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Rzqust [24]
3 years ago
6

A rectangular box has a square base. if the sum of the height and the perimeter of the square base is 12 in, what is the maximum

possible volume?
Mathematics
1 answer:
pychu [463]3 years ago
8 0

Let the square base has length b and the height of the box be h . It is given that 4b+h=12\\ h=4(3-b)

The volume of the box is V=b^2h=4b^2(3-b).

For maximum volume \frac{dV}{db} =0\\ \frac{d(4b^2(3-b))}{db} =0\\ 6b-3b^2=0\\ b=2

The maximum possible volume occurs when b=3 in.

V_{max} =4(2)^2(3-2) =16 in^3

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Answer:

x ≈ 15.0 ft

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Equality Properties

<u>Trigonometry</u>

  • tan∅ = opposite over adjacent

Step-by-step explanation:

<u>Step 1: Define</u>

Angle = 28°

Opposite leg of angle = 8 ft

Adjacent leg of angle = x ft

<u>Step 2: Find </u><em><u>x</u></em>

  1. Substitute:                                        tan28° = 8/x
  2. Multiply <em>x </em>on both sides:                 xtan28° = 8
  3. Divide tan28° on both sides:          x = 8/tan28°
  4. Evaluate:                                          x = 15.0458
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3 years ago
If cells are: a1=90, a2=85, a3=80, a4=75, and a5=75. what will be your formula if you are going to get the average?
swat32
The average can be given by the following formula:
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