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Hello, I am having problems with a word problem and hope someone can help. 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 that supports your conclusion. **I have x=-b/2a=-3.2/2(-0.1)=x=16 and then I took f(16) and substituted 16 in the equation for x and got 22.1. So, the height of the tunnel is 22.1 and the train is only 20 feet so it will fit, correct? Also, is the 22.1 the maximum height of the tunnel, I'm confused on the max and minimum. And, how do I figure the width of the tunnel to make sure the train will fit width-wise?? Thanks for any help!
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Hello,
the way you analysed the problem is not enough (and is not correct).
The section of the train is the rectangle of 20 ft height and 10 ft wide, correct?
So, you need to check if this rectangle does fit to the given parabola.
For it, take x = 5 feet (half of the width) and check, if f(5) is still greater than 20 feet.
It is your criterion.