A freshwater pipeline is to be run from a source on the edge of a lake to a comm

Question

A freshwater pipeline is to be run from a source on the edge of a lake to a community on an island 5 miles of shore, as shown in the figure Answer the question that follow If it costs 1.5 times as much to lay pipe in the lake as it does on land, what should x be(in miles) to minimize the total cost of this project? x = miles (Round to the nearest tenth needed.) (B) If it costs only 1.2 times as much to lay pipe in the lake as it does on land, what should x be )in mils) to minimize the total cost of this project x = miles (Round to the nearest tenth as needed.)

Explanation / Answer

cost= (10-x) + 1.5sqrt(25+x^2)

diffrentiate cost function:

= -1+1.5x/(sqrt(25+x^2))=0

= (1.5x)^2= 25+x^2

= 1.25x^2= 25

x= sqrt(20)

for b part:

cost= (10-x)+ 1.2(sqrt(25+x^2))

diffrentiate cost function:

= -1+1.2x/(sqrt(25+x^2))=0

= (1.2x)^2= 25+x^2

= 0.44x^2= 25

x= sqrt(56.81)

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