I think its not a right triangle because of the cm.
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
Answer:
ok i will try my best to give your questions answer
Step-by-step explanation:
thankyou for free point
Answer:
They are equal.
Step-by-step explanation:
You could use the butterfly method, just set up both ratios as fractions, and multiply them diagonally.
3/2=48/32
Step 1. 48*2=96
Step 2. 32*3=96
The quantity of popcorn each friend of the students receive is 5/36 gallons.
<h3>Division of fraction</h3>
- Number of gallons of popcorn the student .has = 5/9 gallons
- Number of the student's friends = 4
Quantity of popcorn each friend receive = Number of gallons of popcorn the student has / Number of the student's friends
= 5/9 ÷ 4
= 5/9 × 1/4
= (5 × 1) / (9 × 4)
= 5/36
Therefore, the quantity of popcorn each friend of the students receive is 5/36 gallons
Learn more about division of fraction:
brainly.com/question/1622425
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