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

question 159

Multiple Choice

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? ​ ​ ​

• A) 7,900 sq ft
• B) 8,600 sq ft
• C) 8,100 sq ft
• D) 8,400 sq ft

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Definitions:

Shaping

A method of operant conditioning in which successive approximations of a desired behavior are reinforced until the exact behavior is achieved.

Reinforcer

In operant conditioning, any event that strengthens the behavior it follows.

Conditioned Stimulus

An initially neutral stimulus that, upon association with an unconditioned stimulus, elicits a conditioned response.

Unconditioned Stimulus

A trigger that inherently and effortlessly evokes a reaction without the need for previous learning.