(a) Explanation Formula used: The standard equation of the circle with center at ( h , k ) and radius r is ( x − h ) 2 + ( y − k ) 2 = r 2 . Calculation: Consider the circle x 2 + y 2 = 100 . By the formula stated above the circle x 2 + y 2 = 100 has center at ( 0 , 0 ) and radius r = 10 . Consider the circle x 2 + y 2 − 20 x + 75 = 0 . The given equation of the circle is not in the standard form rewrite the equation into standard form as follows, x 2 + y 2 − 20 x + 75 = 0 x 2 − 20 x + y 2 = − 75 In order to complete the square of the x terms add 100 on both sides of the equation as follows, ( x 2 (b) To determine To find: The farthest the shorter path is to the fountain when a rose garden has two intersecting circular paths with a fountain in the center of the longer path. The paths can be represented by the equations x 2 + y 2 − 20 x + 75 = 0 and x 2 + y 2 = 100 . (c) To determine To find: How far apart are the intersection of the paths when a rose garden has two intersecting circular paths with a fountain in the center of the longer path. The paths can be represented by the equations x 2 + y 2 − 20 x + 75 = 0 and x 2 + y 2 = 100 .

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 21.3, Problem 62E

(a)

To determine

To find: The closest path to the fountain when a rose garden has two intersecting circular paths with a fountain in the center of the longer path. The paths can be represented by the equations x2+y2−20x+75=0 and x2+y2=100.

(b)

To determine

To find: The farthest the shorter path is to the fountain when a rose garden has two intersecting circular paths with a fountain in the center of the longer path. The paths can be represented by the equations x2+y2−20x+75=0 and x2+y2=100.

(c)

To determine

To find: How far apart are the intersection of the paths when a rose garden has two intersecting circular paths with a fountain in the center of the longer path. The paths can be represented by the equations x2+y2−20x+75=0 and x2+y2=100.

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Chapter 21.3, Problem 61E

Chapter 21.3, Problem 63E

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Chapter 21 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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The closest path to the fountain when a rose garden has two intersecting circular paths with a fountain in the center of the longer path. The paths can be represented by the equations x 2 + y 2 − 20 x + 75 = 0 and x 2 + y 2 = 100 .

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To find: The closest path to the fountain when a rose garden has two intersecting circular paths with a fountain in the center of the longer path. The paths can be represented by the equations x2+y2−20x+75=0 and x2+y2=100.

To find: The farthest the shorter path is to the fountain when a rose garden has two intersecting circular paths with a fountain in the center of the longer path. The paths can be represented by the equations x2+y2−20x+75=0 and x2+y2=100.

To find: How far apart are the intersection of the paths when a rose garden has two intersecting circular paths with a fountain in the center of the longer path. The paths can be represented by the equations x2+y2−20x+75=0 and x2+y2=100.

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Chapter 21 Solutions