Concept explainers
a.
Draw a sketch of the bridge. Locate the origin of a rectangular
a.
Answer to Problem 72E
Explanation of Solution
Given information:
Each cable of the Golden Gate Bridge is suspended (in the shape of a parabola) between two towers that are
Draw a sketch of the bridge. Locate the origin of a rectangular coordinate system at the centre of the roadway. Label the coordinates of the known points.
Calculation:
Consider Golden Gate Bridge is suspended (in the shape of a parabola) between two towers that are
The height of each tower is
Take the midpoint of suspension bridge as the origin and draw coordinate axis so that the vertex of the parabola is at point
Hence, the a sketch of the bridge is as shown.
b.
Write an equation that models the cables.
b.
Answer to Problem 72E
Explanation of Solution
Given information:
Each cable of the Golden Gate Bridge is suspended (in the shape of a parabola) between two towers that are
Write an equation that models the cables.
Calculation:
Golden Gate Bridge is suspended (in the shape of a parabola) between two towers that are
The height of each tower is
Take the midpoint of suspension bridge as the origin and draw coordinate axis so that the vertex of the parabola is at point
Consider the upward opening parabola standard equation.
Now substitute
Now substitute the value of
Hence, the equation of parabola representing the suspension bridge is as shown.
c.
Write an equation that models the cables.
c.
Answer to Problem 72E
Explanation of Solution
Given information:
Each cable of the Golden Gate Bridge is suspended (in the shape of a parabola) between two towers that are
Complete the table by finding the height of the suspension cables over the roadway at a distance of meters from the centre of the bridge.
Calculation:
Consider the equation,
Now substitute the corresponding value of
For
For
For
For
Hence, the results are tabulated as,
Chapter 10 Solutions
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