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1. A closed box, whose length is twice its width, is to have a surface of 192 square inches. Find the dimensions of the box when the volume is maximum.

2. What number exceeds itself by the maximum amount?

2007-09-09 23:20:50 · 1 answers · asked by trevor 1 in Science & Mathematics Mathematics

1 answers

x= width,y= height
S=2*x^2*2+2xy+4xy = 4x^2 +6xy=192
V=2x^2y maximum

y= (192-4x^2)/6x = (96-2x^2)/3x
V=1/3 (192x-4x^3)
V´=1/3(192-12x^2)=0 so x= sqrt(16)= 4 y=16/3 and length=8 inches
I don´t understand 2nd question

2007-09-10 02:07:59 · answer #1 · answered by santmann2002 7 · 0 0

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