Explanation Given information: It is provided that the top of a 10 − foot ladder is being pulled away from a wall at a rate of 10ft/sec . Formula used: The steps for solving the related rate problem are: A. The Question 1. List the quantities that are related and changed with time. 2. Restate the question in the form of rate of change and write again the question using changing quantities for their derivatives. B. The Relationship 1. Make a diagram that shows the changing quantities. 2. Determine an equation or equations that relates the changing quantities. 3. Determine the derivative with respect to the equation(s) that relates the quantity to find derived equation(s), which relate the rate of change of the quantities. C. The answer 1. Make a substitution to the derived equation(s), the given values of the quantities and their derivatives. 2. Calculate the required derivative. Pythagorean Theorem: In the right angle triangle, the sum of the square of height and square of base is equals to the square of the hypotenuse: If the height is h , base is b , and hypotenuse is a then: h 2 + b 2 = a 2 Calculation: Let the distance from the base of the ladder from the wall is b and the height of the top of the ladder is h . Consider the steps of the formula: Step 1: The problem The changing quantities are base b and height h Since, the top is being pulled away from a wall at a rate of 10 ft/sec Thus, The rate of change of top of the ladder is 10 ft/sec . Thus, d h d t = − 10 Since, the rate at which the base of the ladder is sliding away from the wall is to be determined. Thus, the above sentence can be rephrased as: What is the rate of change of b . Thus, d b d t = ? Step 2: The relationship Consider the Pythagorean theorem in the right triangle: h 2 + b 2 = a 2 Since, the above case of sliding of ladder can be considered as a right angle triangle at particular when the height is h , base is b and the hypotenuse is 5

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 12.5, Problem 16E

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To calculate: The rate at which the base of the ladder is sliding away from the wall at the instant when the top of the ladder is 3 feet from the wall where the top of a 10−foot ladder is being pulled away from a wall at a rate of 10ft/sec.

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Chapter 12.5, Problem 15E

Chapter 12.5, Problem 17E

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Chapter 12 Solutions

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The rate at which the base of the ladder is sliding away from the wall at the instant when the top of the ladder is 3 feet from the wall where the top of a 10 − foot ladder is being pulled away from a wall at a rate of 10ft/sec .

Solution Summary: The author explains how to calculate the rate at which the base of the ladder is sliding away from the wall at the instant.

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To calculate: The rate at which the base of the ladder is sliding away from the wall at the instant when the top of the ladder is 3 feet from the wall where the top of a 10−foot ladder is being pulled away from a wall at a rate of 10ft/sec.

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Chapter 12 Solutions