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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we have point (-6, - 1)
Now we will put these points in each equation,
y = 4x +23
put x = -6 and y = -1
-1 = 4 (-6) +23
-1 = -24 + 23
-1 = -1
LHS = RHS, so this equation has (-6 , -1) as solution.
y = 6x
put x = -6 and y = -1
-1 = 6 (-6)
-1 not= -36
LHS is not equal RHS, so (-6 , -1) is not a solution for that equation,
y = 3x - 5
put x = -6 and y = -1
-1 = 3 (-6) - 5
-1 = -18 - 5
-1 not= -23
LHS is not equal RHS, so (-6 , -1) is not a solution for that equation,
y= 1/6 x
put x = -6 and y = -1
-1 = -6/6
-1 = -1
LHS = RHS, so (-6 , -1) is a solution for that equation,
Answer:
1350 cm^2
Step-by-step explanation:
X+y= 26 and 4.75x + 2.25y= 83.50
y=26-x( substitute this into second equation for y and solve for x)
4.75x + 2.25(26-x)= 83.50
4.75x + 58.5-2.25x= 83.50
x= 10
Now solve for y by substituting your answer for x
10+ y= 26
y=16
Therefore, 16 tickets were purchased for kids and 10 for adults.
Let i = sqrt(-1) which is the conventional notation to set up an imaginary number
The idea is to break up the radicand, aka stuff under the square root, to simplify
sqrt(-8) = sqrt(-1*4*2)
sqrt(-8) = sqrt(-1)*sqrt(4)*sqrt(2)
sqrt(-8) = i*2*sqrt(2)
sqrt(-8) = 2i*sqrt(2)
<h3>Answer is choice A</h3>