A boat is pulled by a winch on a dock, and the winch is 12 feet above the deck of the boat (see figure). The winch pulls the rope at a rate of 4 feet per second. Find the speed of the boat when 15 feet of rope is out. What happens to the speed of the boat as it gets closer and closer to the dock? STEP 1: STEP 2: STEP 4: 2x Let x be the distance from the boat to the dock and y be the length of the rope. Write the original equation. 12² + x² = Differentiate the equation with respect to x and y. dx dt dx 99 99 는 dx dt dt 12 dt dx Not draws to scale STEP 3: Solve for dx/dt (in ft/sec) by substituting the values for x, y, and dy/dt. (Round your answer for dx/dt to one decimal place.) 15 -(-4) 114 ft/sec = = = = ft/sec dy dt dy dt ---Select--- State the appropriate conclusion. As x → 0, dx dt 8
A boat is pulled by a winch on a dock, and the winch is 12 feet above the deck of the boat (see figure). The winch pulls the rope at a rate of 4 feet per second. Find the speed of the boat when 15 feet of rope is out. What happens to the speed of the boat as it gets closer and closer to the dock? STEP 1: STEP 2: STEP 4: 2x Let x be the distance from the boat to the dock and y be the length of the rope. Write the original equation. 12² + x² = Differentiate the equation with respect to x and y. dx dt dx 99 99 는 dx dt dt 12 dt dx Not draws to scale STEP 3: Solve for dx/dt (in ft/sec) by substituting the values for x, y, and dy/dt. (Round your answer for dx/dt to one decimal place.) 15 -(-4) 114 ft/sec = = = = ft/sec dy dt dy dt ---Select--- State the appropriate conclusion. As x → 0, dx dt 8
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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![A boat is pulled by a winch on a dock, and the winch is 12 feet above the deck of the boat (see figure). The winch pulls the rope at a rate of 4 feet per second. Find the speed of the boat when 15 feet of rope is
out. What happens to the speed of the boat as it gets closer and closer to the dock?
STEP 1:
STEP 3:
STEP 4:
12 t
STEP 2: Differentiate the equation with respect to x and y.
dx
2x.
dt
Not drawn to scale
Let x be the distance from the boat to the dock and y be the length of the rope. Write the original equation.
12² + x² =
dx
dt
dx
dt
114 ft/sec
=
=
Solve for dx/dt (in ft/sec) by substituting the values for x, y, and dy/dt. (Round your answer for dx/dt to one decimal place.)
dx
15
dt
-(-4)
ft/sec
dy
dt
dy
dt
---Select---
State the appropriate conclusion.
As x → 0,
dx
dt
O.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3578f3e4-1bc3-4b4b-9f3b-a9b3ea5dbfae%2F219a1622-76f5-49c6-8c0e-34746f9d3922%2F013ya7c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A boat is pulled by a winch on a dock, and the winch is 12 feet above the deck of the boat (see figure). The winch pulls the rope at a rate of 4 feet per second. Find the speed of the boat when 15 feet of rope is
out. What happens to the speed of the boat as it gets closer and closer to the dock?
STEP 1:
STEP 3:
STEP 4:
12 t
STEP 2: Differentiate the equation with respect to x and y.
dx
2x.
dt
Not drawn to scale
Let x be the distance from the boat to the dock and y be the length of the rope. Write the original equation.
12² + x² =
dx
dt
dx
dt
114 ft/sec
=
=
Solve for dx/dt (in ft/sec) by substituting the values for x, y, and dy/dt. (Round your answer for dx/dt to one decimal place.)
dx
15
dt
-(-4)
ft/sec
dy
dt
dy
dt
---Select---
State the appropriate conclusion.
As x → 0,
dx
dt
O.
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