On Saturday, Luke drove 5x − 4 miles. On Sunday, he drove 3x − 3 miles. What is the difference in miles driven?
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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
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.
- Height = x ≈ 4.55 in.
- The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³
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The system of equations has infinite solutions.
<h2>Given to us,</h2>The value of y is already given in equation 1,
substituting the value of y in equation 2,
The solution of the two equations is 0. Also, we can see that both the equations are in ratio.
Further, the image also shows that the line of the two equations are coinciding.
Hence, the system of equations has infinite solutions.
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