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anonymous
 5 years ago
Caculus help please! A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions b=8in by a=10in by cutting out equal squares of side x at each corner and then folding up the sides how much do we cut from each corner in order to maximize the volume?
anonymous
 5 years ago
Caculus help please! A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions b=8in by a=10in by cutting out equal squares of side x at each corner and then folding up the sides how much do we cut from each corner in order to maximize the volume?

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radar
 5 years ago
Best ResponseYou've already chosen the best response.0Let x = the dimension of the corner cut. This is also the height.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0let lenght =102x width = 82x Volume =l x w x h V = x (82x)(102x) Complete and differentiae set to 0 and solve. got to run good luck.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0ok so V'(x)=1*(82x)(102x)+x(2)(102x)+x(82x)(2)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0we can clean that up so finding x from V'=0 is easier

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0V'(x)=8016x20x+4x^220x+4x^216x+4x^2

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0V'(x)=8x^272x+80 unless i made a mistake

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i did make a mistake V'=12x^272x+80

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0now set V'=0 to find critical numbers let me know if you have anymore trouble

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this helps a lot but i can't factor 12x^272x+80=0. and to find x: the cut out corners are x by x

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Divide all terms by 4 getting \[3x ^{2}18x+20=0\]

radar
 5 years ago
Best ResponseYou've already chosen the best response.0a=3, b=18, and c\[(18\pm \sqrt{84})/6\]

radar
 5 years ago
Best ResponseYou've already chosen the best response.0\[(18\pm2\sqrt{21})/6\] Results in x approx 1.4724 in.
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