Mass In Exercises 21 and 22, use cylindrical coordinates to find the mass of the solid Q of density
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Multivariable Calculus
- Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed when the region bounded in Quadrant I by the axes and the lines x = 9 and y = 5 is revolved about the a) x-axis b) y-axisarrow_forwardMoment of inertia about y-axis of a square plate with surface density f(x, y)= k = constant and vertices with coordinates (0,0), (0.2), (2.0) and (2.2) points ? 14 k 3 A) 16 k 3 В) 13 -k 3 10 D) 3 11 E) 3arrow_forwarduse cylindrical coordinates to find the mass of the solid Q of density ρ.arrow_forward
- Use cylindrical coordinates to find the mass of the solid Q of density p. Q = {(x, y, z): 0 0} p(x, y, z) = karrow_forwardDetermine the location of the centroid of the solid formed by revolving about the y- axis, the area bounded by the curve y=x³, the line y=4 and the y-axis. Zoom image O (0,2.5,0) O (0,2.6, 0) (0, 4.6, 0) O (0, 1.6, 0)arrow_forwarduse spherical coordinates to find the mass of the sphere x2 + y2 + z2 = a2 with the given densityThe density at any point is proportional to the distance between the point and the z-axisarrow_forward
- region pounded by the sphere x² + y² + z² = 9. p) Find the mass of a wire shaped as the left half of the circle x² + y² = 4 if its density is p(x, y) = 3xy². wherearrow_forwardFind the center of mass of the laminas in the figures below obtained by removing squares of side b = 1 from a square of side a = 6. Place the square so that the bottom left corner is at (0, 0). (x, y) = ( (x, y) = 6 6 1 1arrow_forwardUse cylindrical coordinates to find the volume of the solid. Solid inside x2 + y2 + z2 = 16 and outside z = sqrt root ( x2 + y2 )arrow_forward
- Find the mass and center of mass of the lamina for each density. R: square with vertices (0, 0), (a, 0), (0, a), (a, a) (a) p = k m (х, у) %3D( ( b) ρ ky m (х, у) %3D ( (c) p = kx m (x, 7) = (х, у) %3D( IIarrow_forwardFind the mass of a thin plate with density p(x, y) = y occupying the triangle with vertices (0,0). (1,1), and (-1, 1). O 01 € 113 O CHA [10/10 ده استarrow_forwardA fluid has density 1100 kg/m³ and flows with velocity v = xi + yj + zk, where x, y, and z are measured in meters, and the components of are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 49 - x² - y² that lies above the xy plane. kg/s Question Help: Video Submit Question Jump to Answerarrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,