34. An ant weighs approximately 1/500 ounce and can lift 1/5 ounce, which is approximately 100 times its weight. Assume that strength is proportional to the cross-section of a muscle and that all organisms on Earth (ants and humans) are geometrically similar. Using these assumptions, determine how much a 150-pound person on Earth can lift.
34. An ant weighs approximately 1/500 ounce and can lift 1/5 ounce, which is approximately 100 times its weight. Assume that strength is proportional to the cross-section of a muscle and that all organisms on Earth (ants and humans) are geometrically similar. Using these assumptions, determine how much a 150-pound person on Earth can lift.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question #34
![Level 2 APPLIED AND THEORY PROBLEMS
34. An ant weighs approximately 1/500 ounce and can
lift 1/5 ounce, which is approximately 100 times its
weight. Assume that strength is proportional to the
cross-section of a muscle and that all organisms on
Earth (ants and humans) are geometrically similar.
Using these assumptions, determine how much a
150-pound person on Earth can lift.
35. A comic book explained Superman's strength by
stating that on Krypton an organism's strength is
directly proportional to its body mass. Based on
this assumption and assuming that Krypton ants
are like Earth ants (see Problem 34), how much
can a 150-pound person on Krypton lift?
36. In a sample of twenty-six trees of a particular
species, wood density, D (kg/m³), is related to break-
ing strength, S (MPa), according to the relation-
ship D x S0.91. If one of the points that this relation-
ship passed through was (D, S) = (300, 10), find the
equation and sketch its graph.
37. A sample based on nineteen mountain ash trees of
different sizes yielded a relationship between the
leaf area, A(m2), of the tree and the stem diameter
at breast height (DBH), d (cm). The relationship
obtained was Ax d2.99. If one of the points that this
relationship passed through was (d, A) = (30, 78),
find the equation and sketch its graph.
38. In Julian Huxley's classic book Problems of Rel-
ative Growth, there are data showing an allomet-
ric relationship between the mass (C milligrams)
of the large claw (chela) and that of the rest of
the body (Bmilligrams) in the male fiddler crab
(Uca pugnax). The exponent of this relationship is
approximately 1.6, that is C = a B6, and it passes
through the point (B, C) = (1000, 500). Calculate
the parameter a and then graph the relationship for
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4db1e84-75df-498d-9686-5cabfd0e0c2f%2Fb8d7d411-08b0-4f0f-8eee-930b70cfd8a8%2Fklbm0vk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Level 2 APPLIED AND THEORY PROBLEMS
34. An ant weighs approximately 1/500 ounce and can
lift 1/5 ounce, which is approximately 100 times its
weight. Assume that strength is proportional to the
cross-section of a muscle and that all organisms on
Earth (ants and humans) are geometrically similar.
Using these assumptions, determine how much a
150-pound person on Earth can lift.
35. A comic book explained Superman's strength by
stating that on Krypton an organism's strength is
directly proportional to its body mass. Based on
this assumption and assuming that Krypton ants
are like Earth ants (see Problem 34), how much
can a 150-pound person on Krypton lift?
36. In a sample of twenty-six trees of a particular
species, wood density, D (kg/m³), is related to break-
ing strength, S (MPa), according to the relation-
ship D x S0.91. If one of the points that this relation-
ship passed through was (D, S) = (300, 10), find the
equation and sketch its graph.
37. A sample based on nineteen mountain ash trees of
different sizes yielded a relationship between the
leaf area, A(m2), of the tree and the stem diameter
at breast height (DBH), d (cm). The relationship
obtained was Ax d2.99. If one of the points that this
relationship passed through was (d, A) = (30, 78),
find the equation and sketch its graph.
38. In Julian Huxley's classic book Problems of Rel-
ative Growth, there are data showing an allomet-
ric relationship between the mass (C milligrams)
of the large claw (chela) and that of the rest of
the body (Bmilligrams) in the male fiddler crab
(Uca pugnax). The exponent of this relationship is
approximately 1.6, that is C = a B6, and it passes
through the point (B, C) = (1000, 500). Calculate
the parameter a and then graph the relationship for
%3D
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