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e. If some cargo airplanes are geometrically similar, the lift capacity of the wings is proportional to the surface area of the wings, and the cargo capacity of an airplane is directly proportional to the lift capacity of its wings, model the cargo capacity of an airplane in terms of its wing span.

e. If some cargo airplanes are geometrically similar, the lift capacity of the wings is proportional to the surface area of the wings, and the cargo capacity of an airplane is directly proportional to the lift capacity of its wings, model the cargo capacity of an airplane in terms of its wing span.

Advanced Engineering Mathematics
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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2.5.2 Derive proportionality models in the following scenarios. Be sure to define variables in each model. a. If some right triangles drawn on a page are geometrically similar, model the area of a triangle in terms of the length of its hypotenuse. b. If some cubes in a bag are geometrically similar, model the volume of a cube in terms of the distance between opposite corners. c. If some rocks in a bag are geometrically similar and have a constant density, model the surface area of a rock in terms of its weight. d. If the sides of certain hollow aluminum tubes are 1 mm thick and the outer surface of the tubes are geometrically similar, model the volume of aluminum used to make a tube in terms of its length. e. If some cargo airplanes are geometrically similar, the lift capacity of the wings is proportional to the surface area of the wings, and the cargo capacity of an airplane is directly proportional to the lift capacity of its wings, model the cargo capacity of an airplane in terms of its wing span.
Transcribed Image Text:2.5.2 Derive proportionality models in the following scenarios. Be sure to define variables in each model. a. If some right triangles drawn on a page are geometrically similar, model the area of a triangle in terms of the length of its hypotenuse. b. If some cubes in a bag are geometrically similar, model the volume of a cube in terms of the distance between opposite corners. c. If some rocks in a bag are geometrically similar and have a constant density, model the surface area of a rock in terms of its weight. d. If the sides of certain hollow aluminum tubes are 1 mm thick and the outer surface of the tubes are geometrically similar, model the volume of aluminum used to make a tube in terms of its length. e. If some cargo airplanes are geometrically similar, the lift capacity of the wings is proportional to the surface area of the wings, and the cargo capacity of an airplane is directly proportional to the lift capacity of its wings, model the cargo capacity of an airplane in terms of its wing span.
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