Algebra Practical Problem. help greatly appreciated
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# Algebra Practical Problem. help greatly appreciated

[From: ] [author: ] [Date: 11-05-20] [Hit: ]
-If x is the length of the side perpendicular to the river,then the lengths of the sides of the pen are x, x,I suppose the domain they want is the one that will make the area positive and the lengths of the sides of the enclosure positive.Then x is negative and 250-x is positive.Then x is positive and 250-x is positive.......
A farmer wants to build a fence along a river. He has 500 feet of fencing and wants to enclose a rectangular pen on three sides (with the river providing the fourth side). If x is the length of the side perpendicular to the river, determine the area of the pen as a function of x. What is the domain of this function?

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If x is the length of the side perpendicular to the river,
then the lengths of the sides of the pen are x, x, and 500-2x

The area of the pen is x(500 - 2x) = 2x(250-x)

I suppose the domain they want is the one that will make the area positive and the lengths of the sides of the enclosure positive.

Notice that 2x(250-x) is zero when x = 0 and x = 250
So we consider three cases

x < 0:
Then x is negative and 250-x is positive. So 2x(250-x) is negative

0 < x < 250:
Then x is positive and 250-x is positive. So 2x(250-x) is positive

x > 250:
Then x is positive and 250-x is negative. So 2x(250-x) is negative

It follows that the domain is [0, 250]

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A(x)=x(500-2x)
Domain:
All set of possible x values
1
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