Question 147511: At the present time, a nutrition bar in the shape of a rectangular solid measures 0.75 inch by 1 inch by 5 inches. To reduce costs the manufacturer has decided to decrease each of the dimensions of the nutrition bar by x inches. What value of x, rounded to the nearest thousandth of an inch, will produce a new nutrition bar with a volume that is 0.75 cu in less than the present bar's volume?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! At the present time, a nutrition bar in the shape of a rectangular solid measures 0.75 inch by 1 inch by 5 inches.
Original volume: 0.75*1*5 = 15/4 cu. in.
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To reduce costs the manufacturer has decided to decrease each of the dimensions of the nutrition bar by x inches.
New volume: (0.75-x)(1-x)(5-x) cu. in.
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What value of x, rounded to the nearest thousandth of an inch, will produce a new nutrition bar with a volume that is 0.75 cu in less than the present bar's volume?
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EQUATION:
new-old = -0.75 cu in
(0.75-x)(1-x)(5-x)-(15/4)= -(3/4)
(0.75-x)(1-x)(5-x)-3 =0
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I graphed the left side and the right side seperately and
found the point of intersection: x = 0.08388499..
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Cheers,
Stan H.
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