Question

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Answer 1

The polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck is:

$f(x) = -0.04x^2 + 18x + 75$

Solution:

The cost of distributing by train can be modeled as:

$-0.07x^2 + 40x - 105$

The cost of distributing by truck can be modeled as:

$-0.03x^2 + 22x - 180$

where x is the number of tons of product distributed

To find: Difference between the cost of distributing by train and the cost of distributing by truck

Difference = cost of distributing by train - cost of distributing by truck

Let f(x) = difference in cost between trains & trucks

$f(x) = (-0.07x^2+40x-105) - (-0.03x^2 +22x - 180)$

$f(x) = -0.07x^2 + 40x -105 + 0.03x^2 -22x + 180$

$Combine\ the\ like\ terms\\\\f(x) = -0.07x^2 +0.03x^2 + 40x - 22x +180-105\\\\Add\ the\ like\ terms\\\\f(x) = -0.04x^2 + 18x + 75$

Thus polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck is found