At noon, ship A is 100 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM? (Round your answer to one decimal place.) 33.4 X km/h Enhanced Feedback Please try again, drawing a diagram for this problem. Draw a straight horizontal line. Label this line with the length between the two ships at the beginning. Draw a vertical line with one end attached to the left of the horizontal line pointing down; label the other end A (for ship A) and the length x. Draw another line on the right-hand side of the horizontal line pointing up; label the end B (for ship B) and the length y. Connect points A and B with a straight line and label it z. Use the Pythagorean theorem and the given values in the exercise to find a relationship among the length of the line segments z, x, and y. Differentiate this equation with respect to time, t, using the Chain Rule, to find the equation for the rate at which the distance between the ships changes, dz Then, use the values from the exercise to dt evaluate the rate of change of the distance between the ships, paying close attention to the signs of the rates of change (positive when increasing, and negative when decreasing). Need Help? Read It Watch It
At noon, ship A is 100 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM? (Round your answer to one decimal place.) 33.4 X km/h Enhanced Feedback Please try again, drawing a diagram for this problem. Draw a straight horizontal line. Label this line with the length between the two ships at the beginning. Draw a vertical line with one end attached to the left of the horizontal line pointing down; label the other end A (for ship A) and the length x. Draw another line on the right-hand side of the horizontal line pointing up; label the end B (for ship B) and the length y. Connect points A and B with a straight line and label it z. Use the Pythagorean theorem and the given values in the exercise to find a relationship among the length of the line segments z, x, and y. Differentiate this equation with respect to time, t, using the Chain Rule, to find the equation for the rate at which the distance between the ships changes, dz Then, use the values from the exercise to dt evaluate the rate of change of the distance between the ships, paying close attention to the signs of the rates of change (positive when increasing, and negative when decreasing). Need Help? Read It Watch It
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...
Related questions
Question
2.7
12
![At noon, ship A is 100 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance
between the ships changing at 4:00 PM? (Round your answer to one decimal place.)
33.4
X km/h
Enhanced Feedback
Please try again, drawing a diagram for this problem. Draw a straight horizontal line. Label this line with the length between the two ships
at the beginning. Draw a vertical line with one end attached to the left of the horizontal line pointing down; label the other end A (for ship
A) and the length x. Draw another line on the right-hand side of the horizontal line pointing up; label the end B (for ship B) and the
length y. Connect points A and B with a straight line and label it z. Use the Pythagorean theorem and the given values in the exercise to
find a relationship among the length of the line segments z, x, and y. Differentiate this equation with respect to time, t, using the Chain
Rule, to find the equation for the rate at which the distance between the ships changes,
dz
Then, use the values from the exercise to
dt
evaluate the rate of change of the distance between the ships, paying close attention to the signs of the rates of change (positive when
increasing, and negative when decreasing).
Need Help?
Watch It
Read It](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3241d4b2-7cea-4408-ac37-56f0a05274af%2F7a00b8f8-4df1-4132-a968-8d7611fd6594%2Fxvk7mc_processed.png&w=3840&q=75)
Transcribed Image Text:At noon, ship A is 100 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance
between the ships changing at 4:00 PM? (Round your answer to one decimal place.)
33.4
X km/h
Enhanced Feedback
Please try again, drawing a diagram for this problem. Draw a straight horizontal line. Label this line with the length between the two ships
at the beginning. Draw a vertical line with one end attached to the left of the horizontal line pointing down; label the other end A (for ship
A) and the length x. Draw another line on the right-hand side of the horizontal line pointing up; label the end B (for ship B) and the
length y. Connect points A and B with a straight line and label it z. Use the Pythagorean theorem and the given values in the exercise to
find a relationship among the length of the line segments z, x, and y. Differentiate this equation with respect to time, t, using the Chain
Rule, to find the equation for the rate at which the distance between the ships changes,
dz
Then, use the values from the exercise to
dt
evaluate the rate of change of the distance between the ships, paying close attention to the signs of the rates of change (positive when
increasing, and negative when decreasing).
Need Help?
Watch It
Read It
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning