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
Learn more about differentiation and integration here:
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Answer:
2.4274
Step-by-step explanation:
This is just a simple multiplication problem.
One way to do this is by converting both decimals into fractions:
1.06 = 1 + 0.06 = 1 + 6/100 = 1 + 3/50 = 53/50
2.29 = 2 + 0.29 = 2 + 29/100 = 229/100
Multiplying these two fractions, we get:
Now, we can just convert this into a decimal by using a calculator:
12137/5000 = 2.4274, which is our answer.
Of course, you could just put the numbers in a calculator, which would be much less time-consuming.
The term that can be added to the list so the GCF is 12h3 would be 48h5.
The reason being is that 48 is first divisible by 12 and does not yield a fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.
Answer:
0,4,8,12,16
Step-by-step explanation:
so for the value of x- just substitute it into the equation
so -2
8+4(-2)
8-8=0
Here is how I completed the problem:
I started by creating a ratio:
<em>Where 'x' is the desired amount of the 18% solution of sulfuric acid.
</em>From here, I solved for 'x':
<em>
</em>
∴You will need to add 1080ml of 18% Sulfuric Acid in order to obtain a 15% solution.
