The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;
- Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.
- Maximum volume of the box is approximately 1048.6 in.³
<h3>How can the dimensions and volume of the box be calculated?</h3>
The given dimensions of the cardboard are;
Width = 18 inches
Length = 35 inches
Let <em>x </em>represent the side lengths of the cut squares, we have;
Width of the box formed = 18 - 2•x
Length of the box = 35 - 2•x
Height of the box = x
Volume, <em>V</em>, of the box is therefore;
V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x
By differentiation, at the extreme locations, we have;
Which gives;
6•x² - 106•x + 315 = 0
Therefore;
x ≈ 4.55, or x ≈ -5.55
When x ≈ 4.55, we have;
V = 4•x³ - 106•x² + 630•x
Which gives;
V ≈ 1048.6
When x ≈ -5.55, we have;
V ≈ -7450.8
The dimensions of the box that gives the maximum volume are therefore;
- Width ≈ 18 - 2×4.55 in. = 8.89 in.
- Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.
- The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³
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I would say solve each diameter equation and order them fromleast to greatest, for example
1 Venus- 7.52×10 to the power of 3
So first simplify 10 to the power of 3 which is, 1000. Then you multiply 7.52 by 1000 which gets you 7520.
So solve each equation and order it
<span>4(c+2)= -28
Use distributive property
4c+8=-28
Subtract 8 from both sides
4c=-36
Divide 4 on both sides
Final Answer: c=-9</span>
The total gallons of sports drink Jaylen made using 9/10 of a large cooler with water and 6 cups of sports drink concentrate is 3.75 gallons
<h3>Total gallons</h3>
- Water in the large cooler = 9/10
Space remaining = 1 - 9/10
= 10-9 / 10
= 1/10
1/10 = 6 cups
- Total gallons of sport drink = x
6 cups / total = 1/10
6 × 10 = total × 1
60 cups = total
Cups to gallons:
16 cups = 1 gallon
Total gallons of sport drink, x = 60 cups / 16
= 3.75 gallons
Complete question:
To make a sports drink for the football team, Jaylen filled 9/10 of a large cooler with water. Then, he filled the remaining space with 6 cups of sports drink concentrate. How many gallons of sports drink did Jaylen make?
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Answer:
n = 13
Step-by-step explanation:
24 = 3 (n-5)
3n - 15 = 24
3n = 24 +15
3n = 39
n = 39/3
n = 13
