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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.

 Feb 8, 2019
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Find the zeroes of the equation....the distance between them will give you the width

Find the Vertex to know the height....

 

vertex is given by   - b / 2a   =    - 3.2 / (2*(-.1) ) = 3.2/.2 = 16  feet     (equation parameters were not supplied...hence the ?)

 

at x = 16     f(x) = -.1(16^2) + 3.2(16) - 3.5    = 22.1 feet (?)   tall

Now we know it is 22.1 feet tall at   x = 16    but we still do not know the width....

Find the zeroes using quadratic equation

 

-3.2 +- ( sqrt(3.2^2 - 4(-.1)(-3.5)   /  2(-.1)  =  30 .86  - 1.134 = 29.76 feet wide     at the BASE

 

The train looks like it will fit.......    this equation is a parabola BUT.....at y = 20   is the equation > 10    for the train to fit???

 

20 = -.1x^2 + 3.2 x - 3.5   ???   Yields   x = 11.417   and  20 .583    which is less than 10 (9.166)

 

The train may not  fit ! 

 Feb 8, 2019
edited by Guest  Feb 8, 2019
edited by Guest  Feb 8, 2019

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