g(t) = 3.49 t^3 - 43.21 t^2 + 142.43 t - 1.75. Estimate the elevation of the bal

Question

g(t) = 3.49 t^3 - 43.21 t^2 + 142.43 t - 1.75. Estimate the elevation of the balloon after Five minutes using this polynomial. A piece of wood paneling must be cut in the shape shown in the figure. The coordinates of several points on its curved surface are also shown (with units of inches). a. Estimate the surface area of the paneling using the Trapezoid Rule. b. Estimate the surface area of the paneling using a left Riemann sum. c. Could two identical pieces be cut from a 9-in by 9-in piece of wood

Explanation / Answer

b) The points are given by (x,f(x)) : (0,0), (1,2.5),(2,3.2), (3,4), (4,6), (6,7), (7.5,3),(8,0)

The left end points are 0, 1,2,3,4,6,7.5

Draw rectnagles at these points

The surface area is approximated by area of these rectangles added together as follows:

Surface area = [ (1)f(0) + (1)f(1) + (1)f(2) + (1)f(3) + (2)f(4) + (1.5)f(6) + (1.5)f(7.5) ]

=> SA = [0 + 2.5 + 3.2 + 4 + 12 + 10.5 + 4.5] = 36.7

(c) No

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