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(1 point) The trough shown below on the left has a length of 1.4 m. All cross-sections parallel to the vertical ends are parabolic with a width of 0.8 m at the top and a height of 0.9 m as shown on the right below. The dashed grey line is at the bottom of the blue curve and is horizontal. Answer the following and use a calculator or a computer algebra system to evaluate the integrals. Round your answer to at least 3 significant figures and include the unit. a. Find the moment of area of the blue-shaded region on the right about the dashed grey line. Moment of area = b. How high is the centroid of the blue-shaded region on the right above? The centroid of the shaded region is above its lowest point c. Find the moment of arc length of the thick blue curve on the right about the dashed grey line. Moment of arc length = d. How high is the centroid of the thick blue curve on the right above? The centroid of the curve is above its lowest point e. The trough has two vertical ends and one curved bottom but no top. How high is the centroid of the entire trough? You may assume that the entire trough is made of the same type of sheet metal whose per area density is uniform. The centroid of the trough is above its lowest point (1 point) The trough shown below on the left has a length of 1.4 m. All cross-sections parallel to the vertical ends are parabolic with a width of 0.8 m at the top and a height of 0.9 m as shown on the right below. The dashed grey line is at the bottom of the blue curve and is horizontal. Answer the following and use a calculator or a computer algebra system to evaluate the integrals. Round your answer to at least 3 significant figures and include the unit. a. Find the moment of area of the blue-shaded region on the right about the dashed grey line. Moment of area = b. How high is the centroid of the blue-shaded region on the right above? The centroid of the shaded region is above its lowest point c. Find the moment of arc length of the thick blue curve on the right about the dashed grey line. Moment of arc length = d. How high is the centroid of the thick blue curve on the right above? The centroid of the curve is above its lowest point e. The trough has two vertical ends and one curved bottom but no top. How high is the centroid of the entire trough? You may assume that the entire trough is made of the same type of sheet metal whose per area density is uniform. The centroid of the trough is above its lowest point

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