Cleaning pumps remove oil at the rate modeled by the function r, given by r of t equals 2 plus the cosine of the quantity pi times t divided by 11 with t measure in hours and and r(t) measured in gallons per hour. how much oil will the pumping stations remove during the 6-hour period from t = 0 to t = 6? give 3 decimal places. (4 points)

Write the inverse of the logarithmic function used to represent the situation in model 1, f(x)=3+2in x . express the answer in radical form.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 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)

Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label its height and width. y= 5x, y=7x^2then find the area s of the region.