Question

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?

Answer 1

please help!

Answer 2

The graph of the function is an inverted parabola.
Ok?

Answer 3

ok

Answer 4

There is a rough sketch of an inverted parabola.
We need to see if up to a height of 20 ft, the width is always greater than 10 ft.
The tunnel is wider at the bottom and narrower as the height increases.
Since we don't know at what height the train is the widest, we must check to see that the tunnel is at least 10 ft wide at a height of 20 ft.