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ayoismeisjjjjuan
21.03.2021 •
Mathematics
Double and Half Angle identities i think, can anyone explain how to do these?
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Ответ:
The largest possible volume of the box is 2000000 cubic meters.
Step-by-step explanation:
The volume (
), in cubic centimeters, and surface area (
), in square centimeters, of the box with a square base are described below:
Where:
By (2), we clear
within the formula:
And we apply in (1) and simplify the resulting expression:
Then, we find the first and second derivatives of this expression:
If
and
, then we find the critical value of the side length of the base is:
Then, we evaluate this result in the expression of the second derivative:
By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:
The largest possible volume of the box is 2000000 cubic meters.