Use polar coordinates to describe the region shown. y L -6 -4 -2 6 OR ((r, e): 0 ≤rs 6 cos(38), 0 ≤ 0 ≤n} OR={(r, 0): 0 ≤rs 3 cos(60), 0≤esn) OR= {(r, e): 0 ≤rs 3 sin(60), 0≤es T} OR= {(r, 0): 0 ≤rs sin(60), 0 ≤es T} OR = {(r, 0): 0 ≤rs 6 sin(30), 0 ≤es n} 4 -X
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- Consider the region bounded by the graphs of y = sin-1 x, y = 0,and x = 1/2. Find the centroid of the region.help me those question 1. Find the centroid (x¯,y¯) of the region bounded by the two curves y=12√x and y=3x. y=4x^2+9x, y=0, x=0, and x=8. 2.Find the centroid (x¯,y¯) of the region bounded by:y=e^2x, y=0, x=0, and x=3.An ice cream cone can be modeled by the region bounded by thehemisphere z = √8 − x2 − y2 and the cone z = √x2 + y2. We wish to find the volumeof the ice cream cone.(a) sketch this ice cream cone in 3 dimensions. (b) Explain why a polar coordinates interpretation of this problem is advan-tageous. include a comparison to the double integral which results fromthe rectangular coordinates interpretation of this problem. (c) Restate using polar coordinates, r and θ, statethe bounds on each.(d) Set up and evaluate the double integral corresponding to the volume ofthe ice cream cone.
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