Concept explainers
(a)
To find: The position of the tacks in the fireplace arch.
(a)
Answer to Problem 54E
The position of the tacks in the fireplace arch is
Explanation of Solution
Given information:
A fireplace arch is to be constructed in the shape of a semiellipse. The opening is to have a height of
Calculation:
As the width of the semi ellipse is
Use the formula for the length of major axis.
So, the value of the
As the height of the semi ellipse is
Use the formula.
As per the diagram the center of the ellipse is origin and the major axis is horizontal.
The points for the foci of the ellipse are:
Therefore, the position of the tacks in the fireplace arch is
(b)
To find: The length of the string used in the semi ellipse fireplace arch.
(b)
Answer to Problem 54E
The length of the string is
Explanation of Solution
Given information:
A fireplace arch is to be constructed in the shape of a semiellipse. The opening is to have a height of
Calculation:
The formula for the length of string is
As solved in part(a), substitute
Therefore, the length of the string is
Chapter 9 Solutions
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