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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
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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**Problem Statement:** 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.) **Answer Box:** 33.4 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, \( \frac{dz}{dt} \). Then, use the values from the exercise to 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). **Help Options:** - **Read It** - **Watch It**
Transcribed Image Text:**Problem Statement:** 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.) **Answer Box:** 33.4 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, \( \frac{dz}{dt} \). Then, use the values from the exercise to 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). **Help Options:** - **Read It** - **Watch It**
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