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Answer:
Each square should have 5 inches of side and area = 25 square inches.
Step-by-step explanation:
Candy box is made that measures 45 by 24 inches.
Let the squares of equal size x inches has been cut out of each corner.
The sides will then be folded up to form a rectangular box.
Now we have to find the size of square that should be cut from each corner to obtain maximum volume of the box.
Now the box is with length = (45 - 2x) inches
and width = (24 - 2x) inches
and height = x inches
Volume of the candy box = Length × width × height
V = (45 - 2x)(24 - 2x)(x)
V = x(1080 - 48x -90x + 4x²)
= x(1080 - 138x + 4x²)
= 4x³ - 138x² + 1080x
Now we will find the derivative of volume and equate it to zero.
12(x² - 23x + 90) = 0
x² - 23x + 90 = 0
x² - 18x - 5x + 90 = 0
x(x - 18) - 5(x - 18) = 0
(x - 5)(x - 18)=0
x = 5, 18
Now for x = 18 Width of the box will be = (24 - 2×18) = 24 - 36 = -12
Which is not possible.
Therefore, x = 5 will be the possible value.
Therefore, square having area 25 square inches should be cut out from each corner to get the maximum volume of candy box.
The simplest form of the given expression is 5x^3-5x^2.
We have given that
We have to determine the simplest form of the given expression.
<h3>What is the distributive property?</h3>
The distributive property of binary operations generalizes the distributive law, which asserts that equality is always true in algebra. elementary.
Use the distributive property we get,
Add like terms we get,
Therefore we get,
Therefore the simplest form of the given expression is 5x^3-5x^2.
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