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Optimizing Simple Systems

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question 1 of 3

You have 100 ft of fencing to use to enclose part of a yard. You first choose to enclose the yard with a rectangular pen 'w' feet in width and 'd' feet in depth. As a function of 'w', what is the equation for the area that you can enclose using 100 ft of fence?

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1. What is the maximum area that you can enclose in a rectangular pen with 150 feet of fencing?

2. A farmer has 2400ft of fencing and wants to fence off a rectangular field that borders a straight river. He doesn't need fencing along the river. What are the dimensions of the field that has the largest area?

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About This Quiz & Worksheet

You can take this quiz to gauge your understanding of optimizing simple systems. The practice problems in this quiz will require you to use math to find the answers to word problems.

Quiz & Worksheet Goals

Questions on this quiz focus on finding the area of shapes. You will need to be able to solve problems that deal specifically with:

  • Equations for area
  • The area of rectangles
  • Circular area

Skills Practiced

Increase the value of your study time by practicing these skills while working on the quiz:

  • Reading comprehension - ensure that you draw the most important information from the related lesson on optimizing simple systems
  • Problem solving - use acquired knowledge to find the maximum area of various shapes
  • Information recall - access the knowledge you've gained regarding the best shape to use to contain the most area

Additional Learning

The lesson that focuses on this subject is titled Optimizing Simple Systems. You can study it and learn even more about these topics:

  • The method for solving optimization problems
  • Optimization problem equations
  • The most difficult steps in finding the solution to optimization problems
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