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3. To understand the spacing between fish in a school or birds in a flock, scientists have defined cohesiveness as R A С (х) %3D хп хт Where A and R are magnitudes of attraction and repulsion, x is the distance between individuals, and m and n determine how fast the interactions fall off with distance. Suppose that R > A and n > m. |п-т a. Show that C(x) = 0 when x = nR\n-m b. Show that C (x) has a relative minimum when x = MA, c. For R = 5, A = 3,n = ÷ and m =, find the value of x for which C (x) = 0, and the value for which C (x) has a relative minimum.

3. To understand the spacing between fish in a school or birds in a flock, scientists have defined cohesiveness as R A С (х) %3D хп хт Where A and R are magnitudes of attraction and repulsion, x is the distance between individuals, and m and n determine how fast the interactions fall off with distance. Suppose that R > A and n > m. |п-т a. Show that C(x) = 0 when x = nR\n-m b. Show that C (x) has a relative minimum when x = MA, c. For R = 5, A = 3,n = ÷ and m =, find the value of x for which C (x) = 0, and the value for which C (x) has a relative minimum.

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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3. To understand the spacing between fish in a school or birds in a flock, scientists have defined cohesiveness as R A С (х) %3D хп хт Where A and R are magnitudes of attraction and repulsion, x is the distance between individuals, and m and n determine how fast the interactions fall off with distance. Suppose that R > A and n > m. |п-т a. Show that C(x) = 0 when x = nR\n-m b. Show that C (x) has a relative minimum when x = MA, c. For R = 5, A = 3,n = ÷ and m =, find the value of x for which C (x) = 0, and the value for which C (x) has a relative minimum.
Transcribed Image Text:3. To understand the spacing between fish in a school or birds in a flock, scientists have defined cohesiveness as R A С (х) %3D хп хт Where A and R are magnitudes of attraction and repulsion, x is the distance between individuals, and m and n determine how fast the interactions fall off with distance. Suppose that R > A and n > m. |п-т a. Show that C(x) = 0 when x = nR\n-m b. Show that C (x) has a relative minimum when x = MA, c. For R = 5, A = 3,n = ÷ and m =, find the value of x for which C (x) = 0, and the value for which C (x) has a relative minimum.
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