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Consider the solid bounded by y = v x2 + z2 and y = 6 with density o(x,y,z) = 35 - y . Assume density
Consider the solid bounded by y = v x2 + z2 and y = 6 with density o(x,y,z) = 35 - y . Assume density is measured in kg/m3. (a) Draw a graph of the given solid and include it with your written work. (b) Set up and evaluate a triple integral using cylindrical coordinates to determine the mass of the solid. (Hint: you may need to reorient the polar plane to rotate about an axis other than the z-axis. ) Evaluate the entire integral by hand, showing all your work and giving an exact answer. m = dy dr de = kg (c) Determine the center of mass of the solid in rectangular coordinates. You may use technology to completely evaluate any integrals. Round your answers to 4 decimal places. ( x , y, Z ) = ( m
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