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:
The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8
Step-by-step explanation:
<u><em>The complete question is</em></u>
Emily and her children went into a grocery store and she bought $20.80 worth of bananas and peaches. Each banana costs $0.80 and each peach costs $2. She bought a total of 14 peaches and bananas altogether. Determine the number of peaches and the number of bananas that Emily bought
Let
x ----> the number of bananas that Emily bought
y ----> the number of peaches that Emily bought
we know that
She bought a total of 14 bananas and peaches altogether
so
-----> equation A
She bought $20.80 worth of bananas and peaches
so
-----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (6,8)
see the attached figure
therefore
The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8
C. -5y -4 = -(x+3)^2 -1/2
Hope I am right.
Answer: it was probably more chocolaty because he added 5 teaspoons instead of 4 which is 2 doubled
Step-by-step explanation: