The largest possible volume of the given box is; 96.28 ft³
<h3>How to maximize volume of a box?</h3>
Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is;
S = b² + 4bh
We are given S = 100 ft². Thus;
b² + 4bh = 100
h = (100 - b²)/4b
Volume of the box in terms of b will be;
V(b) = b²h = b² * (100 - b²)/4b
V(b) = 25b - b³/4
The volume is maximum when dV/db = 0. Thus;
dV/db = 25 - 3b²/4
25 - 3b²/4 = 0
√(100/3) = b
b = 5.77 ft
Thus;
h = (100 - (√(100/3)²)/4(5.77)
h = 2.8885 ft
Thus;
Largest volume = [√(100/3)]² * 2.8885
Largest Volume = 96.28 ft³
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She can cut six pieces and will have ¾ of a piece leftover.
<h3>
Answer: 5/12 (choice C)</h3>
Explanation:
Recall that tangent = opposite/adjacent.
For reference angle M, the side ON = 5 is the opposite side and MN = 12 is the adjacent side. We don't need the hypotenuse.
Step-by-step explanation:
The number of cups of red paint is always 15 of the total number of cups. 0.2 of the total number of cups.
She writes the equation r = 15t (r = 0.2t) to describe the relationship.
In this case, the total no. of cups is an independent variable. No. of cups do not depend on any term.
The number of cups of red paint is a dependent variable as it depends on the number of cups.
Answer:
any decimal under 8...
you can write it as: x<8
x is less than 8
or your number is less than 8
Step-by-step explanation:
