The density of oil in a circular oil slick on the surface of the ocean at a distance r meters from the center of the slick is given by 6(r) = 50/(1+r) kg/m². (a) If the slick extends from r = 0 to r= 10,000 m, find a Riemann sum approximating the total mass of oil in the slick. (b) Find the exact value of the mass of oil in the slick by turning your sum into an integral and evaluating it. (e) Within what distance r is half the oil of the slick contained?

The density of oil in a circular oil slick on the surface of the ocean at a distance r meters from the center of the slick is given by 6(r) = 50/(1+r) kg/m². (a) If the slick extends from r = 0 to r= 10,000 m, find a Riemann sum approximating the total mass of oil in the slick. (b) Find the exact value of the mass of oil in the slick by turning your sum into an integral and evaluating it. (e) Within what distance r is half the oil of the slick contained?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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17 (a)
2xr, (50/(1+r)) Ar
(b) 3.14 106 kg
(c) 5009 meters

The density of oil in a circular oil slick on the surface
of the ocean at a distance r meters from the center of
the slick is given by 6(r) = 50/(1+r) kg/m².
(a) If the slick extends from r = 0 to r = 10,000 m,
find a Riemann sum approximating the total mass
of oil in the slick.
(b) Find the exact value of the mass of oil in the slick
by turning your sum into an integral and evaluating
it.
(e) Within what distance r is half the oil of the slick
contained?

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Step 1: Introducing center of mass

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Step 2: Calculating Riemann sum approximation

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Step 3: Calculating total mass

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Step 4: Calculating the r, within which total oil is half

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