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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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Question

Chapter 10, Problem 65SGA

To determine

To find: Approximately where should the thumbtacks be placed.

Expert Solution & Answer

Answer to Problem 65SGA

The thumbtacks should be placed about 1.8 feet from the center.

Explanation of Solution

Given information: Carpentry: For a remodeling project, a carpenter is building a picture window that is topped with an arch in the shape of a semi-ellipse. The width of the window is to be 7 feet and the height of the arch is to be 3 feet. To sketch the arch above the window, the carpenter uses a 7-foot string attached to two thumbtacks.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10, Problem 65SGA

Calculation:

Determine a .

Notice that:

The width is major axis.

2a=The widtha=The width2a=72=3.5

Determine b .

From the figure we have:

b=3

Conclude c .

c2=b2−a2c2=3.52−32c≈1.8

Thus, the thumbtacks should be placed about 1.8 feet from the center.

Chapter 10, Problem 64SGA

Chapter 10, Problem 1SAP

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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