Concept explainers
To explain: the position of the arm, the length andwhen to use more than one arm
Answer to Problem 63AYU
Square field:
It is concluded that the arm should be positioned at a distance of
Rectangular field:
It is concluded that the arm should be positioned at a distance of
A circle is not circumscribed around a long rectangle with the diagonal as its diameter. Thus, it becomes desirable to use more than one arm.
Explanation of Solution
Given:
First, consider the square field. Let s be the side length of the square field.
From the figure, the arm is positioned at the center of the circle and its length should be the radius.
By the Pythagorean theorem, the diagonal of the square field is
That is, the center of the circle is
Thus, it is concluded that the arm should be positioned at a distance of
Now, consider the rectangular field. Let
In this case also, the arm is positioned at the center of the circle and its length should be the radius.
By the Pythagorean theorem, the diagonal of the rectangular field is
That is, the center of the circle is
Thus, it is concluded that the arm should be positioned at a distance of
When the length of a rectangular field is much larger than its width, the watering pattern cannot be a circle. This is because a circle is not circumscribed around a long rectangle with the diagonal as its diameter.
Thus, it becomes desirable to use more than one arm.
Conclusion:
Square field:
It is concluded that the arm should be positioned at a distance of
Rectangular field:
It is concluded that the arm should be positioned at a distance of
A circle is not circumscribed around a long rectangle with the diagonal as its diameter.Thus, it becomes desirable to use more than one arm.
Chapter 1 Solutions
Precalculus
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