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Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of 0 (Figure 1). Suppose that Matthew runs with velocity v (m/s) and Jessica with velocity v (m/s). Let f(x, y) be the distance from Matthew to Jessica when Matthew is a meters from P and Jessica is y meters from P. A P = FIGURE 1 NO B Show that f(x, y) = √√x² + y² − 2xy cos 0. Assume that 0 = π/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 27, y = 22, v₁ = 5 m/s, and v₂ = 2 m/s. d 97/sqrt619

Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of 0 (Figure 1). Suppose that Matthew runs with velocity v (m/s) and Jessica with velocity v (m/s). Let f(x, y) be the distance from Matthew to Jessica when Matthew is a meters from P and Jessica is y meters from P. A P = FIGURE 1 NO B Show that f(x, y) = √√x² + y² − 2xy cos 0. Assume that 0 = π/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 27, y = 22, v₁ = 5 m/s, and v₂ = 2 m/s. d 97/sqrt619

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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Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of 0 (Figure 1). Suppose that Matthew runs with velocity v (m/s) and Jessica with velocity v (m/s). Let f(x, y) be the distance from Matthew to Jessica when Matthew is a meters from P and Jessica is y meters from P. A P = FIGURE 1 NO B Show that f(x, y) = √√x² + y² − 2xy cos 0. Assume that 0 = π/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 27, y = 22, v₁ = 5 m/s, and v₂ = 2 m/s. de 97/sqrt619
Transcribed Image Text:Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of 0 (Figure 1). Suppose that Matthew runs with velocity v (m/s) and Jessica with velocity v (m/s). Let f(x, y) be the distance from Matthew to Jessica when Matthew is a meters from P and Jessica is y meters from P. A P = FIGURE 1 NO B Show that f(x, y) = √√x² + y² − 2xy cos 0. Assume that 0 = π/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 27, y = 22, v₁ = 5 m/s, and v₂ = 2 m/s. de 97/sqrt619
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