What are the statements and what do the triangles look like?
For this case we must simplify the following equation:
We subtract on both sides of the equation:
Equal signs are added and the same sign is placed:
We add 4 to both sides of the equation:
We multiply by 9 on both sides of the equation:
We divide between 13 on both sides of the equation:
We multiply by -1 on both sides of the equation:
ANswer:
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:
brainly.com/question/13058734
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Formula: V = d / t => d = V*t
Name your relevant variables:
minimum speed limit: v
maximmum speed limit V
1) Tony's distance
2*v + 3.5*V = 355 miles
2) Ray's distance
2*v + 3*V = 300 miles
3) Finding v and V
You have a system of two equations each with the two variables.
You can solve that system by subtracting the second equation from the first one:
=> 0.5V = 55 => V = 55 / 0.5 = 110 mph
Now replace that value of V in any of the equations and solve for v
From the second one: 2v + 3V = 300 => 2v = 300 - 3V = 300 - 3(110) = 300 - 330 = - 30 mph
This value of v indicates that the conditions given are not valid. Both speed should be a positive value.
=> Tony's distance is 2*80 + 3.5*110 = 160 +
Answer:
0.5divided by 3 is the answer
Step-by-step explanation: