1. Find the mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola {image} and the line y = x - 2; {image} 1. 2.
{image}
none of those 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. A lamina occupies the part of the disk {image} in the first quadrant
A lamina occupies the part of the disk {image} in the first quadrant. Find its center of mass if the density at any point is proportional to the square of its distance from the origin. 1. 2.
{image}
none of those 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Use a computer algebra system to find the moment of inertia I0 of the lamina that occupies the region D and has the density function {image} if {image} Select the correct answer. The choices are rounded to the nearest hundredth.
28.8
none of these
38.8
18.8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Is the following function a joint density function? {image}
is a joint density function
unable to define
is not a joint density function 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. When studying the spread of an epidemic, we assume that the probability that an infected individual will spread the disease to an uninfected individual is a function of the distance between them. Consider a circular city of radius 25 mi in which the population is uniformly distributed. For an uninfected individual at a fixed point A(x0, y0), assume that the probability function is given by {image} where d(P,A) denotes the distance between P and A. Suppose the exposure of a person to the disease is the sum of the probabilities of catching the disease from all members of the population. Assume that the infected people are uniformly distributed throughout the city, with k infected individuals per square mile. Choose a double integral that represents the exposure of a person residing at A for k = 45 if D is the disk with radius 25 mi centered at the center of the city.
{image}
none of these 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50