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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 a 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.

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 a 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.

Calculus: Early Transcendentals
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 #36

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
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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