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:

Budget Line

All the consumption bundles available to a consumer who spends all of his or her income.

Price Of Potatoes

The cost at which potatoes are sold in the market, which can vary based on factors such as quality, supply, and demand.

Horizontal Axis

In a graph, the x-axis along which numerical values are plotted, typically representing a variable like time or quantity.

Budget Line

A graphical representation of all the possible combinations of two goods that can be purchased with a given income and prices.