Afarmer needs to build a pen for his sheep. one side of the pen will use a fence already standing. the sheep need 2000 square meters of area to graze. what width y should the farmer build to use the least amount of fencing for his sheep pen? (to the nearest tenth) a) 27.4 m b) 29.5 m c) 31.6 m d) 33.5 m

31.6 m  

Step-by-step explanation:

31.6 m  

The area of the pen:  

yx = 2000

y =  

2000

x

The farmer needs 2y + x fencing:

Substitute in the value of y =  

2000

x

F = 2(

2000

x

) + x

F =  

4000

x

+ x  

Graph this function on a graphing calculator. The minimum value occurs at x = 63.246

Plug 63.246 back into the original equation  

xy = 2000

y =  

2000

x

y =  

2000

63.246

= 31.622

Therefore, a width of 31.6 m would use the least amount of fencing.

picture below

the first dot plot best represents the data

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