Answer:
$13.45
Step-by-step explanation:
Divide $107.60 by 8
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:
16.4
Step-by-step explanation:
To decrease a number by 45% of its value, you subtract the 45%. To get 45%, you multiply the number by 0.45.
So, if x is the original number, then the equation for this word problem would be x - 0.45x = 9.
To solve, we first subtract 0.45x from x, which is 0.55x. This means that 0.55x is equal to 9. To simplify, we can divide both sides by 0.55. 9/0.55 is 16.36363636..., etc. The nearest tenth would be 0.4, so your answer is 16.4
