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# RGO Question 10

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### RGO Question 10 - Page Text Content

FC: Farmer`s Holding Pen | By: Robert owen

1: Question 10: A farmer has 16.4 meters of fencing with which to build a rectangular-shaped holding pen for his sheep. The pen is to be located next to a corner and a wall of an existing shed as shown in the diagram. Fencing is not needed along the shed and wall. | - What is the length of the pen? - What is the width of the pen? - Write a rule, in terms of x, for the area of the pen A(x) in meters ^2. - What is the greatest area? - What are the dimensions of the length and width of the pen that give the greatest area? - What is the domain of the function? The range? - Can the pen have an area of 50 m^2? Explain. | 2.3 meters

2: - What is the length of the pen? | The length of the holding pen is equal to x + 2.3 meters. The length equals 4.675 meters when 2.375 is substituted in for the variable x. | 4.675 meters

3: - What is the width of the pen? | The width of the holding pen is equal to 14.1 - 2x because 16.4= x + y + x + 2.3 (let be the variable for width). When y is solved for, the width equals 14.1 - 2x. The width equals 9.35 meters when 2.375 is substituted in for the variable x. | 9.35 meters

4: - Write a rule, in terms of x, for the area of the pen A(x) in meters ^2. | To find the area of the holding pen, multiply length by width. A(x)=(x + 2.3)(14.1 - 2x)

5: - What is the greatest area? | The greatest area of the holding pen would be 43.71125 meters^2. Substitute 2.375 in for the x variable in the area of the pen equation to find the greatest area. A(x)= (x + 2.3)(14.1 - 2x) A(2.375)= (2.375 + 2.3)(14.1 - 2[2.375]) A(2.375)= (4.675)(9.35) A(2.375)= 43.71125

6: - What are the dimensions of the length and width of the pen that give the greatest area? | The length equals x + 2.3. Substitute 2.375 in for x and the length of the holding pen that gives the greatest area is 4.675 meters. The width equals 14.1 - 2x. Substitute 2.375 in for x and the width of the holding pen that gives the greatest area is 9.35 meters.

7: - What is the domain of the function? The range? | The domain of the function is all real numbers. The range of the function is negative infinity to 43.43.

8: - Can the pen have an area of 50 m^2? Explain. | The pen can not have an area of 50meters^2 because the greatest area the holding pen can have is 43.71125 meters^2.

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