Respuesta :
Let the width be w. Volume=96=w(w-2)(w+8).
w³+6w²-16w-96=0=w²(w+6)-16(w+6)=(w²-16)(w+6). So the only positive root is w=4 inches.
The dimensions are 4” wide, height is 2”, length is 12”.
w³+6w²-16w-96=0=w²(w+6)-16(w+6)=(w²-16)(w+6). So the only positive root is w=4 inches.
The dimensions are 4” wide, height is 2”, length is 12”.
The dimensions of the shipping box shaped like a rectangular prism are as follows:
width = 4 inches
height = 2 inches
length = 12 inches
The shipping box is like a rectangular prism.
volume = 96 in³
volume = lwh
where
l = length
w = width
h = height
h = w - 2
l = w + 8
The dimension of the box can be calculated as follows:
96 = w(w - 2)(w + 8)
96 = w(w² + 8w - 2w - 16)
96 = w(w² + 6w - 16)
96 = w³ + 6w² - 16w
w³ + 6w² - 16w - 96 = 0
(w + 4) • (w - 4) • (w + 6) = 0
The width can't be negative.
w = 4 inches
h = 4 - 2 = 2 inches
l = 4 + 8 = 12 inches
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