Q

View an example | 11 parts remaining X Geographers measure the geographical center of a country (which is the centroid) and the population center of the country (which is the center of mass computed with the population density). A hypothetical country is shown (-4,4) (4,4 ) in the figure to the right with the location and population of five towns. Assuming no one lives outside the towns, (-2,2) find the geographical center of the country and the population center of the country. A B Pop. = 13,000 C (2,3) Pop. = 18,000 (2, 1 2) (2,0) (-3, -2) (-2)-2) Pop. = 25,000 Pop. = 12,000 (-4,-4) (4,-4) Pop. = 1,000 MB = 24 Determine the mass of region C. Notice that the region is a rectangle. mc = 16 Finally, use the masses of each of the subregions to find the mass of the whole region. m = mA + mB + mc = 16+24+ 16 = 56 Add. Determine the limits of integration for x for region A. The lower limit is - 4 and the upper limit is - 2. Determine the limits of integration for y for region A. The lower limit is - 4 and the upper limit is 4.Geographers measure the geographical center of a country (which is the centroid) and the population center of the country (which is the center of mass computed with the population density). A hypothetical country is shown in the figure to the right with the location and population of five towns. Assuming no one lives outside the towns, find the geographical center of the country and the (- 16,16) population center of the country. (16,16) (-8,8) Pop. = 11,000 (8,1 1) Pop. = 16,000 (-8, -8) (8,-8) (8.0) ( - 14, -8) Pop. = 23,000 Pop. = 16,000 (- 16, -16) (16, - 16) Pop. = 7,000 For the geographical center, determine the double integrals to be used to most efficiently find My, the region's first moment about the y-axis. For the geographical center calculations, assume a density of 1. Use increasing limits of integration. Divide the region into three sections, going from left to right. 00 00 00 My = Jayax + S S (Dayax + J J () dy dx (Type exact answers.)