Help please

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 three 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 squared + 3.2x-3.5, should William make arrangements for the train to use the tunnel? Show work that supports your conclusion.

Answer 1

If you plot the equation on Desmos Graphing Calculator and see what the width if the tunnel is at y = 20 (height of the train) you'll see that the two x values (width) are 20.55 and 11.5 (the two points are approximately (20.55,20 and 11.5,20)). Therefore the widest train with a height of 20 ft is 20.55 - 11.5, or around 9 feet. If the train's width is 10 feet, there's going to be a big problem!!

You can also set the equation = 20 Then enter -0.1x² + 3.2x - 23.5 = 0 into an online quadratic equation solver and you'll get similar answers.