Concept explainers
a.
To explain: Why the region in which the boat can travel is bounded by an ellipse.
a.
Answer to Problem 5PS
The total distance that the boat could travel is restricted for a
Explanation of Solution
Given:
The boat has enough fuel for ay13
Calculation:
The region in which the boat can travel is bounded by an ellipse because the total distance that the boat have to travel between the
It is restricted because the boat has fuel for a
Therefore the distance of the boat can travel is restricted to
b.
To explain: Why the region in which the boat can travel is bounded by an ellipse.
b.
Answer to Problem 5PS
The total distance that the boat could travel is restricted for a
Explanation of Solution
Given:
The boat has enough fuel for a
Calculation:
The region in which the boat can travel is bounded by an ellipse because the total distance that the boat have to travel between the
It is restricted because the boat has fuel for a
Therefore the distance of the boat can travel is restricted to
c.
To find: The coordinates of each island.
c.
Answer to Problem 5PS
The coordinate of island
The coordinate of island
Explanation of Solution
Given:
The boat has enough fuel for a
Calculation:
We know that the distance between two islands is
Where, distance between two island is the distance between two foci
If the center is at
Thus we can find the coordinates of each island.
d.
To find: How many miles does the boat travel.
d.
Answer to Problem 5PS
The boat travels the total distance of
Explanation of Solution
Given:
The boat has enough fuel for a
Calculation:
Distance between one island and the vertex near the other is given by
We know that the reach is bounded by an ellipse.
Therefore the total distance is
e.
To find: An equation of ellipse that bounds the region in which the boat can travel.
e.
Answer to Problem 5PS
The equation of the ellipse which the boat can travel is
Explanation of Solution
Given:
The boat has enough fuel for a
Calculation:
The distance between the center and the focus is
The distance between the center and vertex is
By using
The equation of the ellipse is,
Thus we can find the equation of the ellipse.
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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