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anonymous

  • 5 years ago

The parabolic arch of a bridge over a one-way road can be described by the equation y = -x^2 + 6, where x and y ar emeasured in metres. A transpor truck is 3m wide and 3.5m high. What is the maximum clearance of the truck's top corners if it passes under the bridge?

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  1. anonymous
    • 5 years ago
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    This is an Optimization problem.

  2. dumbcow
    • 5 years ago
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    so you want the max distance from the top corner of truck to arch ??

  3. dumbcow
    • 5 years ago
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    distance from top center of arch to top corner of truck is 2.915 m

  4. anonymous
    • 5 years ago
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    Yes How were you able to work that out?

  5. dumbcow
    • 5 years ago
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    d^2 = 2.5^2 + 1.5^2

  6. anonymous
    • 5 years ago
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    How did you come to this equation?

  7. dumbcow
    • 5 years ago
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    truck is 3.5m so vertical distance from top is (6-3.5) = 2.5 truck is 3m wide, 1.5m on either side of center line imagine a triangle formed from right side of top of truck to top center of arch d is hypotenuse and is the longest distance from arch to truck top corner

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