The blue whale feeds on krill, a small shrimp-like animal of length 2 to 5 cm. Suppose that the density of krill (the number per cubic meter) is given by p(x) = 0.70xe 0.0001x where x is the distance (in meters) from the Antarctic coast. The distribution in this problem is horizontal rather than vertical, but this does not change the fact that p(x) dx gives the total number of krill from distance a to distance b. Suppose that the blue whale acts as a strainer with a cross-sectional area of 1 square meter. (a) Find the total number of krill the whale can catch in a run from the coast of Antarctica to 1500 m off the coast.
The blue whale feeds on krill, a small shrimp-like animal of length 2 to 5 cm. Suppose that the density of krill (the number per cubic meter) is given by p(x) = 0.70xe 0.0001x where x is the distance (in meters) from the Antarctic coast. The distribution in this problem is horizontal rather than vertical, but this does not change the fact that p(x) dx gives the total number of krill from distance a to distance b. Suppose that the blue whale acts as a strainer with a cross-sectional area of 1 square meter. (a) Find the total number of krill the whale can catch in a run from the coast of Antarctica to 1500 m off the coast.
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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Transcribed Image Text:The blue whale feeds on krill, a small shrimp-like animal of length 2 to 5 cm.
Suppose that the density of krill (the number per cubic meter) is given by
0.0001x
p(x) = 0.70xe
where x is the distance (in meters) from the Antarctic coast. The distribution
in this problem is horizontal rather than vertical, but this does not change the
fact that
p(x) dx
gives the total number of krill from distance a to distance b. Suppose that the
blue whale acts as a strainer with a cross-sectional area of 1 square meter.
(a) Find the total number of krill the whale can catch in a run from the coast
of Antarctica to 1500 m off the coast.
(b) Find the distance from the coast at which the density of krill is the largest.
What is the density of krill at this distance?
(c) Suppose that a blue whale starts feeding 500 m off the coast of Antarctica
and continues swimming away from the coast at a speed of 25 km/h for
20 minutes. Find the total number of krill the blue whale catches over this
feeding run.
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