Figure (A) Shows a Vacant Lot with a 100-Ft Frontage

question 226

Short Answer

Figure (a) shows a vacant lot with a 100-ft frontage in a development.To estimate its area, we introduce a coordinate system so that the x-axis coincides with the edge of the straight road forming the lower boundary of the property, as shown in Figure (b).Then, thinking of the upper boundary of the property as the graph of a continuous function f over the interval [0, 100], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 100].To estimate the area of the lot using a Riemann sum, we divide the interval [0, 100] into five equal subintervals of length 20 ft.Then, using surveyor's equipment, we measure the distance from the midpoint of each of these subintervals to the upper boundary of the property.These measurements give the values of f(x) at x = 10, 30, 50, 70, and 90.What is the approximate area of the lot? __________ square feet

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Definitions:

Garden of Earthly Delights

A triptych painting by Hieronymus Bosch, depicting a vivid and allegorical panorama of fantastical, earthly, and heavenly scenes.

Triptych

An art piece consisting of three panels that are hinged together and can be displayed either folded or extended, often used for altarpieces.

Battle of Issus

The historic confrontation in 333 BC between Alexander the Great and the Persian king Darius III, notable for Alexander's significant victory.

Contemporary Conflict

Modern or currently ongoing disputes or wars between states, groups, or ideologies, often involving issues such as territory, religion, and resources.