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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Concept explainers

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 10.5, Problem 5MCQ

(a)

To determine

To find: The greatest and least distance of the satellite from the surface of Earth, if the mean diameter of Earth is 7920 miles.

(a)

Expert Solution

Answer to Problem 5MCQ

Greatest distance = 2095.2 miles

Least distance = 424.8 miles

Explanation of Solution

Given information: Astronomy: A satellite orbiting Earth follows an elliptical path with the center of Earth as one focus. The eccentricity of the orbit is 0.16 and the major axis is 10,440 miles long.

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.5, Problem 5MCQ

Since e=ca→0.16=c104402→c=835.2

Least distance =a−c− radius→

5220−835.2−79202=424.8

The least distance = 424.8 miles

Greatest distance c−radius+5220→2095.2

(b)

To determine

To write: The equation of the orbit of the satellite, assuming that the center of the ellipse is the origin and the foci lie on the x -axis.

(b)

Expert Solution

Answer to Problem 5MCQ

x252202+y25152.752=1

Explanation of Solution

Calculation:

a2−b2=c252202−b2=835.22b=5152.75

This gives us:

x252202+y25152.752=1

Chapter 10.5, Problem 4MCQ

Chapter 10.5, Problem 6MCQ

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFU Ch. 10.1 - Prob. 2CFU Ch. 10.1 - Prob. 3CFU Ch. 10.1 - Prob. 4CFU Ch. 10.1 - Prob. 5CFU Ch. 10.1 - Prob. 6CFU Ch. 10.1 - Prob. 7CFU Ch. 10.1 - Prob. 8CFU Ch. 10.1 - Prob. 9CFU Ch. 10.1 - Prob. 10CFU

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