3. As your friends paint, the base of a 10-ft ladder against a wall slides away from the wall at 1 ft/s. To find how fast the top of the ladder slides down the wall when its base is 6 ft from the wall, your friends do this: wall y 10ft X Start with the equation x² + y² = 100 dy We want when x = 6, so 6² + y² = 100 gives us y² = 64 dt dy dy Differentiating with respect to t yields 2y = 0, so = 0 dt dt ground (a) What would = 0 mean in this problem? Explain whether this answer makes sense. dy dt (b) Did they make any errors in their work? If so, what exactly, and how would they correct it? (c) Rework the problem correctly and explain your answer in the context of the problem. Include units.
3. As your friends paint, the base of a 10-ft ladder against a wall slides away from the wall at 1 ft/s. To find how fast the top of the ladder slides down the wall when its base is 6 ft from the wall, your friends do this: wall y 10ft X Start with the equation x² + y² = 100 dy We want when x = 6, so 6² + y² = 100 gives us y² = 64 dt dy dy Differentiating with respect to t yields 2y = 0, so = 0 dt dt ground (a) What would = 0 mean in this problem? Explain whether this answer makes sense. dy dt (b) Did they make any errors in their work? If so, what exactly, and how would they correct it? (c) Rework the problem correctly and explain your answer in the context of the problem. Include units.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Can you do a, b, and c please
Transcribed Image Text:3. As your friends paint, the base of a 10-ft ladder against a wall slides away from the wall at 1 ft/s. To find
how fast the top of the ladder slides down the wall when its base is 6 ft from the wall, your friends do this:
wall
y
10ft
X
Start with the equation x² + y² = 100
dy
We want when x = 6, so 6² + y² = 100 gives us y² = 64
dt
dy
dy
Differentiating with respect to t yields 2y = 0, so = 0
dt
dt
ground
(a) What would = 0 mean in this problem? Explain whether this answer makes sense.
dy
dt
(b) Did they make any errors in their work? If so, what exactly, and how would they correct it?
(c) Rework the problem correctly and explain your answer in the context of the problem. Include units.
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