Volume
of a rectangular box = length x width x height<span>
From the problem statement,
length = 60 - 2x
width = 10 - 2x
height = x</span>
<span>
where x is the height of the box or the side of the equal squares from each
corner and turning up the sides
V = (60-2x) (10-2x) (x)
V = (60 - 2x) (10x - 2x^2)
V = 600x - 120x^2 -20x^2 + 4x^3
V = 4x^3 - 100x^2 + 600x
To maximize the volume, we differentiate the expression of the volume and
equate it to zero.
V = </span>4x^3 - 100x^2 + 600x<span>
dV/dx = 12x^2 - 200x + 600
12x^2 - 200x + 600 = 0</span>
<span>x^2 - 50/3x + 50 = 0
Solving for x,
x1 = 12.74 ; Volume = -315.56 (cannot be negative)
x2 = 3.92 ;
Volume = 1056.31So, the answer would be that the maximum volume would be 1056.31 cm^3.</span><span>
</span>
Answer:
D
Step-by-step explanation:
Given
x² - 10x = - 36
Solve using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 5)x + 25 = - 36 + 25
(x - 5)² = - 11 ( take the square root of both sides )
x - 5 = ± 
( add 5 to both sides )
x = 5 ± i
Thus
x = 5 - i
or x = 5 + i
Answer:
24 Bricks.
Step-by-step explanation:
We know the radius is 6 feet and that the diameter is twice that.
We also know the radius is 12 'bricks' in length.
If we divide both numbers by 12, we get that 1 'brick' is half a foot.
Since that's the radius and we want the diameter, we multiply the radius by 2 to get the diameter.
This results in 12 feet, or 24 'bricks'.
I can burly read that but the fraction should be right
