The boundary of a lamina consists of the semicircles y = sqrt(1 − x2) and y...

The boundary of a lamina consists of the semicircles

y =

sqrt(1 − x²)

and y =

sqrt(9 − x²)

together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin.

Expert Solution

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milcah answered 1 year ago

The boundary of a lamina consists of the semicircles y = 1 − x2 and y...

The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 25 − x2 together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin. Hint: use polar coordinates

solve for x: [x * sqrt(1+x2)] + ln[x + sqrt(1+x2)] = 25

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