The manufacturer of a boat needs to approximate the center of mass of a section of the hull. A coordinate system is superimposed on a prototype (see figure). The measurements (in feet) for the right half of the symmetric prototype are listed in the table.

(a) Use Simpson’s Rule to approximate the center of mass of the hull section.
(b) Use the regression capabilities of a graphing utility to find fourth-degree polynomial models for both curves shown in the figure. Plot the data and graph the models.
(c) Use the integration capabilities of a graphing utility and the models to approximate the center of mass of the hull section. Compare with the result in part (a).

Transcribed Image Text:

X 7 -2.0 0 -1.0 1.0 d 0.50 0.5 y 1.50 1.45 d 1.0 1.0 2.0 1.30 X 0.99 0.48 0.43 0.33 0 1.5 2 0