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Consider the plate bounded by y2 = 8x and x = 2 with density 8 = 2-x. (a) Sketch a graph of the plate. Shade in the region and number the axes so that the important points on the plate can be read from the graph. (b) Express the mass of the plate as a double integral and evaluate to find the mass. (c) Express the x-coordinate of the center of mass of the plate as a double integral and evaluate to find the value of . As a side note, by the symmetry of the plate and density, the y-coordinate of the center of mass y = 0. It might be good practice to confirm this though.

Consider the plate bounded by y2 = 8x and x = 2 with density 8 = 2-x. (a) Sketch a graph of the plate. Shade in the region and number the axes so that the important points on the plate can be read from the graph. (b) Express the mass of the plate as a double integral and evaluate to find the mass. (c) Express the x-coordinate of the center of mass of the plate as a double integral and evaluate to find the value of . As a side note, by the symmetry of the plate and density, the y-coordinate of the center of mass y = 0. It might be good practice to confirm this though.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the plate bounded by y² = 8x and x = 2 with density d = 2 - x. (a) Sketch a graph of the plate. Shade in the region and number the axes so that the important points on the plate can be read from the graph. (b) Express the mass of the plate as a double integral and evaluate to find the mass. (c) Express the x-coordinate of the center of mass of the plate as a double integral and evaluate to find the value of . As a side note, by the symmetry of the plate and density, the y-coordinate of the center of mass y = 0. It might be good practice to confirm this though.
Transcribed Image Text:Consider the plate bounded by y² = 8x and x = 2 with density d = 2 - x. (a) Sketch a graph of the plate. Shade in the region and number the axes so that the important points on the plate can be read from the graph. (b) Express the mass of the plate as a double integral and evaluate to find the mass. (c) Express the x-coordinate of the center of mass of the plate as a double integral and evaluate to find the value of . As a side note, by the symmetry of the plate and density, the y-coordinate of the center of mass y = 0. It might be good practice to confirm this though.
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