Mass In Exercises 25-28, find the total mass of the wire with density
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- Please provide Handwritten answer. Advanced Math We consider a thin plate occupying the region D located in the upper half-plane (where y ≥ 0) and between the parabolas of equations : y = 2 - x2 and y = 1 - 2x2 The density of the plate is proportional to the distance from the x axis. a) Calculate the moments of inertia (second moments) of the plate with respect to the coordinate axes.b) Is it easier to rotate the plate around the x-axis or the y-axis? Justify your answer.arrow_forwardThe question is: Locate the centroid of the shaded area (all dimensions are in meter)arrow_forwardUse spherical coordinates. Let H be a solid hemisphere of radius 5 whose density at any point is proportional to its distance from the center of the base. (Let K be the constant of proportionality.) (a) Find the mass of H. (b) Find the center of mass of H. (Assume the upper hemisphere of a sphere centered at the origin.) (x, y, z) = ( (c) Find the moment of inertia of H about its axis Iz =arrow_forward
- A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter 6 ft. Set-up the integral for the force exerted by the milk on one end of the tank when the tank is full. O 129.2 25°(6. (6-y)√6y-y² dy 0 O 1.655° (6-y)√√6y-y²dy O 64.6 (3-y)√√6y-y² dy 129.2 [13-yi√6y-y²dy 64.6arrow_forwardFill in the box. I will rate and like. Thank you.arrow_forwardFind the moments of inertia I, I, Io for a lamina that occupies the part of the disk x² + y² ≤ 4 in the first quadrant if the density at any point is proportional to the square of its distance from the origin. (Assume that the coefficient of proportionality is k.) Ix = Iy= Io = Need Help? Read Itarrow_forward
- how do i solve the attached calculus problem?arrow_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_forwardEvaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =arrow_forward
- Using spherical coordinates calculate ſſſzsqrt(x²+y²)dV where E={(x,y,z) | x²+y²+z²0,y>0,z>0}arrow_forwardCoulomb's law states the electric field E due to a point charge q at the origin is given by E = kar where k is a constant and r = xi + yj + zk. Determine the flux out of a sphere x? + y? + z² = b².arrow_forwardCALCULUS IIarrow_forward
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