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:
Step-by-step explanation:z=180
Interior angle =180
Answer: 2/3
Step-by-step explanation:
3(y-1) = 2x + 2
Expand: 3y - 3 = 2x + 2
Isolate the y by adding 3 to both sides: 3y = 2x +5
Isolate the y by dividing 3 from both sides: y = 2/3x +5/3
Remember, in y = mx + b, m = slope.
So, 2/3 is the slope.
For example, 1/2 in not an equivalent ratio