4. Find the centroid of the area bounded by the curve x2 (y-4), the x-axis and the y-axis on the first quadrant. A....
Math232 2 Consider the region in first quadrant area bounded by y x,x=6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method, and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution Find the moment of inertia of the solid of revolution with respect to the x-axis. d) Math232 2 Consider...
Create a bucket by rotating around the y axis the curve y=2ln(x−4)y=2ln(x-4) from y = 0 to y = 4. If this bucket contains a liquid with density 820 kg/m3 to a height of 3 meters, find the work required to pump liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity
6. (20 points) Find the centroid of the region in the first quadrant bounded by the z-axis. 1-y2, and the line x + y 2. 6. (20 points) Find the centroid of the region in the first quadrant bounded by the z-axis. 1-y2, and the line x + y 2.
Math23 2 Consider the region in first quadrant area bounded by y x, x 6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution. c) Find the coordinates of the centroid of the plate; on the sketch above, show the vertical...
The shaded area shown below is bounded by the line x - 9m on the left, the x-axis on top, and the curve y - (-18x + x2) m on the right. 9 m 18 m y=(-18x+x®) m -81 m Determine the coordinates of the centroid of the area in meters. m y = m Determine the coordinates of the centroid of the shaded area in millimeters. y 4 mm y = (0.9x* - 57.6 x) mm mm XI mm
Create a bucket by rotating around the y-axis the curve y=5ln(x−4) from y = 0 to y = 6. If this bucket contains a liquid with density 720 kg/m3 filled to a height of 2 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity. Work =_____ Joules
The shaded area shown below is bounded by the line x = 9 m on the left, the x-axis on top, and the curve y = (-18x + x2) m on the right. 9 m 18 m y=(-18 x + x) m -81 m Determine the coordinates of the centroid of the area in meters. m IX I m
Calculus Find the centroid of the region in the first quadrant bounded by the given curves. y = x4, x=yt (3, 3) = ( A vertical dam has a semicircular gate as shown in the figure. The total depth d of the figure is 14 m, the height h of air above the water level is 2 m, and the width w of the gate is 2 m. Find the hydrostatic force against the gate. (Round your answer to the...
Find the net area and the area of the region bounded by y= 8 cos x and the x-axis between x--2 and x = π. Graph the function and find the region indicated in this question The net area is(Simplify your answer.) Find the net area and the area of the region bounded by y= 8 cos x and the x-axis between x--2 and x = π. Graph the function and find the region indicated in this question The net...
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4