Order the following decimals in order from least to greatest 3.5 3.57 -2.34 -2.3 4.21 4.233
2 answers:
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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.
So we know that the perimeter is 1260 feet and that the length is 100 more than the width, but we don't know that the width is.
So we're going to start with finding the width.
from there we need to combine like terms
now we have
From there, we will need to remove 100 from both sides, leaving us with
now we'll need to divide both sides by 2
We now know that the width is 580, or more simply put, x=580.
Finding the length will be the easy part, as we know that it is just 100 more than the width
If you want an easier way of finding the length, just subtract the width from the perimeter.
Leaving the final answer to be
Width = 580
Length = 680
So we're going to start with finding the width.
from there we need to combine like terms
now we have
From there, we will need to remove 100 from both sides, leaving us with
now we'll need to divide both sides by 2
We now know that the width is 580, or more simply put, x=580.
Finding the length will be the easy part, as we know that it is just 100 more than the width
If you want an easier way of finding the length, just subtract the width from the perimeter.
Leaving the final answer to be
Width = 580
Length = 680