The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at a height of 10 feet midway between the towers, what is the height of the cable at a point 50 feet from the center of the bridge?
Hello, magentarita!
Place the parabola on a graph.The cables of a suspension bridge are in the shape of a parabola.
The towers supporting the cable are 400 feet apart and 100 feet high.
If the cable is at a height of 10 feet midway between the towers,
what is the height of the cable at a point 50 feet from the center of the bridge?Code:| (-200,100)* | *(200,100) : | : :* | *: : * | * : : * | * : : * : : |(0,10) : : | : - - + - - - + - - - + -- -200 | 200
The parabola opens upward and is symmetric to the y-axis.
. . Its general form is: .
Its y-intercept is (0, 10) . . . Hence: .
It passes through (200, 100).
. . We have: .
Hence: .
When
Therefore, 50 feet from the center, the cable isfeet high.
What a marvelous explanation. How do you make your diagrams?Originally Posted by Soroban
Hello, magentarita!
Place the parabola on a graph.The parabola opens upward and is symmetric to the y-axis.Code:| (-200,100)* | *(200,100) : | : :* | *: : * | * : : * | * : : * : : |(0,10) : : | : - - + - - - + - - - + -- -200 | 200
. . Its general form is: .
Its y-intercept is (0, 10) . . . Hence: .
It passes through (200, 100).
. . We have: .
Hence: .
When
Therefore, 50 feet from the center, the cable is
  |
LinkBack URL
About LinkBacks