) Consider the surface given by a-y-z? = 0. Use the method of traces to identify the cross sections of the surface when a =1 and when z = -2. Your sketch should include at least 3 major points and give the general shape of the curve. Be sure to label your axes. Cross section when r = 1 Cross section when z = -2
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- Find an equation for the surface obtained by rotating the curve y = sqrt(x) about the x-axis. Identify the surface. You must show all work to receive full credit.Describe the surface. x2 − y2 = 5 Write an equation for the cross section at z = −5 using x and y.) (Write an equation for the cross section at z = 0 using x and y.) (Write an equation for the cross section at z = 5 using x and y.)Find the areas of the surfaces generated by revolving the curves about the indicated axes. If you have a grapher, you may want to graph these curves to see what they look like. y =(x)^1/2 , 3/4 … x … 15/4; x-axis
- Find the areas of the surfaces generated by revolving the curves about the indicated axes. If you have a grapher, you may want to graph these curves to see what they look like. y =(x + 1)^1/2 , 1 … x … 5; x-axisHow would I solve this problem? Find an equation for the surface of revolution formed by revolving the curve in the indicated coordinate plane about the given axis. Equation of Curve: z^2=64y Coordinate Plane: yz-plane Axis of Revolution: y-axisUse traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) y = 3z2 − 3x2 (Write an equation for the cross section at z = −1 using x and y.) (Write an equation for the cross section at z = 0 using x and y.) (Write an equation for the cross section at z = 1 using x and y.) (Write an equation for the cross section at y = −1 using x and z.) (Write an equation for the cross section at y = 0 using x and z.) (Write an equation for the cross section at y = 1 using x and z.) (Write an equation for the cross section at x = −1 using y and z.) (Write an equation for the cross section at x = 0 using y and z.) (Write an equation for the cross section at x = 1 using y and z.)
- Match the equation with the surface it defines. Identify the surface by type (paraboloid, ellipsoid, etc.). 3x2+3z2 = 54. Choose the correct graph of the equation below.(b) Find the equation of the level curve which passes through the point (x, y) = (3, 4). (c) Sketch the cross-section of the surface in the xz plane. And surface SThe parametric equations x=2acot(θ),y=2asin^2(θ) describe the curve known as the witch of Maria Agnesi. With a=7, suppose this curve is rotated about the x-axis. Estimate the area of the resulting surface using Simpson's Rule with n=4. Make sure your answer is correct to three decimal places. Surface Area?
- Find the area of the surface obtained by rotating the curve y=4x3 from x=0 to x=2 about the x-axis. The area is square units.The curve given by x =sqrt(a2+y2) where -a ≤ y ≤ a; is rotated about the y –axis. Find the resultingarea of the surfaceFind an equation of the surface of revolution generated by revolving the plane curve about the indicated axis. Draw a sketch of the surface. (a) x² = 4y; about the y - axis