Math Problem Statement
A company wants to run a pipeline from a point A on the shore to a point B on an island which is 6km from the shore. It costs Birr 4000 per kilometre to run the pipe line on shore, and 5000 Birr per kilometre to run it underwater. There is a point on the shore so that is at the right angles to . The straight shoreline is the line . The distance is 9km. Find how the pipeline should be laid to minimize the cost
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Optimization
Pythagorean Theorem
Formulas
Cost Function: C(x) = 4000x + 5000 * sqrt((9 - x)^2 + 36)
Derivative of the Cost Function: C'(x) = 4000 + 5000 * (- (9 - x)) / sqrt((9 - x)^2 + 36)
Theorems
Pythagorean Theorem
Optimization using Calculus
Suitable Grade Level
Grades 11-12
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