0.5 a= 5 -0.5 2 For the above plot of the ellipsoid ()² + (†)² + (-)². a, b and c are positive integers between 1 and 6 inclusive. Use the mouse to rotate the surface. xb= 3 XC= 5 X Enter an integer or decimal number [more..] = 1, find the parameters a, b and c. Note that
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- Help me. 1. What is the area of the region bounded by the ellipse with the equation x^2+9y^2+3x - 18y + 9 = 0 A. 9/16 π sq. units B. 3/4 π sq. units C. 3/4 π sq. units D. 3 π sq. units 2.The length of the latus rectum for the ellipse with the given equation is x^2+ 4y^2 = 64 A. 2 UNITS B. 4 UNITS C. 16 UNITS D. 32 UNITS 3. Which of the following is true about the curve y^2 = 4x^2/1+x^2? A. The curve is symmetric with respect to the x-axis, y-axis and the origin. B. The curve is symmetric with respect to the x and y axes only. C. The curve is symmetric with respect to the y-axis only. D. The curve is symmetric with respect to the x-axis only.You are given a cylinder S in R3 with equation x = z2 + 2. Let C be the curve in the xz-plane whose equation is the same as that of S. Find the equation of the surface of revolution generated by revolving C about the x-axis.The given curve is rotated about the y-axis. Find thearea of the resulting surface. y = 1 -x2 0≤ x ≤1
- 9.3.16. Compute the surface area of the surface obtained by revolving the given curve about the indicated axis. (a) about the x-axis (b) about x = 4 please answer both a and b 1 to t to 2 x=4t, y=sqrt(t^2) but if you can only do one please do bYou are given a cylinder S in R3 with equation x = z2 + 2. Let C be the curve in the xz-plane whose equation is the same as that of S. Find an equation of the surface of revolution generated by revolving C about the z-axis. (Please sketch the graph)10.2 37)Find the area enclosed by the given parametric curve and the y-axis.
- 7. Graph the surface z = f (x, y) = x ^ 2 + 2 y ^ 2 - 2x + 4y + 2. Also write the reduced equation of the intersection curve of the surface with the z = 0 plane.Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V , and rotated along the y-axis with constant angular speed ω. This makes the liquid rotate, and eventually at the same angular speed as the container. The surface of the liquid becomes convex as the centrifugal force on the liquid increases with the distance from the axis of the container. The surface of the liquid is a paraboloid of revolution generated by rotating the parabola y = h + ω2x2/2g around the y-axis, where g is gravitational acceleration and h is shown below. (You can take g=32ft/s2 or 9.8m/s2). Express h as a function of ω. (2) At what angular speed ω will the surface of the liquid touch the bottom? At what speed will it spill over the top? (3) Suppose the radius of the container is 2 ft, the height is 7 ft, and the container and liquid are rotating at the same constant angular speed ω. The surface of the liquid is 5 ft below the top of the tank at the central…Consider the ellipsoid x2+4y2+z2=18. The implicit form of the tangent plane to this ellipsoid at (−1,−2,−1)is_________________. The parametric form of the line through this point that is perpendicular to that tangent plane is L(t)=_______________
- Find a generating curve and the axis of revolution for the surface x2 + 3y2 + z2 = 9.Consider the surface S shown in the graph, whose parametrization is given by: r (u, v) = (1 + 2v, 3uv, 4 - u2), where 0 ≤ u ≤ 2, 0 ≤ v ≤ 2 (see attached image with the graph) The surface differential, dS, is given by: (see image with possible answers)a. Find a parametrization for the hyperboloid of one sheet x2 + y2 - z2 = 1 in terms of the angle u associated with the circle x2 + y2 = r2 and the hyperbolic parameter u associated with the hyperbolic function r2 - z2 = 1. (Hint: cosh2 u - sinh2 u = 1.) b. Generalize the result in part (a) to the hyperboloid (x2/a2 ) + (y2/b2 ) - (z2/c2 ) = 1.