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- 8.3 27)Visually estimate the location of the centroid of the region shown. Then find the exact coordinates of the centroid.The first quadrant area bounded by y2=8x, x=2 and y=0 is revolved about the x-axis. Find the centroid of the solid revolution.An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it on display. The artwork has constant density and must be balanced at its centroid. The shape of the artwork was created on a computer program then casted and fabricated. The following equation was put into the computer to generate the shape: y=1sin(πx)+5 bounded by x = 0, x = 2, and y = 0 Draw the Lamina in an x-y plane and put a dot where the centroid should be. Show all work and formulas you are using. The centroid is at (¯x,¯y), where ¯x= ¯y=
- 3. Find the coordinates of the centroid of the triangle enclosed by x = 1, y = 0,and y = 4x.(a) Find the centroid of the area between the x axis and one arch of y = sin x.(b) Find the volume formed if the area in (a) is rotated about the x axis.(c) Find Ix of a mass of constant density occupying the volume in (b).An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it on display. The artwork has constant density and must be balanced at its centroid. The shape of the artwork was created on a computer program then casted and fabricated. The following equation was put into the computer to generate the shape:y=1sin(πx)+5y=1sin(πx)+5 bounded by x = 0, x = 2, and y = 0Draw the Lamina in an x-y plane and put a dot where the centroid should be. Show all work and formulas you are using.The centroid is at (¯x,¯y)(x¯,y¯), where
- An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it on display. The artwork has constant density and must be balanced at its centroid. The shape of the artwork was created on a computer program then casted and fabricated. The following equation was put into the computer to generate the shape:y=2sin(πx)+5y=2sin(πx)+5 bounded by x = 0, x = 2, and y = 0Draw the Lamina in an x-y plane and put a dot where the centroid should be. Show all work and formulas you are using.The centroid is at (¯x,¯y) where ¯x = ¯yThe area bounded by y = 3, x = 2, y = -3 and x = 0 is revolved about the y-axis. a.The x-coordinate of its centroid is… b. The y-coordinate of the centroid of the solid is… c. The moment of inertia of the solid is…Find the centroid of the semicircular area inside x2+ y2 = a2 with y ≥ 0. Show the graph for it.