Suppose you have 76 feet of fencing to enclose a rectangular dog pen. The function A = 38x – x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.

width = 19 ft; area = 361 ft2

width = 38 ft; area = 760 ft2

width = 38 ft; area = 361 ft2

width = 19 ft; area = 1083 ft2

The answer to your question is width = 19 ft; area = 361 ft²

Step-by-step explanation:

Data

A = 38x - x²

Process

1.- Find the derivative of A

A' = 38 - 2x

2.- Equal to zero

      38 - 2x = 0

3.- Solve for x

      38 = 2x

      x = 38/2

      x = 19 ft

4.- Find the area

A = 38(19) - (19)²

- Simplification

A = 722 - 361

-Result

A = 361 ft²  

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.