An oil platform is 7 miles off the coast, and a pipeline needs to run to a refinery that is 15 miles north of the platform along the coast. This requires that some of the pipeline will be offshore and some will run on land along the coast. If the pipeline comes on shore $x$ miles north of the platform, the underwater distance is given by $f(x)=\sqrt{49+x^{2}}$, and the distance on land is given by $g(x)=15$ - $\mathrm{x}$. The cost of the underwater pipeline is $\$ 500,000$ per mile, and the cost of the pipeline on land is $\$ 350,000$ per mile. If the pipeline comes on shore 6 miles north of the platform, what is the total cost of the pipeline? Do not round until the final step and then round to the nearest cent.
A) $\$ 7,759,772.23$
B) $\$ 6,709,772.23$
C) $\$ 7,287,817.78$
D) $\$ 7,726,840.56$

Question

Quizplus · Accepted Answer

First, calculate the underwater distance using $f(x)=\sqrt{49+x^{2}}$ with $x=6$: $f(6)=\sqrt{49+6^{2}}=\sqrt{49+36}=\sqrt{85}$ miles. The cost of the underwater pipeline is $\$500,000$ per mile, so the total underwater cost is $\$500,000 \times \sqrt{85}$.Next, calculate the on land distance using $g(x)=15-x$ with $x=6$: $g(6)=15-6=9$ miles. The cost of the on land pipeline is $\$350,000$ per mile, so the total on land cost is $\$350,000 \times 9$.Total cost = Underwater cost + On land cost= $\$500,000 \times \sqrt{85}$ + $\$350,000 \times 9$= $\$500,000 \times 9.219544457292887$ + $\$3,150,000$= $\$4,609,772.2286464435$ + $\$3,150,000$= $\$7,759,772.2286464435$, which rounds to $\$7,759,772.23$.

An Oil Platform Is 7 Miles Off the Coast, and a Pipeline