A carnival ride has a sign at the beginning of the line that says "Must be at least 48 inches tall to ride." Which of the follow
2 answers:
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Answer:
2.67 inches.
Step-by-step explanation:
Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).
The formula for a rectangular box = L × B × W
= (23 -2y)(13-2y) (y)
= (299 - 46y - 26y + 4y²)y
= 299y - 72y² + 4y³
Now for the maximum volume:
dV/dy = 0
This implies that:
299y - 72y² + 4y³ = 299 - 144y + 12y² = 0
By using the quadratic formula; we have :
where;
a = 12; b = -144 and c = 299
Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33
Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.
The easiest way is if it doesn't need to be simplified. Multiply -2.105 by 
. You get the fraction 
. While this is technically the answer, you can simplify this down to 
. Because 421 is a prime number, this can not be simplified any further. Therefore, the solution is .
.