2.8 A mass density in space is given by ρ(r, z) ¼ r(r + a) + z(z + d) kg/m3 (in cylindrical coordinates). (a) Calculate the total mass of a cylinder of length d, radius a, centered at the origin with its axis along the z axis.
(b) Calculate the total mass of a sphere of radius a centered at the origin.

centre = (- 2, 3 ), radius = 3

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + 4x + y² - 6y = - 4

Using the method of completing the square.

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(2)x + 4 + y² + 2(- 3)y + 9 = - 4 + 4 + 9, that is

(x + 2)² + (y - 3)² = 9 ← in standard form

with centre = (- 2, 3 ) and r = = 3