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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It can either be the negative sign of the number by the x so it should either be 2 or -
Answer:
Step-by-step explanation:
To find the required probability,
We can split the 40 years of Eric into very small pieces of time dt. Now, If Eric dies at time t and Gary dies before Eric, the probability is :
Hence the probability that Gary dies first is given by :
For first pound it is = $2.41
For next six, = 0.41 * 6 = $2.46
Remaining = 7.99 - (2.41 + 2.46) = 7.99 - 4.87 = 3.12
Now, additional pounds = 3.12 / 0.39 = 8
Total weight = 1 + 6 + 8 = 15
In short, Your Answer would be 15 pounds
Hope this helps!
