Find the Area, I'm pretty sure you suppose to add them all up but my teacher is saying it's wrong
1 answer:
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Dipesh is looking at two different options for a new video rental plan. Plan A has a fee of $7.95 plus an additional fee of $1.25 per rental. With this plan, the first 2 rentals are free. Plan B has a fee of $5.00 plus an additional fee of $3.90 per rental. With this plan, the first 6 rentals are free. After how many rentals would both options cost the same amount?
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.