Explanation Given information: It is provided that she is 60 feet from third base where a baseball diamond is a square with side 90 feet and a batter hits the ball and running from the third base to home at a speed 30 ft./sec. The provided figure is: Formula used: The steps for solving the related rate problem are: A. The Problem 1. List the related, changing quantities. 2. Restate the problem in terms of rate of change and rewrite the problem using for the changing quantities for their derivatives. B. The Relationship 1. Draw a diagram, if appropriate, showing the changing quantities. 2. Find an equation or equations relating the changing quantities. 3. Take the derivative with respect to the equation(s) relating the quantity to get derived equation(s), which relate the rate of change of the quantities. C. The solution 1. Substitute into the derived equation(s) the given values of the quantities and their derivatives. 2. Solve for the derivative required. Pythagorean theorem: If the right angle triangle has base of length b , height of length a and the hypotenuse of length c then: a 2 + b 2 = c 2 Calculation: Let x be the distance of the batter from third base, and let h be the distance from the second base. Consider the steps of the formula: Step 1: The problem The changing quantities are Since, the batter is 60 feet from third base where a baseball diamond is a square with side 90 feet and a batter hits the ball and running from the third base to home at a speed 30 ft/sec. Thus, The rate of change of x is 30 ft./sec and x = 60 feet Thus, d x d t = 24 when x = 60 Since, the rate at which the distance from third base is increasing is to be determined. Thus, the above sentence can be rephrasing as: What is the rate of change of h Thus, d h d t = ? Step 2: The relationship Consider the figure: Since, the area is behave like the right angle triangle with base x , hypotenuse h and height 90

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 36E

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To calculate: The rate at which the distance from second base is increasing when she 60 feet from third base where a baseball diamond is a square with side 90 feet and a batter hits the ball and running from the third base to home at a speed 30 ft./sec.

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Chapter 12.5, Problem 35E

Chapter 12.5, Problem 37E

Chapter 12 Solutions

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The rate at which the distance from second base is increasing when she 60 feet from third base where a baseball diamond is a square with side 90 feet and a batter hits the ball and running from the third base to home at a speed 30 ft./sec.

Solution Summary: The author calculates the rate at which the distance from second base is increasing when the batter is 60 feet from third base.

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To calculate: The rate at which the distance from second base is increasing when she 60 feet from third base where a baseball diamond is a square with side 90 feet and a batter hits the ball and running from the third base to home at a speed 30 ft./sec.

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Chapter 12 Solutions