Calculus - Math - question from samathsn001

Math > Calculus

A) determine the dimensions that will result in the maximum swimming area.

B) What is the maximim swimming area?

Please help me with this question as soon as possible.

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A lifeguard uses 700 m of marker buoys to rope off a rectangular swimming area in a lake. one side of the swimming area is a sandy beach.

Asked by samathsn001 3 years ago

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Answer:

perimeter = 700m

700 = 2L + W since one side is a sandy beach.

700-2L = W

Now area = L*W

= L(700-2L) domain [0,350]

700L-2L^2 distributing the L through

700-4L taking the first derivative

=4(175-L) the only critical number here is 175

substituting 175 for L in L(700-2L)

175(700-350)

175(350)

=61250 the maximum area

we first started with w = 700-2L

w = 700-2L=175

Dimension: p = 700' and maximum area is a sq

Answered by The_Engineer 3 years ago

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