Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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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Chapter 10.3, Problem 52E

(a)

To determine

To find: Where should the thumbtacks be placed

(a)

Expert Solution
Check Mark

Answer to Problem 52E

The thumbtacks should be 3.71 feet from center

Explanation of Solution

Given information: Construction: The arch of a fireplace is to be constructed in the shape of a semi-ellipse. The opening is to have a height of 3 feet at the center and a width of 8 feet along the base. To sketch the outline of the fireplace, the contractor uses an

8-foot string tied to two thumbtacks.

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.3, Problem 52E , additional homework tip 1

Calculation:

Creating the equation with a=4,b=1.5 ,

You can find the location of the foci by:

  a2−b2=c2c2=16−2.25c=13.75c=3.71

This means the thumbtacks should be 3.71 feet from the center.

(b)

To determine

To explain: Why this technique works.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given information: Construction: The arch of a fireplace is to be constructed in the shape of a semi-ellipse. The opening is to have a height of 3 feet at the center and a width of 8 feet along the base. To sketch the outline of the fireplace, the contractor uses an

8-foot string tied to two thumbtacks.

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.3, Problem 52E , additional homework tip 2

Calculation:

This works on the principal of the ellipse.

By placing the thumbtacks 3.71 feet from center using and 8 foot string, will allow to create the elliptical shape desired.

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Chapter 10.3, Problem 51E
Next
Chapter 10.3, Problem 53E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFUCh. 10.1 - Prob. 2CFUCh. 10.1 - Prob. 3CFUCh. 10.1 - Prob. 4CFUCh. 10.1 - Prob. 5CFUCh. 10.1 - Prob. 6CFUCh. 10.1 - Prob. 7CFUCh. 10.1 - Prob. 8CFUCh. 10.1 - Prob. 9CFUCh. 10.1 - Prob. 10CFU
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Prob. 8CFUCh. 10.3 - Prob. 9CFUCh. 10.3 - Prob. 10CFUCh. 10.3 - Prob. 11CFUCh. 10.3 - Prob. 12CFUCh. 10.3 - Prob. 13CFUCh. 10.3 - Prob. 14CFUCh. 10.3 - Prob. 15CFUCh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Prob. 49ECh. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Prob. 55ECh. 10.3 - Prob. 56ECh. 10.3 - Prob. 57ECh. 10.3 - Prob. 58ECh. 10.3 - Prob. 59ECh. 10.3 - Prob. 60ECh. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 1GCECh. 10.3 - Prob. 2GCECh. 10.3 - Prob. 3GCECh. 10.3 - Prob. 4GCECh. 10.3 - Prob. 5GCECh. 10.3 - Prob. 6GCECh. 10.3 - Prob. 7GCECh. 10.3 - Prob. 8GCECh. 10.4 - Prob. 1CFUCh. 10.4 - Prob. 2CFUCh. 10.4 - Prob. 3CFUCh. 10.4 - Prob. 4CFUCh. 10.4 - Prob. 5CFUCh. 10.4 - Prob. 6CFUCh. 10.4 - Prob. 7CFUCh. 10.4 - Prob. 8CFUCh. 10.4 - Prob. 9CFUCh. 10.4 - Prob. 10CFUCh. 10.4 - Prob. 11CFUCh. 10.4 - Prob. 12CFUCh. 10.4 - Prob. 13CFUCh. 10.4 - Prob. 14CFUCh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.5 - Prob. 1CFUCh. 10.5 - Prob. 2CFUCh. 10.5 - Prob. 3CFUCh. 10.5 - Prob. 4CFUCh. 10.5 - Prob. 5CFUCh. 10.5 - Prob. 6CFUCh. 10.5 - Prob. 7CFUCh. 10.5 - Prob. 8CFUCh. 10.5 - Prob. 9CFUCh. 10.5 - Prob. 10CFUCh. 10.5 - Prob. 11CFUCh. 10.5 - Prob. 12CFUCh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Prob. 42ECh. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - Prob. 45ECh. 10.5 - Prob. 1MCQCh. 10.5 - Prob. 2MCQCh. 10.5 - Prob. 3MCQCh. 10.5 - Prob. 4MCQCh. 10.5 - Prob. 5MCQCh. 10.5 - Prob. 6MCQCh. 10.5 - Prob. 7MCQCh. 10.5 - Prob. 8MCQCh. 10.5 - Prob. 9MCQCh. 10.5 - Prob. 10MCQCh. 10.6 - Prob. 1GCECh. 10.6 - Prob. 2GCECh. 10.6 - Prob. 3GCECh. 10.6 - Prob. 4GCECh. 10.6 - Prob. 5GCECh. 10.6 - Prob. 1CFUCh. 10.6 - Prob. 2CFUCh. 10.6 - Prob. 3CFUCh. 10.6 - Prob. 4CFUCh. 10.6 - Prob. 5CFUCh. 10.6 - Prob. 6CFUCh. 10.6 - Prob. 7CFUCh. 10.6 - Prob. 8CFUCh. 10.6 - Prob. 9CFUCh. 10.6 - Prob. 10CFUCh. 10.6 - Prob. 11CFUCh. 10.6 - Prob. 12CFUCh. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - Prob. 18ECh. 10.6 - Prob. 19ECh. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - Prob. 23ECh. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - Prob. 27ECh. 10.6 - Prob. 28ECh. 10.6 - Prob. 29ECh. 10.6 - Prob. 30ECh. 10.6 - Prob. 31ECh. 10.6 - Prob. 32ECh. 10.6 - Prob. 33ECh. 10.6 - Prob. 34ECh. 10.6 - Prob. 35ECh. 10.6 - Prob. 36ECh. 10.6 - Prob. 37ECh. 10.6 - Prob. 38ECh. 10.6 - Prob. 39ECh. 10.6 - Prob. 40ECh. 10.6 - Prob. 41ECh. 10.6 - Prob. 42ECh. 10.6 - Prob. 43ECh. 10.6 - Prob. 44ECh. 10.6 - Prob. 45ECh. 10.6 - Prob. 46ECh. 10.6 - Prob. 47ECh. 10.6 - Prob. 48ECh. 10.6 - Prob. 49ECh. 10.6 - Prob. 50ECh. 10.6 - Prob. 51ECh. 10.6 - Prob. 52ECh. 10.6 - Prob. 53ECh. 10.6 - Prob. 54ECh. 10.6 - Prob. 55ECh. 10.6 - Prob. 56ECh. 10.7 - Prob. 1CFUCh. 10.7 - Prob. 2CFUCh. 10.7 - Prob. 3CFUCh. 10.7 - Prob. 4CFUCh. 10.7 - Prob. 5CFUCh. 10.7 - Prob. 6CFUCh. 10.7 - Prob. 7CFUCh. 10.7 - Prob. 8CFUCh. 10.7 - Prob. 9CFUCh. 10.7 - Prob. 10CFUCh. 10.7 - Prob. 11CFUCh. 10.7 - Prob. 12CFUCh. 10.7 - Prob. 13ECh. 10.7 - Prob. 14ECh. 10.7 - Prob. 15ECh. 10.7 - Prob. 16ECh. 10.7 - Prob. 17ECh. 10.7 - Prob. 18ECh. 10.7 - Prob. 19ECh. 10.7 - Prob. 20ECh. 10.7 - Prob. 21ECh. 10.7 - Prob. 22ECh. 10.7 - Prob. 23ECh. 10.7 - Prob. 24ECh. 10.7 - Prob. 25ECh. 10.7 - Prob. 26ECh. 10.7 - Prob. 27ECh. 10.7 - Prob. 28ECh. 10.7 - Prob. 29ECh. 10.7 - Prob. 30ECh. 10.7 - Prob. 31ECh. 10.7 - Prob. 32ECh. 10.7 - Prob. 33ECh. 10.7 - Prob. 34ECh. 10.7 - Prob. 35ECh. 10.7 - Prob. 36ECh. 10.7 - Prob. 37ECh. 10.7 - Prob. 38ECh. 10.7 - Prob. 39ECh. 10.7 - Prob. 40ECh. 10.7 - Prob. 41ECh. 10.7 - Prob. 42ECh. 10.7 - Prob. 43ECh. 10.7 - Prob. 44ECh. 10.7 - Prob. 45ECh. 10.7 - Prob. 46ECh. 10.7 - Prob. 47ECh. 10.7 - Prob. 48ECh. 10.7 - Prob. 49ECh. 10.7 - Prob. 50ECh. 10.7 - Prob. 51ECh. 10.7 - Prob. 52ECh. 10.7 - Prob. 53ECh. 10.7 - Prob. 54ECh. 10.7 - Prob. 55ECh. 10.7 - Prob. 56ECh. 10.7 - Prob. 57ECh. 10.7 - Prob. 58ECh. 10.7 - Prob. 59ECh. 10.8 - Prob. 1CFUCh. 10.8 - Prob. 2CFUCh. 10.8 - Prob. 3CFUCh. 10.8 - Prob. 4CFUCh. 10.8 - Prob. 5CFUCh. 10.8 - Prob. 6CFUCh. 10.8 - Prob. 7CFUCh. 10.8 - Prob. 8CFUCh. 10.8 - Prob. 9CFUCh. 10.8 - Prob. 10CFUCh. 10.8 - Prob. 11CFUCh. 10.8 - Prob. 12CFUCh. 10.8 - Prob. 13ECh. 10.8 - Prob. 14ECh. 10.8 - Prob. 15ECh. 10.8 - Prob. 16ECh. 10.8 - Prob. 17ECh. 10.8 - Prob. 18ECh. 10.8 - Prob. 19ECh. 10.8 - Prob. 20ECh. 10.8 - Prob. 21ECh. 10.8 - Prob. 22ECh. 10.8 - Prob. 23ECh. 10.8 - Prob. 24ECh. 10.8 - Prob. 25ECh. 10.8 - Prob. 26ECh. 10.8 - Prob. 27ECh. 10.8 - Prob. 28ECh. 10.8 - Prob. 29ECh. 10.8 - Prob. 30ECh. 10.8 - Prob. 31ECh. 10.8 - Prob. 32ECh. 10.8 - Prob. 33ECh. 10.8 - Prob. 34ECh. 10.8 - Prob. 35ECh. 10.8 - Prob. 36ECh. 10.8 - Prob. 37ECh. 10.8 - Prob. 38ECh. 10.8 - Prob. 39ECh. 10.8 - Prob. 40ECh. 10.8 - Prob. 41ECh. 10.8 - Prob. 42ECh. 10.8 - Prob. 43ECh. 10.8 - Prob. 44ECh. 10.8 - Prob. 45ECh. 10.8 - Prob. 46ECh. 10.8 - Prob. 47ECh. 10.8 - Prob. 48ECh. 10.8 - Prob. 49ECh. 10.8 - Prob. 50ECh. 10.8B - Prob. 1GCECh. 10.8B - Prob. 2GCECh. 10.8B - Prob. 3GCECh. 10.8B - Prob. 4GCECh. 10.8B - Prob. 5GCECh. 10.8B - Prob. 6GCECh. 10 - Prob. 1SGACh. 10 - Prob. 2SGACh. 10 - Prob. 3SGACh. 10 - Prob. 4SGACh. 10 - Prob. 5SGACh. 10 - Prob. 6SGACh. 10 - Prob. 7SGACh. 10 - Prob. 8SGACh. 10 - Prob. 9SGACh. 10 - Prob. 10SGACh. 10 - Prob. 11SGACh. 10 - Prob. 12SGACh. 10 - Prob. 13SGACh. 10 - Prob. 14SGACh. 10 - Prob. 15SGACh. 10 - Prob. 16SGACh. 10 - Prob. 17SGACh. 10 - Prob. 18SGACh. 10 - Prob. 19SGACh. 10 - Prob. 20SGACh. 10 - Prob. 21SGACh. 10 - Prob. 22SGACh. 10 - Prob. 23SGACh. 10 - Prob. 24SGACh. 10 - Prob. 25SGACh. 10 - Prob. 26SGACh. 10 - Prob. 27SGACh. 10 - Prob. 28SGACh. 10 - Prob. 29SGACh. 10 - Prob. 30SGACh. 10 - Prob. 31SGACh. 10 - Prob. 32SGACh. 10 - Prob. 33SGACh. 10 - Prob. 34SGACh. 10 - Prob. 35SGACh. 10 - Prob. 36SGACh. 10 - Prob. 37SGACh. 10 - Prob. 38SGACh. 10 - Prob. 39SGACh. 10 - Prob. 40SGACh. 10 - Prob. 41SGACh. 10 - Prob. 42SGACh. 10 - Prob. 43SGACh. 10 - Prob. 44SGACh. 10 - Prob. 45SGACh. 10 - Prob. 46SGACh. 10 - Prob. 47SGACh. 10 - 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What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY