The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 64 − 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 proportional to its distance from the origin.

The center mass of the lamina =  

Step-by-step explanation:

Let take a look at the boundary of the lamina that comprises of the semicircles and

We are also informed that the density at any point is proportional to its distance from the origin.

Thus, the main task required is to find the center mass of the lamina.

In as much as the density is proportional to the distance from the origin;

Then;

Thus; the mass of the lamina is determined as:

Now, about the y-axis, the moment of the entire lamina can be computed as:

Similarly; about the x-axis, the moment of the entire lamina can be computed as:

Hence,  The center mass of the lamina is:

the answer to the expression is 83

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000

answer is 10,500,000 nappies