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 v₁ (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. P FIGURE 1 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 = 17, y = 23, va = 4 m/s, and v= 5 m/s. df =
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 v₁ (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. P FIGURE 1 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 = 17, y = 23, va = 4 m/s, and v= 5 m/s. df =
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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Please both questions, thank you very much!!
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 v₁ (m/s) and Jessica with velocity v (m/s).
Let f(x, y) be the distance from Matthew to Jessica when Matthew is x meters from P and Jessica is y meters from
P.
df
P
=
FIGURE 1
• Show that f(x, y) = √√x² + y² - 2xy cos 0.
• Assume that 0 T/3. Use the Chain Rule to determine the rate at which the distance between Matthew and
Jessica is changing when
X = 17, y = 23, va = 4 m/s, and vz = 5 m/s.
B
Transcribed Image Text:Corn production, C, is a function of rainfall, R (in inches), and temperature, T (in degrees C). The first figure
below shows how rainfall is predicted to vary with time because of global warming; the second, how temperature
is predicted to vary with time because of global warming.
15
14
=
13
27
25
23
Suppose that we know that (currently)
2020
Hence, estimate dC/dt when t = 2020.
dC/dt:
2040
Graph of rainfall, R vs. time, t
2020
2040
AC 3.8AR - 5.4AT
Use this to estimate the change in corn production between the year
Change
Graph of temperature, T vs. time, t
2020 and the year 2021.
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