The shaded region shown in the accompanying figure is a parking lot for a shopping mall. The dimensions are in hundreds of feet. To improve parking security, the mall manager plans to place a surveillance kiosk in the center of the lot (see the definition preceding Exercises 65 and 66).

Where would you place the kiosk? Describe the location you choose in terms of the coordinate system indicated in the figure.

Definition

Let f(x) be a continuous function with f(x) ≥ 0 for a ≤ x ≤ b. Let R be the region with area A that is bounded by the curve y = f(x), the x axis, and the lines x = a and x = b. Then the centroid (or center) of R is the point (x̅, y̅), where

Transcribed Image Text:

2x² - y² = 1 1 Shops 5 Shops -X