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kvv77 [185]
3 years ago
5

GIVING BRAINLIEST!!!!!!

Mathematics
1 answer:
vovikov84 [41]3 years ago
5 0
A mistake first occurs in step 1. (24+3+10) is not equal to (8+10). It is equal to (27+10).
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A chocolate chip cookie recipe calls for 6 cups of chopped nuts and 8 cups of chocolate chips. When Gregory made a batch of thes
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He did not

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If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in
Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume (V), in cubic centimeters, and surface area (A_{s}), in square centimeters, of the box with a square base are described below:

A_{s} = l^{2}+h\cdot l (1)

V = l^{2}\cdot h (2)

Where:

l - Side length of the base, in centimeters.

h - Height of the box, in centimeters.

By (2), we clear h within the formula:

h = \frac{V}{l^{2}}

And we apply in (1) and simplify the resulting expression:

A_{s} = l^{2}+ \frac{V}{l}

A_{s}\cdot l = l^{3}+V

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Then, we find the first and second derivatives of this expression:

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V'' = -6\cdot l (5)

If V' = 0 and A_{s} = 30000\,cm^{2}, then we find the critical value of the side length of the base is:

30000-3\cdot l^{2} = 0

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Then, we evaluate this result in the expression of the second derivative:

V'' = -600

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

V = 30000\cdot l - l^{3}

V = 2000000\,cm^{3}

The largest possible volume of the box is 2000000 cubic meters.

4 0
3 years ago
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