Algebra II

posted by .

I'm confused..

1. The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 600 feet apart and 80 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point 150 feet from the middle of the bridge?

2. A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, how deep should the search light be?

What is be best to set up a graph for these? And what is a paraboloid?

  • Algebra II -

    1. The parabola shape is of the form y = a x^2, where y is the height and x is the horiziontal distance from the lowest point.

    80 = a (300)^2
    a = 80/(300)^2
    When x = 150, y = 80*150^2/300^2 = 80*(1/4) = 20 feet

    2. A paraboloid is the solid shape that you get when you rotate a parabola about its axis of symmetry. The light source will be located at the focus of the parabola so that the light that imerges is a parallel beam. (They should have told you that). Figure out the equation of the parabola from those facts and then calculate the depth of the parabola when the width is 5 feet.

  • Algebra II -

    Ah thanks!

  • Algebra II -

    The main cables of a suspension bridge uniformly distribute the weight of the bridge when in the form of a parabola. The main cables of a particular bridge are attached to towers that are 600 fi apart. The cables are attached to the towers at a height of 110 ft above the roadway and are 10 ft above the roadway at their lowest points. If vertical support cables are at 50-ft intervals along the level roadway, what are the lengths of these vertical cables?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    the lions gate bridge in vancuver BC, is a suspension bridge that spans 1516m. Large cables are attached to the tops of the towers, 50m above the road. the road is suspended from the large cables with small vertical cables, the smallest …
  2. Math

    The Lions Gate bridge in Vancouver is a suspension bridge. The main span between the two towers, is 427m long. Large cables are attached to the ends of the both towers, 50m above the road. Each large cable forms a parabola. The road …
  3. Pre - Cal

    1. Find the vertex of the parabola: 4y^2+4y-16x=0 2. Find an equation of the parabola, opening down, with vertex (-3,1) and solution point (4,-5). 3. The main cables of a suspension bridge are 20 meters above the road at the towers …
  4. math

    In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 400 m apart, and the lowest point of the suspension cables is 100 m below the top of the towers. Find the equation …
  5. precalculus

    one section of a suspension bridge has its weight uniformly distributed between twin towers that are 400 feet apart and rise 90 feet above the horizontal roadway. a cable strung between the tops of the towers has the shape of a parabola, …
  6. analytic geometry

    The main cables of a suspension bridge uniformly distribute the weight of the bridge when in the form of a parabola. The main cables of a particular bridge are attached to towers that are 600 ft apart. The cables are attached to towers …
  7. Pre - Cal

    ) The main cables of a suspension bridge are 20 meters above the road at the towers and 4 meters above the road at the center. The road is 80 meters long. Vertical cables are spaced every 10 meters. The main cables hang in the shape …
  8. Pre calc quadratic stuff

    The main suspension bridge has cables in shape of a parabola. suppose pinte on tops of where towers and cables are attatched are 168 m apart and 24 m vertically above the minimum height. determine the quadratic function in vertex form …
  9. analytic geometry

    16. A cable of a suspension bridge hangs in the form of a parabola, the Supporting towers of the cable being 300 meters apart. over the supporting towers at a height of 60 meters above the roadwayand the lowest point of the cable is …
  10. analytic geometry

    16. A cable of a suspension bridge hangs in the form of a parabola, the Supporting towers of the cable being 300 meters apart. over the supporting towers at a height of 60 meters above the roadwayand the lowest point of the cable is …

More Similar Questions