Problema Solution
William needs to find a route to 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 he make arrangements for the train to use the tunnel?
Answer provided by our tutors
If this is *seriously* all that William knows - he would be an absolute *idiot* to route a train through *any* tunnel - let alone one that is mathematically modelled.
(Engineer & Project manager....harrrumph!!)
However, just to stick within the given boundaries of the question (grumble, grumble, what moron gives tunnel dimensions like this... grrr...)
then let us see if there is even any possible shape that the train might be shaped so it fits the criteria given and still fits under the curve of the tunnel.
Plot the curve on graph paper (or on your graphing calculator)
You will see that it reaches its maximum height at 'x = 16'and at that 'x' , the height is 73.3 ft tall.
You will also see that the curve crosses the '0' line at x = 1.13 and again at x = 30.87
So just by that criteria, the train will 'fit'
Now - what you *really* need to check - what is the height of the tunnel at x = 11 and x = 21 (16 +/- 5)
This would be the 10 ft width of the train - if it is more than 20 ft in both locations, the train will make it through.
(Grumbles some more - still a stupid way to specify where you would route a train...)