A lamina occupies the part of the disk x2 + y2 ≤ 49 in the first quadrant. Find its center of mass if the density at any point is proportional to its distance from the x-axis. (x, y) =

xcm = 21/4

ycm = 21/4

Step-by-step explanation:

The region of integration (part of the disk x ² +y² ≤ 49 in the first quadrant) is

described easily in polar coordinates as the set of all (r, θ) with 0 ≤ r ≤ 7 and 0 ≤ θ ≤  π /2 .

Also, the density is ρ(x, y) = k*y = k*r*Sin θ , where k is a constant of  proportionality.

We can see the solution in the pic shown.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

560

hope this : )