3. Suppose that a lamina occupies the region D in the xy-plane which is bounded by...

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3. Suppose that a lamina occupies the region D in the xy-plane which is bounded by the semicircles given by y= 4-x and y = 1-x together with the portions of the x-axis that join the semicircles. Moreover, suppose that the lamina has density function: p(x,y)=. 1 (assume the units on density are kg/m). (a) (0.5pt) Carefully sketch a picture of the region D in the xy-plane. (b) (1pt) Find the exact mass of the lamina. Hint: work in polar. (c) (2pts) Find the exact coordinates of the center of mass of the lamina. Hint: work in polar. 3. Suppose that a lamina occupies the region D in the xy-plane which is bounded by the semicircles given by y= 4-x and y = 1-x together with the portions of the x-axis that join the semicircles. Moreover, suppose that the lamina has density function: p(x,y)=. 1 (assume the units on density are kg/m). (a) (0.5pt) Carefully sketch a picture of the region D in the xy-plane. (b) (1pt) Find the exact mass of the lamina. Hint: work in polar. (c) (2pts) Find the exact coordinates of the center of mass of the lamina. Hint: work in polar.