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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Answer: $112.50 ; $4612.5
Step-by-step explanation:
a) Determine how much interest Christine paid at the end of 1 year.
This will be:
Simple interest = PRT/100
where
P = principal = $4500
R = rate = 2.5%
T = time = 1 year
Interest = (4500 × 2.5 × 1)/100
= 11250/100
= $112.50
b) Determine the total amount Christine will repay the bank at the end of 1 year.
Total amount = Principal + Interest
= $4500 + $112.50
= $4612.5
Answer:
your answer would be X>-4
The slope is 5. This is because the coefficient of x is the slope of a line.
What is this asking I have no idea
