Answer:
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,

- Now, x-coordinate of center of mass is
. in polar coordinate 




![=3k\big[-\cos\theta\big]_{0}^{\pi}](https://tex.z-dn.net/?f=%3D3k%5Cbig%5B-%5Ccos%5Ctheta%5Cbig%5D_%7B0%7D%5E%7B%5Cpi%7D)
![=3k\big[-\cos\pi+\cos 0\big]](https://tex.z-dn.net/?f=%3D3k%5Cbig%5B-%5Ccos%5Cpi%2B%5Ccos%200%5Cbig%5D)

Then, 
- y-coordinate of center of mass is
. in polar coordinate 




![=3k\big[\sin\theta\big]_{0}^{\pi}](https://tex.z-dn.net/?f=%3D3k%5Cbig%5B%5Csin%5Ctheta%5Cbig%5D_%7B0%7D%5E%7B%5Cpi%7D)
![=3k\big[\sin\pi-\sin 0\big]](https://tex.z-dn.net/?f=%3D3k%5Cbig%5B%5Csin%5Cpi-%5Csin%200%5Cbig%5D)

Then, 
Hence center of mass 
<span>You only need an estimate? Great. Think of the necessary material as 6 yards, so ten costumes would take 60 yards. Then think of the fabric on hand as 240 yards, so taking 60 yards away from that would leave [an estimated] 180 yards of fabric.
For an equation, use:
F" = F' - 5.8 C
Where F' is the initial fabric stock, F" is the remaining fabric, and C is the count of costumes.
In exact numbers, the formula works out to:
F" = 238.2 - (5.8 * 10)
F" = 180.2
The estimate was very close.
Good luck.</span>
Answer:
Yes,
Step-by-step explananation
The quotient of two rational numbers is always rational, and the reason for this lies in the fact that the product of two integers is always an rational number.
Answer:
The area of the polygon is 
Step-by-step explanation:
Sketch the polygon to obtain the figure in the attachment.
The polygon can then be divided into a rectangle and a triangle.
The area of the polygon

We use the absolute value method to find the lengths



