X(x+6) = x*x+6*x = x^2+6x
These cannot be simplified any further
(2x-24)/8
the only way to simplify it is divide every number by 2
(x-12)/4=(1/4)x-3
The dimensions of the square base after cutting the corners will be (40-2x). The depth of the box will be x, so its volume is given by
V = x(40-2x)²
You can differentiate this to get
V' = 12x² -320x -1600
Setting this to zero and factoring gives
(3x-20)(x-20) = 0
The appropriate choice of solutions is
x = 20/3 = 6 2/3
The
dimensions of the box of maximum volume are
26 2/3 in square by 6 2/3 in deepThe
maximum volume is
(80/3 in)²(20/3 in) =
4740 20/27 in³
Answer: 72 feet
Step-by-step explanation: 1 yard is equal to 3 feet, so if there are 24 yards, we can multiply 24 by 3. This can be shown using the following formula: y · 3 = f (where y = number of yards and f = feet.) So:
24 · 3 = 72