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## Homework Statement

The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed v. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the cost of running this ferry (labor, maintenance, and so on) is $3125 per hour.

(a) Find the proportionality constant for the cost of the fuel per hour.

(b) Express the cost per mile in terms of v only.

(c) At what speed should the boat travel so as to minimize the cost per mile traveled?

## Homework Equations

## The Attempt at a Solution

a) C=kv^3

100=k1000

k=.1

b)C(v)=.1kv^3 + 3125

This is where i get stuck because apparently this is wrong?