f(x) = 22.1 - .1(x-16)^2
Going with the most reasonable assumption that the train is rectangular in cross-section, then the corner of its diagonal will be at (5,20) from the center of the base.
f(21) = 19.6
So, 5 ft from the middle, the tunnel is only 19.6 ft high, so the corner of the car will not fit.
William, a logistician, needs to route a freight train that is 20 feet at its tallest point and 10 feet at its widest point within 3 days. The most direct path includes a single-track tunnel that needs 24 hour notice prior to use. If the tunnel is roughly modeled by f(x)=-0.1x^2+3.2x-3.5, should William make arrangements for the train to use the tunnel? Show work the supports your conclusion.
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