This sort of question is answered easily by a graphing calculator. The square cut from each corner should be
1.962 inches on each side.
_____
After creating a fold-up flap of x inches in width, the base of the box will be
(10 - 2x) by (15 - 2x)
and the depth of the box will be the width of the fold-up flap: x.
Then the volume of the box is
v = x(10 -2x)(15 -2x) = 150x -50x^2 +4x^3
The derivative of the volume will be zero at the maximum volume.
0 = dv/dx = 150 -100x +12x^2
This has roots at
x = (100 ±√(100² - 4(12)(150)))/(2·12)
x = (100 ± √2800)/24 = (25 ± 5√7)/6
Only the smaller of these solutions gives a maximum volume.
You should cut
(5/6)(5-√7) ≈ 1.962 inches to obtain the greatest volume.
Answer:
No
Step-by-step explanation:
When working with negative numbers in terms of depth, greater depth are depicted by values as we move farther to the left of the number line.
With this in mind, - 75 feets is farther to the left of the number line and as such represents a greater depth value Than - 68 feets
Therefore, when expressing depth or elevation distances, the values should be iewwd in absolute terms. Then |75| > |68|. While bearing in mind that depth is downward and thus negative
Answer:
360 = x + 30
x = 390 meters
Step-by-step explanation: