(a) Answer x 2 + y 2 = 400 Explanation Given information: Gardening: Migina bought a new sprinkler that covers part or all of a circular area. With the center of the sprinkler as the origin, the sprinkler sends out water far enough to reach a point located at ( 12 , 16 ) . Calculation: Determine the radius: r = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 r = ( 12 − 0 ) 2 + ( 16 − 0 ) 2 r = 20 The equation representing the farthest points is the circle with center ( 0 , 0 ) and radius r . x 2 + y 2 = r 2 x 2 + y 2 = 20 2 ⇒ x 2 + y 2 = 400 (b) To determine To find: The percent of her backyard will not be watered directly, if Migina waters her backyard without moving the sprinkler. Migina’s backyard is 40 feet wide and 50 feet long. Answer 37 % Explanation Given information: Gardening: Migina bought a new sprinkler that covers part or all of a circular area. With the center of the sprinkler as the origin, the sprinkler sends out water far enough to reach a point located at ( 12 , 16 ) . Calculation: Determine the area of backyard: The area of backyard = l w = 50 × 40 = 2000 ft 2 Determine area of watered portion: Area of watered portion = π r 2 = π × 20 = 1256.6 ft 2 Determine the area of no watered portion: Area of no water portion = Area of backyard − Area of watered portion ≈ 2000 − 1256.6 ≈ 743.4 ft 2 Conclude the percent: Percent not watered ≈ 743.4 2000 = 0.37 = 37 %

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 10, Problem 63SGA

(a)

To determine

To find: An equation representing the farthest points the sprinkler can reach.

(a)

Expert Solution

Answer to Problem 63SGA

x2+y2=400

Explanation of Solution

Given information: Gardening: Migina bought a new sprinkler that covers part or all of a circular area. With the center of the sprinkler as the origin, the sprinkler sends out water far enough to reach a point located at (12,16) .

Calculation:

Determine the radius:

r=(x2−x1)2+(y2−y1)2r=(12−0)2+(16−0)2r=20

The equation representing the farthest points is the circle with center (0,0) and radius r .

x2+y2=r2x2+y2=202⇒x2+y2=400

(b)

To determine

To find: The percent of her backyard will not be watered directly, if Migina waters her backyard without moving the sprinkler. Migina’s backyard is 40 feet wide and 50 feet long.

(b)

Expert Solution

Answer to Problem 63SGA

37%

Explanation of Solution

Calculation:

Determine the area of backyard:

The area of backyard =lw

=50×40=2000 ft2

Determine area of watered portion:

Area of watered portion =πr2

=π×20=1256.6 ft2

Determine the area of no watered portion:

Area of no water portion = Area of backyard − Area of watered portion

≈2000−1256.6≈743.4 ft2

Conclude the percent:

Percent not watered ≈743.42000=0.37=37%

Chapter 10, Problem 62SGA

Chapter 10, Problem 64SGA

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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