parallelSketch the following surfaces. 1) 4x^2+9z^2=9y^2 2)y^2-x^2=z Show all work.
- Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3yEvaluate .n dS and .ndS if F = (x + 2y)i– 3zj +xk, , and S is the surface of 2x + y + 2z = 6 bounded by x =0, x = 1, y =0 and y = 2.Let L be the line segment between (1, 2) and (4, -4). Find the area of the surface generated when L is revolved around the line y=2.