Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Two circles have circumferences that add up to $12 π cm$ and areas that add up to $20 π {cm}^{2}$ . Find the radius of each circle.

The radius of the two circles are $2 a n d 4$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Assume x to be the radius of the first circle and y to be the radius of the second circle.

From the question,

$2 πx + 2 πy = 12 π . . . . . . (i) {πx}^{2} + {πy}^{2} = 20 π . . . . . . (ii)$

Take out the common factors from equation (i),

$2 π (x + y) = 2 π (6) x + y = 6 . . . . . . . (iii)$

Take out the common factors from equation (ii),

$π (x^{2} + y^{2}) = 20 π x^{2} + y^{2} = 20 . . . . . . (iv)$

Step 2. Solve equation (iii) for x.

Solving equation (iii) for x,

$x = 6 - y$

Substitute the value of x in equation (iv),

localid="1646849857123" role="math" ${(6 - y)}^{2} + y^{2} = 20 (y - 4) (y - 2) = 0 y = 4, 2$

Substitute $y = 4$ in equation (iii),

$x + 4 = 6 x = 2$

Substitute $y = 2$ in equation (iii),

$x + 2 = 6 x = 4$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Two circles have circumferences that add up to $12 π cm$ and areas that add up to $20 π {cm}^{2}$ . Find the radius of each circle.

Step by Step Solution

Step 1. Given information.

Step 2. Solve equation (iii) for x.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Two circles have circumferences that add up to 12π cm and areas that add up to 20π cm2. Find the radius of each circle.

Step by Step Solution

Step 1. Given information.

Step 2. Solve equation (iii) for x.

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Two circles have circumferences that add up to $12 π cm$ and areas that add up to $20 π {cm}^{2}$ . Find the radius of each circle.