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location to meet. Your positions at time t are denoted by x1(t) and x2(t), and are real valued. Both of you do not have a GPS device and can only measure the relative distance between each other. (a) equation Construct two functions (or strategies) R1(y) and R2(y) such that for the differential dx1 R1 (x1 – x2) (3) dt dx2 R2 (®1 – 22) (4) %3D dt we get lim0 |x1(t) – x2(t)| = 0, irrespective of your initial positions x1(0) and x2(0). Note: R1(y) and R2(y) should not depend on your initial positions (because you don't have GPS). Additionally, note that the right hand-side in Equation (3) means we are evaluating R1(y) at y = xı – x2 and similarly, we are evaulating R2(y) at y = x1 – x2. (b) tancing and maintain p units distance at equilibrium. Modify your functions R1(y) and R2(y) so that lim0 |æ1(t) – x2(t)| = p, irrespective of your initial positions x1(0) and x2(0). As in Consider the alternative scenario that you and your friend must practice social dis- part o) R. (4) and Rolu) should not denend on vour initial positions

location to meet. Your positions at time t are denoted by x1(t) and x2(t), and are real valued. Both of you do not have a GPS device and can only measure the relative distance between each other. (a) equation Construct two functions (or strategies) R1(y) and R2(y) such that for the differential dx1 R1 (x1 – x2) (3) dt dx2 R2 (®1 – 22) (4) %3D dt we get lim0 |x1(t) – x2(t)| = 0, irrespective of your initial positions x1(0) and x2(0). Note: R1(y) and R2(y) should not depend on your initial positions (because you don't have GPS). Additionally, note that the right hand-side in Equation (3) means we are evaluating R1(y) at y = xı – x2 and similarly, we are evaulating R2(y) at y = x1 – x2. (b) tancing and maintain p units distance at equilibrium. Modify your functions R1(y) and R2(y) so that lim0 |æ1(t) – x2(t)| = p, irrespective of your initial positions x1(0) and x2(0). As in Consider the alternative scenario that you and your friend must practice social dis- part o) R. (4) and Rolu) should not denend on vour initial positions

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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PART A

3. You and your friend wish to meet for coffee. Your goal is to agree on a location to meet. Your positions at time t are denoted by x1(t) and x2(t), and are real valued. Both of you do not have a GPS device and can only measure the relative distance between each other. (a) equation Construct two functions (or strategies) R1 (y) and R2(y) such that for the differential dx1 = R1 (x1 – x2) (3) dt dx2 R2 (x1 – x2) (4) dt we get lim,→0 |¤1(t) – x2(t)| = 0, irrespective of your initial positions x1(0) and x2(0). Note: R1(y) and R2(y) should not depend on your initial positions (because you don't have GPS). Additionally, note that the right hand-side in Equation (3) means we are evaluating R1 (y) at y = x1 – x2 and similarly, we are evaulating R2(y) at y = x1 – x2. (b) tancing and maintain p units distance at equilibrium. Modify your functions R1(y) and R2 (y) so that lim;→0 |x1(t) – x2(t)| = p, irrespective of your initial positions x1 (0) and x2(0). As in part a), R1(y) and R2(y) should not depend on your initial positions. Consider the alternative scenario that you and your friend must practice social dis-
Transcribed Image Text:3. You and your friend wish to meet for coffee. Your goal is to agree on a location to meet. Your positions at time t are denoted by x1(t) and x2(t), and are real valued. Both of you do not have a GPS device and can only measure the relative distance between each other. (a) equation Construct two functions (or strategies) R1 (y) and R2(y) such that for the differential dx1 = R1 (x1 – x2) (3) dt dx2 R2 (x1 – x2) (4) dt we get lim,→0 |¤1(t) – x2(t)| = 0, irrespective of your initial positions x1(0) and x2(0). Note: R1(y) and R2(y) should not depend on your initial positions (because you don't have GPS). Additionally, note that the right hand-side in Equation (3) means we are evaluating R1 (y) at y = x1 – x2 and similarly, we are evaulating R2(y) at y = x1 – x2. (b) tancing and maintain p units distance at equilibrium. Modify your functions R1(y) and R2 (y) so that lim;→0 |x1(t) – x2(t)| = p, irrespective of your initial positions x1 (0) and x2(0). As in part a), R1(y) and R2(y) should not depend on your initial positions. Consider the alternative scenario that you and your friend must practice social dis-
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