(a)
To find: The standard equation that describes the outer boundary of the earthquake if the epicenter is at
(a)
Answer to Problem 41E
The standard equation that describes the outer boundary of the earthquake is
Explanation of Solution
Given information:
An earthquake was felt up to
Formula Used:
Use the general equation of circle with center at
Calculation:
An earthquake was felt up to
The earthquake was felt up to
Substitute
Therefore, the standard equation that describes the outer boundary of the earthquake is
(b)
To check: The earthquake was felt
(b)
Answer to Problem 41E
Yes, the earthquake was felt at the
Explanation of Solution
Given information:
An earthquake was felt up to
Calculation:
If the earthquake was felt at given location, then the distance of the distance of the given point from the epicenter must be less than or equal to the radius of the circle.
The location for
Use the distance formula between the two points
Substitute
As the distance of the location from the epicenter is less than the radius of the circle representing the boundary of the earthquake.
Therefore, the earthquake was felt at the
(c)
To prove: The answer of part(b) by graphing the equation of the outer boundary of earthquake and the location and also calculate the distance of the location from the boundary of the earthquake.
(c)
Answer to Problem 41E
The graph of the equation of outer boundary of earthquake and location is plotted in Figure (1). The distance of the location from the outer boundary of the earthquake is
Explanation of Solution
Given information:
An earthquake was felt up to
Calculation:
The graph of the equation of outer boundary of earthquake and location is shown below.
Figure (1)
As the point of location is lying inside the circle of the outer boundary of earthquake.
Therefore, the earthquake was felt at the
As calculated in part(b), the distance of the location from the epicenter is
Therefore, the distance of the location from the outer boundary of the earthquake is
Chapter 9 Solutions
Precalculus with Limits: A Graphing Approach
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