Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) | 1 ≤ x ≤ 9, 1 ≤ y ≤ 4}; rho(x, y) = ky2

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

Let's solve this integral:

So the mass will be:

Now we need to find the x-coordinate of the center of mass.

Now we need to find the y-coordinate of the center of mass.

Therefore the center of mass is:

I hope it helps you!

the equation for this situation is y=122+45. to solve the equation you would add 45 and 122 to get a total of 167lbs. in conclusion, grace's weight eight weeks ago was 167lbs.