Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal. Use the table and the method of this example to find an equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute). Weight, x 25 Galloping Speed, y 194.5 In y Take the natural logarithm of each coordinate to obtain points of the form (In x, In y). (Round your answers to three decimal places.) Weight, x Galloping Speed, y In x y = 35 50 75 500 181.7 173.8 162.2 124.9 25 194.5 35 181.7 1000 115.2 50 173.8 75 162.2 Find the least squares regression line for the transformed points. (Round your answers to three decimal places.) In y = In x 500 124.9 1000 115.2 Find an equation of the form y = ax that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute). (Round your value for a to one decimal place and your value for b to three decimal places.)
Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal. Use the table and the method of this example to find an equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute). Weight, x 25 Galloping Speed, y 194.5 In y Take the natural logarithm of each coordinate to obtain points of the form (In x, In y). (Round your answers to three decimal places.) Weight, x Galloping Speed, y In x y = 35 50 75 500 181.7 173.8 162.2 124.9 25 194.5 35 181.7 1000 115.2 50 173.8 75 162.2 Find the least squares regression line for the transformed points. (Round your answers to three decimal places.) In y = In x 500 124.9 1000 115.2 Find an equation of the form y = ax that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute). (Round your value for a to one decimal place and your value for b to three decimal places.)
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:Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an
animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop
depends on the weight of the animal. Use the table and the method of this example to find an equation that relates an animal's weight x (in pounds) and its lowest galloping
speed y (in strides per minute).
Weight, x
25
Galloping Speed, y 194.5
35
50
75
500
181.7 173.8 162.2 124.9
Take the natural logarithm of each coordinate to obtain points of the form (In x, In y). (Round your answers to three decimal places.)
Weight, x
Galloping Speed, y
In x
In y
25
194.5
y =
35
181.7
1000
115.2
50
173.8
75
162.2
Find the least squares regression line for the transformed points. (Round your answers to three decimal places.)
In y =
+
In x
500
124.9
1000
115.2
Find an equation of the form y = axb that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute). (Round your value for a to one
decimal place and your value for b to three decimal places.)
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