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For positive constants A and B, the force between two atoms is a function of the distance, r, between them: A f(r) B r > 0 (a) For which values of r is f(r) positive? For which values is f(r) negative? Your answer should involve A and B. Hint: There is no calculus in this part of the problem. It's just algebra. (b) Find all the values of r where f(r) has a global max or min on the interval (0, 0). Your answer should involve A and B. Be sure to verify that the function actually has a global max or min where you claim it does.

For positive constants A and B, the force between two atoms is a function of the distance, r, between them: A f(r) B r > 0 (a) For which values of r is f(r) positive? For which values is f(r) negative? Your answer should involve A and B. Hint: There is no calculus in this part of the problem. It's just algebra. (b) Find all the values of r where f(r) has a global max or min on the interval (0, 0). Your answer should involve A and B. Be sure to verify that the function actually has a global max or min where you claim it does.

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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4:36 64% Math 151 Written Homework 8 1. For positive constants A and B, the force between two atoms is a function of the distance, r, between them: A f(r) r > 0 (a) For which values of r is f (r) positive? For which values is f(r) negative? Your answer should involve A and B. Hint: There is no calculus in this part of the problem. It's just algebra. (b) Find all the values of r where f(r) has a global max or min on the interval (0, 0). Your answer should involve A and B. Be sure to verify that the functio actually has a global max or min where you claim it does. 2. A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can she do this so as to minimize the cost of the fence? Note: Be careful with your units! 1.5 is different from 1.5 million. 3. An internet provider needs to run an underground cable from station A, on one side of a river, to station C on the other side of the river. The river is 300 meters across (the shortest way) and station C is 400 meters along the river to a point directly across from station A (see diagram). Laying the cable costs $100 per meter under dry ground, and $200 per meter under the river. The company will lay the cable under the ground along the river until it gets to point B (which is a distance x from A), and then lay the cable in a straight line under the river from B to C. How far apart should point B be from station A in order to minimize the cost of laying the cable? Hint: Label a point D directly across the river from B, and write the objective function in terms of the distance from D to C. 400 m 300 m A B
Transcribed Image Text:4:36 64% Math 151 Written Homework 8 1. For positive constants A and B, the force between two atoms is a function of the distance, r, between them: A f(r) r > 0 (a) For which values of r is f (r) positive? For which values is f(r) negative? Your answer should involve A and B. Hint: There is no calculus in this part of the problem. It's just algebra. (b) Find all the values of r where f(r) has a global max or min on the interval (0, 0). Your answer should involve A and B. Be sure to verify that the functio actually has a global max or min where you claim it does. 2. A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can she do this so as to minimize the cost of the fence? Note: Be careful with your units! 1.5 is different from 1.5 million. 3. An internet provider needs to run an underground cable from station A, on one side of a river, to station C on the other side of the river. The river is 300 meters across (the shortest way) and station C is 400 meters along the river to a point directly across from station A (see diagram). Laying the cable costs $100 per meter under dry ground, and $200 per meter under the river. The company will lay the cable under the ground along the river until it gets to point B (which is a distance x from A), and then lay the cable in a straight line under the river from B to C. How far apart should point B be from station A in order to minimize the cost of laying the cable? Hint: Label a point D directly across the river from B, and write the objective function in terms of the distance from D to C. 400 m 300 m A B
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