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kandsbbf

  • 2 years ago

You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y = –0.000471x² + .837x where x and y are measured in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch? The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 1,777.07 ft. The bridge is about 371.85 ft. above the river, and the length of the bri

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  1. kandsbbf
    • 2 years ago
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    The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 1,777.07 ft. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 371.85 ft.

  2. kandsbbf
    • 2 years ago
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    plss help???

  3. campbell_st
    • 2 years ago
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    ok... to find the distance spanned by the arch you need to solve it so \[-0.00047x^2 + 0.837x = 0... or... -x(0.00047x - 0.837)\] so x = 0 or 0.837/0.00047 the distance between the points will be the distance spanned. |dw:1358113884987:dw|

  4. campbell_st
    • 2 years ago
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    ok... do you know to differentiate..?

  5. kandsbbf
    • 2 years ago
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    no lol what is that?

  6. campbell_st
    • 2 years ago
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    ok... do you know how to find the line of symmetry of the curve...?

  7. kandsbbf
    • 2 years ago
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    no

  8. campbell_st
    • 2 years ago
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    what answer did you get got the distance spanned by the bridge..?

  9. kandsbbf
    • 2 years ago
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    1,780.851

  10. kandsbbf
    • 2 years ago
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    @campbell_st

  11. campbell_st
    • 2 years ago
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    oops missed a digit it should be 0.837/0.000471 and you should get 1777.07

  12. campbell_st
    • 2 years ago
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    ok so the parabola is symmetric and the highest point of the arch is on the line of symmetry... do you know how to find the line of symmetry..?

  13. kandsbbf
    • 2 years ago
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    is it the line that goes down the middle?

  14. campbell_st
    • 2 years ago
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    thats it...

  15. kandsbbf
    • 2 years ago
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    so how do i figure it out?

  16. campbell_st
    • 2 years ago
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    ok... so find half the distance spanned by the arch... then substitute that value into the equation for the bridge... that will give the height does that make sense..

  17. kandsbbf
    • 2 years ago
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    soooo divide 1777.07 by 2?

  18. campbell_st
    • 2 years ago
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    yep... then substitute it... the highest point is at the centre of the acrch

  19. kandsbbf
    • 2 years ago
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    which equation?

  20. campbell_st
    • 2 years ago
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    the original equation 0.000471x^2 + 0.837x

  21. kandsbbf
    • 2 years ago
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    okay so when i divided it by 2 i got 888.535..... which number do i sub that for in the equation?

  22. campbell_st
    • 2 years ago
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    thats correct...

  23. kandsbbf
    • 2 years ago
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    so do i sub that in for x?

  24. campbell_st
    • 2 years ago
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    yes so its \[-0.000471\times(888.535)^2 + 0.837\times888.535\]

  25. kandsbbf
    • 2 years ago
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    so it's D

  26. campbell_st
    • 2 years ago
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    what did you get for the height..? the length is 1777.07

  27. kandsbbf
    • 2 years ago
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    371.85

  28. campbell_st
    • 2 years ago
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    ok... which answer has height 371.85 and length 1777.07

  29. kandsbbf
    • 2 years ago
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    B

  30. campbell_st
    • 2 years ago
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    thats it.. well done

  31. kandsbbf
    • 2 years ago
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    did we answer the last part of the question? How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch?

  32. campbell_st
    • 2 years ago
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    yes... you have all the answers you need height = 371.85 and length 1777.07

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