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erik [133]
3 years ago
6

An automobile repair facility recently purchased a 200-foot roll of flexible plastic tubing for $47.03 . Compute the cost in cen

ts per foot. (round to the nearest cent.)
Mathematics
1 answer:
mojhsa [17]3 years ago
7 0
The cost is 24 cents per foot.

We find this by dividing the cost of the roll by the number of feet in the roll:

47.03/200 = 0.235 ≈ 0.24
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The velocity function is the derivative of the position:

\begin{gathered} V(t)=\frac{2}{3}(3t^2)-\frac{9}{2}(2t)-18 \\ \text{Simplifying:} \\ V(t)=2t^2-9t-18 \end{gathered}

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Solve by using the formula:

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Substituting:

\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}

We have two possible answers:

\begin{gathered} t=\frac{9+15}{4}=6 \\ t=\frac{9-15}{4}=-\frac{3}{2} \end{gathered}

We only accept the positive answer because the time cannot be negative.

Now calculate the position for t = 6:

undefined

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