Dianar4308
11.12.2019 •
Mathematics
Richard has a 9-inch by 13.5-inch sheet of cardboard. he cuts squares from 4 corners to create an open container with the largest possible volume.
what is the greatest volume possible? express your answer as a decimal to the nearest cubic inch.
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Ответ:
96.256 in³
Step-by-step explanation:
Given,
The dimension of the sheet = 9-inch by 13.5-inch,
Suppose x be the side of the square which is cut from each corner,
So, the dimension of the resultant open container,
(9-2x) inch × (13.5 - 2x) inch × x inch
Thus, the volume of the box,
V(x) = (9-2x) × (13.5 - 2x) × x
Differentiating with respect to x,
Again differentiating,
For maxima or minima,
Using the quadratic formula,
For x = 1.766, V''(x) = negative,
Thus, V(x) is maximum at x = 1.766,
For x =5.734, V''(x) = positive,
Thus, V(x) is minimum at x = 5.734,
Hence, the maximum possible volume, V(1.766) = (9-2(1.766)) × (13.5 - 2(1.766)) × 1.766
≈ 96.256 in³
Ответ:
Option B
Step-by-step explanation:
Because if you start with one dollar and by day 3 you get 301 dollars and option A only gives you 8 cents on day 3 you get more money by the end of the month if you choose option B.