MATH 101 HOMEWORK 9
Due on Wednesday, November 19
Covers sections 7.4, 7.5, 7.8. For full credit, show all work.
2. (5 marks) Find the mass of the solid ball of radius 4 cm centered at the origin, if the
density at a point P is r 2 g/cm3 , where r is the distance from P to the x axis.
2. (5 marks) Find the mass and the centre of mass of the solid lying above the plane
z = 0, inside the sphere x2 + y 2 + z 2 = 100 cm2 , and outside the sphere x2 + y 2 + z 2 = 36
cm2 , if the density at (x, y, z) is z 2 + 1 g/cm3 .
3. (5 marks) Find the centroid of the region in Figure 7.41(b) in the textbook.
4. Suppose that a point P is chosen at random from the planar region 0 ≤ x ≤ π/3,
0 ≤ y ≤ sin x. We define the random variable X to be the x-coordinate of P .
(a) (2 marks) Find the probability density function f for X.
(b) (3 marks) Find the expectation of X.
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