Use polar coordinates to find the volume of the solid that is above the
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- Find the coordinates of the centroid of the region bounded by y=10x² and y=2x³. The region is covered by a thin, flat plate. Find the coordinates of the centroid of the solid generated by revolving the region bounded by y=7-x, x=0, and y=0 about the y-axis. Assume the region is covered by a thin, flat plate. The coordinates of the centroid are (Type an ordered pair.) The coordinates of the centroid are (Type an ordered pair. Round each coordinate to two decimal places as needed.) ECCO d=cm (Round to one decimal place as needed.) Find the center of mass (in cm) of the particles with the given masses located at the given points on the x-axis. 36 g at (-3.7,0), 29 g at (0,0), 21 g at (2.2,0), 80 g at (2.9,0)arrow_forwardFind the volume of the solid by subtracting two volumes. the solid enclosed by the parabolic cylinders y = 1 - x², y = x² - 1 and the planes x + y + z = 2, 3x + 6y -z + 15 = 0arrow_forwardUsing polar coordinates, evaluate the volume of the solid in the first octant bounded by thehemisphere (Handwritten please)arrow_forward
- Find the volume of the solid under the surface z = 3x + 5y2 and above the region in the first quadrant bounded by y = x³ and y = 4x. Use polar coordinates to find the volume of the solid that is bounded by the paraboloids z = 16-r² - y², z = x² + y² - 16. Use polar coordinates to find the volume of the solid that is bounded by the plane z = 0 and the cone z = 3-√√√x² + y². . Find the area enclosed by r = cos(30) and the cardioid r = 1 + cos(0). pu mi 1. Fin 2. Fin 3. Con 4. Comarrow_forwardFind the center of mass of a thin plate of constant density & covering the given region. The region bounded by the parabola y = 3x - 2x° and the line y = - 3x The center of mass is O (Type an ordered pair.)arrow_forwardQ1- Determine the coordinates of the centroid of the area.: ¥y y=x,arrow_forward
- Use spherical coordinates to describe the region above the xy-plane between the spheres of radius 1 and 3 centered at the origin. Determine the Cartesian equation of the surface with spherical coordinate equation ρ = 2cosθsinφ−2sinθsinφ+2cosφ. It turns out this describes a sphere. What is the center and radius of this sphere?arrow_forwardUsing polar coordinates, evaluate the volume of the solid in the first octant bounded by thehemisphere (Handwritten pls)arrow_forwardFind the volume of the solid by subtracting two volumes. the solid enclosed by the parabolic cylinders y = 1 − x2, y = x2 − 1 and the planes x + y + z = 2, 3x + 4y − z + 17 = 0arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,