A ladder 28 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 3 feet per second. Use this image to find the relation between r, y and ladder using the Pythagorean theorem. y dy dt y X dx dt Part 1: State the Pythagorean theorem for this problem as function of x,y and^ the ladder 28 feet. The Pythagorean theorem for this problem is: Part 2: Find the value of y using Part 1. dy using part Part 1. dt Part 3: Find the rate of change of the top of the ladder, ||

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.5: Transformation Of Functions
Problem 3SE: When examining the formula of a function that is the result of multiple transformations, how can you...
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A ladder 28 feet long is leaning against the wall of a house. The base of the ladder is
pulled away from the wall at a rate of 3 feet per second.
Use this image to find the relation between x, y and ladder using the Pythagorean
theorem.
y
dx
dt
Part 1: State the Pythagorean theorem for this problem as function of x,y and^
the ladder 28 feet.
The Pythagorean theorem for this problem is:
Part 2: Find the value of y using Part 1.
dy
-, using part Part 1.
dt
Part 3: Find the rate of change of the top of the ladder,
Part 4: Find the velocity of the top of the ladder using the value of x, y and
dx /dt when x is 18 feet.
Part 5: Find the area of the right triangle as a function of x.
Part 6: Find the first derivative of the area with respect to time t.
Part 7: Find tan(0) as a function of æ and y.
Part 8: Find the rate of change of theta with respect to t.
Transcribed Image Text:A ladder 28 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 3 feet per second. Use this image to find the relation between x, y and ladder using the Pythagorean theorem. y dx dt Part 1: State the Pythagorean theorem for this problem as function of x,y and^ the ladder 28 feet. The Pythagorean theorem for this problem is: Part 2: Find the value of y using Part 1. dy -, using part Part 1. dt Part 3: Find the rate of change of the top of the ladder, Part 4: Find the velocity of the top of the ladder using the value of x, y and dx /dt when x is 18 feet. Part 5: Find the area of the right triangle as a function of x. Part 6: Find the first derivative of the area with respect to time t. Part 7: Find tan(0) as a function of æ and y. Part 8: Find the rate of change of theta with respect to t.
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