Question 1204361
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Let the origin be the point on the roadway directly below the top of the arch.  Then the equation of the parabola is<br>
{{{y=ax^2+16}}}<br>
where a is a negative constant to be determined.<br>
With the arch having a span of 20 meters, the coordinates of the two bases of the arch are (-10,0) and (10,0).  Use one of them to determine the constant a.<br>
{{{0=a(10^2)+16}}}
{{{100a=-16}}}
{{{a=-0.16}}}<br>
The equation of the parabola is<br>
{{{y=-0.16x^2+16}}}<br>
The smallest clearance between the tank on the truck and the arch will be if the truck is centered under the arch. Since the tank is 14m wide, that clearance will be 7m from the center of the arch.  Use the equation of the parabola to find the height of the arch 7m from the center.<br>
{{{y=-0.16(7^2)+16=8.16}}}<br>
Then, since the top of the tank is 7.5m above the roadway, the clearance is 8.16m - 7.5m = 0.66m.<br>
ANSWER: 0.66 meters<br>