Figure (A) Shows a Vacant Lot with a 80-Ft Frontage

question 91

Multiple Choice

Figure (a) shows a vacant lot with a 80-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, 80], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 80]. To estimate the area of the lot using a Riemann sum, we divide the interval [0, 80] into four 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, and 70. What is the approximate area of the lot? ​ ​ ​

• A) 7,860 sq ft
• B) 7,980 sq ft
• C) 7,910 sq ft
• D) 7,890 sq ft

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Definitions:

Asch Experiment

A social psychology experiment by Solomon Asch studying if and how individuals yielded to or defied a majority group and the effect of such influences on beliefs and opinions.

Group Conformity

The phenomenon where individuals adjust their behaviors, attitudes, or beliefs to match those of the group to which they belong, often due to real or perceived pressure.

Group Size

The number of individuals forming a social group or gathering, which can influence the group's dynamics, interactions, and outcomes.

Specific Purpose

A distinct aim or objective for which something is used, created, or exists.