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kikojuarez12 Group Title

An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 4 inches tall and stand 40 inches apart. At some point along the road from the lowest point of the cable, the cable is 0.64 inches above the roadway. Find the distance between that point and the base of the nearest tower.

  • one year ago
  • one year ago

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  1. Sujay Group Title
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    I might be mistaken, but it looks like there isn't enough information. Based on the information provided--the diagram looks like this.

    • one year ago
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  2. kikojuarez12 Group Title
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    can someone explain me in words plz

    • one year ago
  3. scarydoor Group Title
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    There's enough information. Can more than likely assume the towers are of equal height. Then that's enough to derive the coefficients of the parabola. Then you just take the inverse of it, sort of.

    • one year ago
  4. scarydoor Group Title
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    You've got a parabola f(x) = x^2 + ax + b. Where f(40)=f(0)=4, and f(20)=0. Use that to find the coefficients a, b. Now set f(x) = 0.64, and rearrange to find what value of x makes that happen.

    • one year ago
  5. kikojuarez12 Group Title
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    a= 4 b=0?

    • one year ago
  6. scarydoor Group Title
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    No. f(0) = b = 4.

    • one year ago
  7. scarydoor Group Title
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    f(40) = 40^2 + a*40 + b = 40^2 + a*40 + 4 = 4. implies that 1600 + 40 * a = 0. implies that a = -1600 / 40.

    • one year ago
  8. kikojuarez12 Group Title
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    the answer I got is -14396

    • one year ago
  9. scarydoor Group Title
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    |dw:1355013328506:dw|

    • one year ago
  10. scarydoor Group Title
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    Can you show your derivation? I've shown my derivation above and it's different, and I can't see any error in it...

    • one year ago
  11. Sujay Group Title
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    That can't be true, it is a bridge, that means the towers must be above AND below the road.

    • one year ago
  12. scarydoor Group Title
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    It's not realistic though. The arch should also be a catenary, but it's not...

    • one year ago
  13. kikojuarez12 Group Title
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    now i got 4

    • one year ago
  14. scarydoor Group Title
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    I bet the question designers meant it to be interpreted as the tower height measured from road level. Otherwise the description would be more complicated again and wouldn't add anythign except to make people happy who want it measured as it would be in real life, in some circumstances.

    • one year ago
  15. Sujay Group Title
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    A suspension bridge has the roadway in between the top and bottom of the towers, the roadway won't be at the bottom (then it won't really be a bridge at all...).

    • one year ago
  16. Sujay Group Title
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    Scarydoor, you may be right

    • one year ago
  17. scarydoor Group Title
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    Probably am. Questions like this, designed to present basic calculus with some variation, don't want to confuse people with the intricacies of engineering...

    • one year ago
  18. scarydoor Group Title
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    Maybe we should account for material expansion due to seasons, as well? We might need to know the latitude as well.

    • one year ago
  19. Sujay Group Title
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    I am just surprised at how badly this problem was described :P. I mean seasonal expansion would have to involve advanced statistics and advanced calculus. But the tower thing is a pretty big error. My worst fear is always that test makers end up doing something like this on a test :(.

    • one year ago
  20. kikojuarez12 Group Title
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    is all the given information

    • one year ago
  21. scarydoor Group Title
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    a=-40. b=4. Pretty sure my derivation above is right. But feel free to show how you got something different...

    • one year ago
  22. scarydoor Group Title
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    so now you want to solve for x: f(x) = x^2 -40x + 4 = 0.64. Use the quadratic formula.

    • one year ago
  23. scarydoor Group Title
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    I made a mistake somewhere.

    • one year ago
  24. scarydoor Group Title
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    I haven't done this stuff for years. So my brain got all confused about what you can do with polynomials, and what the point is. So actually you want to shift the polynomial so that it's in [-20,20]. Then you get f(x) = 1/100 x^2 to describe the bridge thing.

    • one year ago
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