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# AP Calculus AB March 11, 2009

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More applications of integrals using a function defined symbolically or numerically as the problem stem.

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### AP Calculus AB March 11, 2009

1. 1. The quot;Boston By The Seaquot; Problem Boston Harbor Dusk
2. 2. Suppose the density of a circular oil slick on the surface of a body of water kg/m2. is given by (a) Suppose that the slick extends from r = 0 to r = 1000 m. Determine the mass of the oil slick to the nearest kg.
3. 3. Suppose the density of a circular oil slick on the surface of a body of water 2. is given by kg/m (a) Suppose that the slick extends from r = 0 to r = 1000 m. Determine the mass of the oil slick to the nearest kg. 4340 (b) What is the smallest radius that contains 75% of the oil slick’s mass? (177.8)
4. 4. Suppose the density of cars, in cars/km for the ﬁrst 30 km along Main Street during certain hours of the day can be modeled by where x represents the number of kilometers from the corner of Portage and Main. (a) Write a function that gives the number of cars from Portage and Main to a point x km along Main Street. Do not simplify.
5. 5. Suppose the density of cars, in cars/km for the ﬁrst 30 km along Main Street during certain hours of the day can be modeled by where x represents the number of kilometers from the corner of Portage and Main. (b) To the nearest car, how many cars are there on this 30 km stretch of road?
6. 6. Greater Boston can be approximated by a semicircle of radius 8 miles with its centre on the coast. Moving away from the centre along a radius, the population density is constant for the ﬁrst mile. Beyond that, the density starts to decrease according to the data given in the table, where ρ(r), thousands/mile2 , is the population density at a distance r miles from the centre. (a) Using this data and a Riemann sum, estimate the total population living in the 8 mile radius. (b) Determine a possible formula for ρ(r). Use this formula to make another estimate of the population.
7. 7. (a) Using this data and a Riemann sum, estimate the total population living in the 8 mile radius. HOMEWORK