Question : 31) If f(x, y) = (3000ey)/(1 + |x|/2) represents the : 1757212

31) If f(x, y) = (3000ey)/(1 + |x|/2) represents the population density of a planar region on Earth, where x and y are measured in miles, find the number of people within the rectangle -9 ≤ x ≤ 9 and -4 ≤ y ≤ 0.

A) 12,000(1 - e-4) ln 11/2 ≈ 20,082 B) 3000(1 - e-4) ln 11/2 ≈ 5021

C) 6000(1 - e-4) ln 5 ≈ 14,124 D) 6000(1 - e-4) ln 11/2 ≈ 10,041

32) z = 6x²y; R = {(x, y): 0 ≤ x ≤ 4, 0 ≤ y ≤ 3}

A) 576 B) 2256 C) 1256 D) 676

33) z = x² + y²; R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}

A) 4/3 B) 2/3C) 8/3 D) 1/3

34) z = 8x + 4y + 7; R = {(x, y): 0 ≤ x ≤ 1, 1 ≤ y ≤ 3}

A) 36 B) 38 C) 26 D) 28

35) z = 4x² + 9y²; R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}

A) 13/3 B) 5/3 C) 17/3 D) 26/3

36) z = x/y ; R = {(x, y): 0 ≤ x ≤ 1, 1 ≤ y ≤ e}

A) 1/6 B) 1/3 C) 1/4 D) 1/2

37) The coordinate axes and the line x + y = 3

38) The coordinate axes and the line x/6 + y/8 = 1

39) The lines x = 0, y = 7x, and y = 5

40) The parabola y = x² and the line y = 7x + 30