Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A 18-ft ladder is leaning against a wall, and the top of the ladder is sliding down the wall at a constant rate of 3.25 ft/s. How fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 4 ft above the ground? Solution: Let x be the distance from the bottom of the ladder to the wall, and let y be the distance from the top of the ladder to the ground. Draw a labeled sketch! The related variables equation is Related Variables Equation: = 324 Implicitly differentiate both sides of the related variables equation with respect to t, using x' for 4 and y' for dy The related rates equation is dt Related Rates Equation: Therefore, a formula for the rate at which the bottom of the ladder is sliding away from the wall is dr x' = dt Finally, when the top of the ladder is 4 ft above the ground, the rate at which the bottom of the ladder is sliding away from the wall is da ft/s dt

A 18-ft ladder is leaning against a wall, and the top of the ladder is sliding down the wall at a constant rate of 3.25 ft/s. How fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 4 ft above the ground? Solution: Let x be the distance from the bottom of the ladder to the wall, and let y be the distance from the top of the ladder to the ground. Draw a labeled sketch! The related variables equation is Related Variables Equation: = 324 Implicitly differentiate both sides of the related variables equation with respect to t, using x' for 4 and y' for dy The related rates equation is dt Related Rates Equation: Therefore, a formula for the rate at which the bottom of the ladder is sliding away from the wall is dr x' = dt Finally, when the top of the ladder is 4 ft above the ground, the rate at which the bottom of the ladder is sliding away from the wall is da ft/s dt

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter8: Areas Of Polygons And Circles
Section8.4: Cicumference And Area Of A Cicle
Problem 45E: The diameter of a carousel merry-go-round is 30ft. At full speed, it makes a complete revolution in...
See similar textbooks
icon
Related questions
Question
A 18-ft ladder is leaning against a wall, and the top of the ladder is sliding down the wall at a constant rate of 3.25 ft/s. How fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 4 ft above the ground? Solution: Let æ be the distance from the bottom of the ladder to the wall, and let y be the distance from the top of the ladder to the ground. Draw a labeled sketch! The related variables equation is Related Variables Equation: = 324 Implicitly differentiate both sides of the related variables equation with respect to t, using x' for and y' for dy The related rates equation is Related Rates Equation: Therefore, a formula for the rate at which the bottom of the ladder is sliding away from the wall is r' = Finally, when the top of the ladder is 4 ft above the ground, the rate at which the bottom of the ladder is sliding away from the wall is da dt ft/s %3D
Transcribed Image Text:A 18-ft ladder is leaning against a wall, and the top of the ladder is sliding down the wall at a constant rate of 3.25 ft/s. How fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 4 ft above the ground? Solution: Let æ be the distance from the bottom of the ladder to the wall, and let y be the distance from the top of the ladder to the ground. Draw a labeled sketch! The related variables equation is Related Variables Equation: = 324 Implicitly differentiate both sides of the related variables equation with respect to t, using x' for and y' for dy The related rates equation is Related Rates Equation: Therefore, a formula for the rate at which the bottom of the ladder is sliding away from the wall is r' = Finally, when the top of the ladder is 4 ft above the ground, the rate at which the bottom of the ladder is sliding away from the wall is da dt ft/s %3D
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Indefinite Integral
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
SEE MORE TEXTBOOKS