Two cars start moving from the same point. One travels south at 20 mi/h and the other travels west at 15 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is 2-? +y² 7 + y² Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. dz dx + 2y = 2x dt dy dt dt dt 1 v (x

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Two cars start moving from the same point. One travels south at 20 mi/h and the other travels west at 15 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
Step 1
Using the diagram of a right triangle given below, the relation between x, y, and z is
z? =
2
1² + y²
Step 2
We must find dz/dt. Differentiating both sides and simplifying gives us the following.
dz
dz
dx
dy
+ 2y
dt
= 2x
dt
dt
dt
dz
dx
+y
dt
dy
dt
dt
II
Transcribed Image Text:Two cars start moving from the same point. One travels south at 20 mi/h and the other travels west at 15 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z? = 2 1² + y² Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. dz dz dx dy + 2y dt = 2x dt dt dt dz dx +y dt dy dt dt II
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