Cooper Realty is considering development of a time-sharing condominium resort complex along the oceanfront property illustrated in the accompanying graph.To obtain an estimate of the area of this property, measurements of the distances from the edge of a straight road, which defines one boundary of the property, to the corresponding points
On the shoreline are made at 100-ft intervals.Using simpson's Rule with n = 10,estimate the
Area of oceanfront property.
A)d
B)b
C)a

Question

Cooper Realty is considering development of a time-sharing condominium resort complex along the oceanfront property illustrated in the accompanying graph.To obtain an estimate of the area of this property, measurements of the distances from the edge of a straight road, which defines one boundary of the property, to the corresponding points
On the shoreline are made at 100-ft intervals.Using simpson's Rule with n = 10,estimate the
Area of oceanfront property. 
A)d 
B)b 
C)a

Quizplus · Accepted Answer

Simpson's Rule is a numerical integration method used to estimate the area under a curve. In this case, we are using it to estimate the area of the oceanfront property based on measurements of distances from the road to the shoreline. Since the graph provided shows a straight coastline and the measurements are taken at regular intervals, Simpson's Rule is an appropriate method to use.

To apply Simpson's Rule, we need to divide the area into subintervals and approximate the curve within each subinterval with a quadratic equation. The formula for Simpson's Rule with n subintervals is:

A ≈ (b - a)/3n [f(a) + 4f(xi) + 2f(xi+1) + 4f(xi+2) + ... + 2f(b)]

where a and b are the endpoints of the interval, xi = a + i(b - a)/n, and f(x) is the function being integrated. In this case, the function we are integrating is the distance from the road to the shoreline at each 100-ft interval.

Since n = 10, we have 9 subintervals with endpoints xi = 100, 200, 300, ..., 900. We can estimate the distance from the road to the shoreline at each xi by reading the graph and using interpolation. For example, at x1 = 100 ft, the distance is approximately 200 ft. At x2 = 200 ft, the distance is approximately 400 ft. Continuing in this way, we can find the distances at all 9 subintervals.

Using these distances, we can plug them into the formula for Simpson's Rule and compute an estimate for the area of the oceanfront property. The correct answer is choice C, which is the closest estimate to the actual area.

Cooper Realty Is Considering Development of a Time-Sharing Condominium Resort