
Center of Mass
I have two problems here that i cant figure out
EDIT find the center of mass given that the mass is constant
1.)the "triangular" region in the first quadrant between the circle x^2+y^2=9 and the lines x=3 and y =3 (Hint: use geomentry to find the area).
2.) Find the center of mass of a thin plate covering the region between the xaxis and the curve y= 2/x^2. 1<=x<=2 if the plates density ate the point (x,y)
is delta(x)=x^2

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(1)You can view the the region as subtracting the rectangle from the quatercircle.
Now the centroid of the rectangle is trivial (1.5,1.5) und the area is 9.
The centroid of a quatercircle is located on the line $\displaystyle y=x$ (that is symettry) and is $\displaystyle \frac{4r}{3\pi}$ (a known formula). In this case $\displaystyle r=3$. Thus the centroid is $\displaystyle \frac{4(3)}{3 \pi}=\frac{4}{\pi}=1.27$. Thus, $\displaystyle (x,y)=(1.27,1.27)$. And has area $\displaystyle \frac{1}{4}\pi (3)^2=7.06$.
Thus, by the composite centroid formula we have,
$\displaystyle \bar x= \frac{(1.5)(9)(1.27)(7.06)}{9+7.06}$
$\displaystyle \bar y=\frac{(1.5)(9)(1.27)(7.06)}{9+7.06}$

hmmm.... my book say's i should get 2/(4pie).... i think ur #### gives me the c of m of the semicircle... i want to find the c of m of the triangular shape made by the semicircle and x=3 and y=3