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A thin plate in the shape of a lamina occupies the region bounded by the graphs of y = x² and x = 4y². The plate has a constant density of p = 20- gm cm². Sketch the region, and then find both the mass of the plate, and the center of mass of the plate. Set up an integral for each value and then integrate (Show each step). Then evaluate at the limits using the Fundamental Theorem of Calculus. For each quantity, give both the exact value and a decimal approximation that is accurate to three decimal places.

A thin plate in the shape of a lamina occupies the region bounded by the graphs of y = x² and x = 4y². The plate has a constant density of p = 20- gm cm². Sketch the region, and then find both the mass of the plate, and the center of mass of the plate. Set up an integral for each value and then integrate (Show each step). Then evaluate at the limits using the Fundamental Theorem of Calculus. For each quantity, give both the exact value and a decimal approximation that is accurate to three decimal places.

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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A thin plate in the shape of a lamina occupies the region bounded by the graphs of y = x² and x = 4y². The plate has a constant density of p Sketch the region, and then find both the mass of the plate, and the center of mass of the plate. Set up an integral for each value and then integrate (Show each step). Then evaluate at the limits using the Fundamental Theorem of Calculus. For each quantity, give both the exact value and a decimal approximation that is accurate to three decimal places. gm = 20. cm²
Transcribed Image Text:A thin plate in the shape of a lamina occupies the region bounded by the graphs of y = x² and x = 4y². The plate has a constant density of p Sketch the region, and then find both the mass of the plate, and the center of mass of the plate. Set up an integral for each value and then integrate (Show each step). Then evaluate at the limits using the Fundamental Theorem of Calculus. For each quantity, give both the exact value and a decimal approximation that is accurate to three decimal places. gm = 20. cm²
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