Explanation Given information: It is provided that the H.M.S Dreadnaught is 40 miles south of Montauk and streaming due south at 20 mph, while the U.S Mona Lisa is 50 miles east of Montauk and streaming due east at an even 30 mph. Formula used: The steps for solving the related rate problem are: Step1: List the changing and related quantities followed by restating the problem in rate of change of terms. Step 2: Rewrite the problem using for the changing quantities for their derivatives. Step 3: If possible draw the diagram of the changing quantities and find an equation relating the changing quantities. Step 4: Differentiate with respect to the equation (s) in order to get rate of change in relating quantity. Step 5: Now substitute the values of the provided quantity and their derivative into the derived equation and solve them to get answer. The Pythagorean Theorem: In a right angle triangle with base of length b , height of length h and the hypotenuse of length c , the sum of the square of base length and the square of height length is equals to the length of hypotenuse. b 2 + h 2 = c 2 Calculation: Let x be the distance of the Mona Lisa from Montauk and let y be the distance of the Dreadnaught from Montauk and let z be the distance between the two ships. Consider the steps of the formula: The changing quantities are x , y , z described above. Since, the H.M.S Dreadnaught is 40 miles south of Montauk and streaming due south at 20 mph. Thus, the rate of change of y is 20 mph and the value of x is 40 miles. Thus, d y d t = 20 when y = 40 Since, the U.S Mona Lisa is 50 miles east of Montauk and streaming due east at an even 30 mph. Thus, the rate of change of x is 30 and the value of x is 50 . Thus, d x d t = 30 when x = 50 Since, the rate at which the distance between ships increasing. What is the rate of change of z ? d z d t = ? Since, the approach of the two ships to a particular point is observed and thus it forms a right angle triangle where the perpendicular at the common point, Thus, consider the Pythagorean theorem

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 12.5, Problem 33E

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To calculate: The rate at which the distance between ships increasing where the H.M.S Dreadnaught is 40 miles south of Montauk and streaming due south at 20 mph, while the U.S Mona Lisa is 50 miles east of Montauk and streaming due east at an even 30 mph.

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Chapter 12.5, Problem 32E

Chapter 12.5, Problem 34E

Chapter 12 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

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The rate at which the distance between ships increasing where the H.M.S Dreadnaught is 40 miles south of Montauk and streaming due south at 20 mph, while the U.S Mona Lisa is 50 miles east of Montauk and streaming due east at an even 30 mph.

Solution Summary: The author explains how to calculate the rate at which the distance between ships is increasing, based on the Pythagorean Theorem.

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To calculate: The rate at which the distance between ships increasing where the H.M.S Dreadnaught is 40 miles south of Montauk and streaming due south at 20 mph, while the U.S Mona Lisa is 50 miles east of Montauk and streaming due east at an even 30 mph.

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Chapter 12 Solutions