(a)
Area under the parabolic arch.
(a)
Answer to Problem 64E
Area under the parabolic arch,
Explanation of Solution
Given information:
Such that
For
With
Area under the parabolic arch,
(b)
Height of the arch.
(b)
Answer to Problem 64E
Height of the arch is
Explanation of Solution
Given information:
The height of the arch is the y − coordinate of the parabola’s vertex.
The vertex of a parabola of the form
Is at
For
With
Thus,
The vertex is at:
Now,
To find the y − coordinate of the vertex:
Substitute
Into
Thus,
(c)
Area is two − thirds the base times the height.
(c)
Answer to Problem 64E
Area will be same as area under the parabolic arch.
Explanation of Solution
Given information:
Base,
From Part (b) result,
The height is
Now,
This is same as value for area under parabolic arch obtained in Part (a).
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
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