Answer:
Step-by-step explanation:
Let the length of one side of the square base be x
Let the height of the box by y
Volume of the box V = x²y
Since the box is opened at the top, the total surface area S = x² + 2xy + 2xy
S = x² + 4xy
Given
S = 7500sq in.
Substitute into the formula for calculating the total surface area
7500 = x² + 4xy
Make y the subject of the formula;
7500 - x² = 4xy
y = (7500-x²)/4x
Since V = x²y
V = x² (7500-x²)/4x
V = x(7500-x²)/4
V = 1/4(7500x-x³)
For us to maximize the volume, then dV/dx = 0
dV/dx = 1/4(7500-3x²)
1/4(7500-3x²) = 0
(7500-3x²) = 0
7500 = 3x²
x² = 7500/3
x² = 2500
x = √2500
x = 50in
Since y = (7500-x²)/4x
y = 7500-2500/4(50)
y = 5000/200
y = 25in
Hence the dimensions of the box that will maximize its volume is 50in by 50in by 25in.
The Volume of the box V = 50²*25
V = 2500*25
V= 62,500in³
Hence the maximum volume is 62,500in³
25 in 1/2minute
10 1/2 minutes in 5 minutes
25*10=250
Hope this helps :)
The 7th term of the geometric sequence is 8,192!
Total = 28
Girls. Boys.
4. 3
28/4= 7
7 x 3 = 21
ANSWER = 21
Answer:
49 prizes each, with 5 left
Step-by-step explanation:
985/20 is 49 with 5 left over.
