The National Park Service has conducted a cactus Distance, x (miles east) 10 20 30 census in Arizona. In order to collect data, the service divided the desert into a grid whose lines are 10 miles apart in each direction. The entries in the table to the right represent thousands of cacti per square mile at grid points in Saguaro East National Park, where the visitor center is located at (0,0). 8.5 8.2 7.9 8.1 Distance, y 10 9.5 10.6 10.5 10.1 (miles south) 20 9.3 10.5 10.4 9.5 30 8.3 8.6 9.3 9.1 (a) Let f(x, y) be the number of cacti (in thousands) per square mile x miles east and y miles south of the c30 -30 visitor center. Explain what I| $(x,y) dy dr represents in the context of this problem. (b) Give the best estimate you can based on the data of the number of cacti in the 30 by 30 test area.

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