The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 16 − 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.

Required center of mass

Step-by-step explanation:

Given semcircles are,

whose radious are 1 and 4 respectively.

To find center of mass, , let density at any point is and distance from the origin is r be such that,

where k is a constant.

Mass of the lamina=m= where A is the total region and D is curves.

then,

Then,

Then,

Hence center of mass

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

need more detail

step-by-step explanation:

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