Solve the Problem $A ( x ) = 12 x ^ { 2 } - x$

question 217

Multiple Choice

Solve the problem.
-Elissa wants to set up a rectangular dog run in her backyard. She has 20 feet of fencing to work with and wants to use it all. If the dog run is to be x feet long, express the area of the dog run as a function of x.

• A) \(A ( x ) = 12 x ^ { 2 } - x\)
• B) \(A ( x ) = 9 x - x ^ { 2 }\)
• C) \(A ( x ) = 10 x - x ^ { 2 }\)
• D) \(A ( x ) = 11 x - x ^ { 2 }\)

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Definitions:

Consumption

The consumption of products and services by individuals in a household.

Impossibility Theorem

A proposition demonstrated by Kenneth Arrow showing that no system of aggregating individual preferences into social decisions will always yield consistent, nonarbitrary results.

Voting Paradox

A simple demonstration of how majority-rule voting can lead to seemingly contradictory and inconsistent results. A commonly cited illustration of the kind of inconsistency described in the impossibility theorem.

Social Choice

The problem of deciding what society wants. The process of adding up individual preferences to make a choice for society as a whole.