In all of the problems below sketch the situation first 1. Find the centroid of a region under y-...
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...
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...
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.
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...
(10 points) Let R be the region in the first quadrant bounded by the x and y axes and the line y = 1 – 1. Notice R is a triangle with area 1/2 (you do not need to verify this). Find the coordinate of the centroid of R. For extra credit, determine the y coordinate without calculating an integral. (Note: If we regard R as a plate, then the centroid of R can also be thought of as the...
486 (1 point) Sketch the first quadrant region bounded below by the graph of g(x) = - apri or 9(2) = about the y-axis generates a solid whose volume is 2, above by f(x) = 12 – 100 . 6, and at the right by x = 1. Rotating that region (1 point) Find the volume of the solid obtained by rotating the region bounded by the curves y=x?, x=2, x= 3, and y=0 about the line x = 4....
Find the area of the region described. The region in the first quadrant bounded by y = 1 and y=sin x on the interval The area of the region is (Type an exact answer, using a as needed.)
Please do #2
40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 and y (3x-)dA by changing to polar coordinates, where R is the region in the first 3x. Sketch the region. 2. [6 pts) Find the volume below the cone z = 3、x2 + y2 and above the disk r-3 cos θ. your first attempt you might get zero. Think about why and then tweak your integral....
Find the centroid of the region that is bounded below by the x-axis and above by the ellipse 1. Question 1 What are the coordinates of the centroid? (Simplify your answers. Round to four decimal places as needed.) Match the equation with the graph. Include the directrix that corresponds to the focus at the origin. Label the vertices with appropriate polar coordinates. If the equation is an ellipse, label the center as well. 910 35 + 7 sino Question 2...
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1. Find the area of the region bounded by the curves below. Sketch a graph of the region first. a. x = y2, x = VD, y = 0 b. y = x2 – 4, y == x2 + 4