Concept explainers
(a)
To find: the coordinates of the focus.
(a)
Answer to Problem 71E
Therefore the focus of the suspension bridge is at
Explanation of Solution
Given information:
Given cable of a suspension bridge is suspected between two towers.
Calculation:
Consider that a suspension bridge is suspended in the shape of a parabola between two towers 120 feet apart. The height of given tower is 20 feet.
Take the midpoint of the suspension bridge as the origin and draw coordinate axes so that the vertex of the parabola is at the point
Let us find the focus of the parabola.
With the vertex at the origin and the coordinate axes as shown in the figure, and the parabola opening upwards, the standard equation of the parabola is given by
Since the points
Since, the axis of the parabola is
(b)
To write: an equation that models the cables.
(b)
Answer to Problem 71E
The equation the parabola representing the suspension bridge is given by
Explanation of Solution
Calculation:
Let us now find the equation of the parabola.
Substitute the value of
Therefore the equation the parabola representing the suspension bridge is given by
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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