a.
To write: and graph a system of inequalities that describes the requirements of the facility.
a.
Answer to Problem 34E
The system of inequality is:
The graph will be
Explanation of Solution
Given
A physical fitness facility is constructing an indoor running track with space for exercise equipment inside the track. The track must be at least 125 meters long, and the exercise space must have an area of at least 500 square meters.
Concept used:
Area of rectangle: length
Radius of the circle is
Calculation:
Let x be the length and y be the breadth
The area inside the rectangle must be at least 500 square meters, so
The length of track must be at least 125m
The length of the track consists of two semicircles at the breadth side and a rectangle in middle.
Here breadth is equal to diameter of the semicircles
Since we have two semicircles having equal radius
The length of the track will be
From the given condition
The dimensions (length and breadth) are always greater or equal to 0
So,
The system of inequality is:
Here
The table for
Plot the points and join them along with all the conditions mentioned above
b.
To calculate: two solutions of the system and interpret their meanings in the context of the problem.
b.
Answer to Problem 34E
The two solutions are
Explanation of Solution
Given information
A physical fitness facility is constructing an indoor running track with space for exercise equipment inside the track. The track must be at least 125 meters long, and the exercise space must have an area of at least 500 square meters.
The systems of equations are
The solution to the above system is
Concept used:
Any points on the solution region can be solutions of the system
Calculation:
From the graph we can see that
Hence
For
The area of the space will be
For
The area of the space will be
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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