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Unformatted text preview: tal cost C of connecting the Junction Box to the Outpost as a function of x,
the number of miles the cable is run along Route 117 before heading oﬀ road directly towards
the Outpost. Determine a reasonable applied domain for the problem.
2. Use your calculator to graph y = C (x) on its domain. What is the minimum cost? How far
along Route 117 should the cable be run before turning oﬀ of the road?
1. The cost is broken into two parts: the cost to run cable along Route 117 at $15 per mile, and
the cost to run it oﬀ road at $20 per mile. Since x represents the miles of cable run along
Route 117, the cost for that portion is 15x. From the diagram, we see that the number of
miles the cable is run oﬀ road is z , so the cost of that portion is 20z . Hence, the total cost is
C = 15x + 20z . Our next goal is to determine z as a function of x. The diagram suggests we
can use the Pythagorean Theorem to get y 2 + 302 = z 2 . But we also see x + y = 50 so that
y = 50 − x. Hence, z 2 = (50 − x)2 + 900. Solving for z , we...
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