Given f(x) > 0 with f ′(x) < 0, and f ′′(x) > 0 for all x in the interval [0, 2] with f(0) = 1 and f(2) = 0.2, the left, right, trapezoidal, and midpoint rule approximations were used to estimate the integral from 0 to 2 of f of x, dx. The estimates were 0.7811, 0.8675, 0.8650, 0.8632 and 0.9540, and the same number of subintervals were used in each case. Match the rule to its estimate. Please need help asap!

Ahomeowner plans to hang wallpaper on one wall of a bedroom that is 10 feet long if a stripe of wallpaper is 20 inches wide and stripes or hung vertically how many stripes on wall paper with the homeowner required

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

Two rectangular prisms have the same volume. the area of the base of the blue prism is 418 4 1 8 square units. the area of the base of the red prism is one-half that of the blue prism. which statement is true?