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.
Answer:
6 packages of forks
Step-by-step explanation:
If Jasmine wants to have an equal quantity of forks and spoons, we need to list the multiples of each quantity and determine the least common multiple (LCM).
Forks: 10, 20, 30, 40, 50, 60, 70, 80, 90
Spoons: 12, 24, 36, 48, 60, 72, 84, 96
The LCM in this example is 60. In order to have exactly 60 forks and 60 spoons, Jasmine will need to buy 6 packages of forks [60 ÷ 10 = 6] and 5 packages of spoons [60 ÷ 12 = 5].
Answer:
Step-by-step explanation:
First what we must do is rewrite the table to find a solution:
0.25^x −0.75x+1
64 3.25
16 2.5
4 1.75
1 1
0.25 0.25
0.0625 −0.5
0.015625 −1.25
We see where the values of the function are the same:
x = 0 (1)
x = 1 (0.25)
answer:
x = 0
x = 1
Answer:
-50 dollars per month
Step-by-step explanation: