. (15.4) A thin lamina is formed by considering the region inside the circle x 2 + y 2 = 6y and outside the circle x 2+y 2 = 9. Find the center of mass of the lamina if the density at any point (in grams per meter squared) is inversely proportional to its distance from the origin. Follow up question: why do we not care what the constant of proportionality is?

Center of mass=

Step-by-step explanation:

Given equation of circles are,

To convert into parametric equation let

we get,

and

when,

Therefore density function is,

where k is constant of proportionality.

Then,

mass=m=

By the symmetry of the domain and the function f(x)=x, and,

Hence,

Center of mass=

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.