You can divide it and get 2.2
Let the lengths of the bottom of the box be x and y, and let the length of the squares being cu be z, then
V = xyz . . . (1)
2z + x = 16 => x = 16 - 2z . . . (2)
2z + y = 30 => y = 30 - 2z . . . (3)
Putting (2) and (3) into (1) gives:
V = (16 - 2z)(30 - 2z)z = z(480 - 32z - 60z + 4z^2) = z(480 - 92z + 4z^2) = 480z - 92z^2 + 4z^3
For maximum volume, dV/dz = 0
dV/dz = 480 - 184z + 12z^2 = 0
3z^2 - 46z + 120 = 0
z = 3 1/3 inches
Therefore, for maximum volume, a square of length 3 1/3 (3.33) inches should be cut out from each corner of the cardboard.
The maximum volume is 725 25/27 (725.9) cubic inches.
52 would be less, 918 inches converts to 76.5 feet.
You mark it up 20% Price + 20% = p + 20/100p = p (1 + 0.20 ) = 1.2 p
6.45 * 1.2 = 7.74
You take off 5% which by the same reasoning (almost) means p/1.05
7.74 / 1.05 = 7.37
Now you need a sales tax
7.37 * 1.06 = 7.81 dollars.
Answer: The customer paid 7.81 <<<<=====
Answer:
a.) w = 103 * 1.08^t
b.) 3.5weeks
Step-by-step explanation:
If Her current weight is 103 pounds and she hopes to multiply her her weight each week by 1.08, then
her weight after 1 week = 103 * 1.08 = 103 * 1.08¹
Her weight after 2 weeks = [weight of week 1] * 1.08 = [103* 1.08] * 1.08 = 103 * 1.08²
Weight after 3 weeks= [weight of week 2] * 1.08 = [103 * 1.08 * 1.08] * 1.08 = 103 * 1.08³
Hence weight (W) after t weeks = 103 * 1.08^t
b.) If W = 135, Then
103 * 1.08^t = 135
1.08^t = 135/103
1.08^t = 1.31
Taking log of both sides,
log 1.08^t = log 1.31
t log 1.08 = log 1.32
t = log 1.32/log 1.08
t = 3.5 weeks.
Hence, it will take her 3½ weeks to get to 135pounds weight.
