# math

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A box must have base x cm by 2x cm. what are the dimensions of the box of maximum volume if its length+width+depth<140cm

• math -

2 x^2 h = v
h = 140-3x

v =2 x^2 (140-3x)
v = 280 x^2 - 6 x^3
dv/dx = 0 = 560 x - 18 x^2
x(560 - 18x) = 0
18 x = 560
x = 31.1

2x = 62.2

h = 140 - 3(31.1) = 46.7

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