marcelie
  • marcelie
help please !!!! Find the dimensions of the rectangular corral producing the greatest enclosed area given 200 feet of fencing.
Mathematics
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SOLVED
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katieb
  • katieb
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imqwerty
  • imqwerty
ok so its like-|dw:1442384074892:dw| ur given that- x+y=200 y=200-x and the area should be maximum area=x*y area=x*(200-x) area=200x-x^2 u can get the value of x for which the area will be max by differentiating the area equation which we got with respect to x and equating it to 0 so u get \[\frac{ d}{ dx }(200x-x^2) =0\] after differentiating u get- 200-2x=0 200=2x x=100 and we know that y=200-x so y=200-100 y=100 so the dimensions are x=100 and y=100 so basically if u are maximizing the area then the figure has to become a square even tho we are given that its a rectangle :)
marcelie
  • marcelie
how did u get 200x-x^2 =0
imqwerty
  • imqwerty
we are given x+y=200 right so after subtracting x from both sides u get y=200-x -equation 1 nd we knw that the area is= x*y area=x*y put the value of y from equation 1 u get- area=x*(200-x) open the bracket u get- area=200x-x^2 :)

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marcelie
  • marcelie
okay so then how did u get 200-2x =0 ?
imqwerty
  • imqwerty
yes u get that after differentiating nd thats the way u do it :)
marcelie
  • marcelie
how do u do that ? by subtracting ?
imqwerty
  • imqwerty
no the differentiation of x^n with respect to x can be given as- \[\frac{ d }{ dx }x^n =nx^\left( n-1 \right)\] and if u have something like this - ax^n + b where a and b are constants then the differentiation of this thing with respect to x will be- \[\frac{ d }{ dx }(ax^n +b) =\frac{ d }{ dx }ax^n + \frac{ d }{ dx }b\]\[=anx^\left( n-1 \right)+0\] basically differentiation of m with respect to n indicates the rate of change of m with respect to n nd here we had a constant b nd we knw that constants are constants so differentiating it with respect to x gave us a 0 but ax^n is not a constant tho it has a but it has also got x^n which keeps changing so we get anx^(n-1) on differentiating it ) nd we used this to get 200-2x from 200x-x^2 :)
marcelie
  • marcelie
Got it now !! tyyy
imqwerty
  • imqwerty
no prblm :)
marcelie
  • marcelie
how would i solve this one ? Find the dimensions of the rectangular corral producing the greatest enclosed area split into 3 pens of the same size given 500 feet of fencing.

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