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>
<h2>
Explanation:</h2>
An exponential function is given by the following form:
Here we know two points:
![\bullet \ (0,6) \\ \\ x=0, \ y=6 \\ \\ 6=ab^0 \\ \\ \boxed{a=6} \\ \\\ \\ \bullet \ (3,750) \\ \\ x=3, \ y=750 \\ \\ 750=6b^3 \\ \\ b^3=\frac{750}{6} \\ \\ b=\sqrt[3]{125} \\ \\ \boxed{b=5}](https://tex.z-dn.net/?f=%5Cbullet%20%5C%20%280%2C6%29%20%5C%5C%20%5C%5C%20x%3D0%2C%20%5C%20y%3D6%20%5C%5C%20%5C%5C%206%3Dab%5E0%20%5C%5C%20%5C%5C%20%5Cboxed%7Ba%3D6%7D%20%5C%5C%20%5C%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20%283%2C750%29%20%5C%5C%20%5C%5C%20x%3D3%2C%20%5C%20y%3D750%20%5C%5C%20%5C%5C%20750%3D6b%5E3%20%5C%5C%20%5C%5C%20b%5E3%3D%5Cfrac%7B750%7D%7B6%7D%20%5C%5C%20%5C%5C%20b%3D%5Csqrt%5B3%5D%7B125%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7Bb%3D5%7D)
Finally, our exponential function is:
<h2>Learn more:</h2>
Behavior of functions: brainly.com/question/12891789
#LearnWithBrainly
Answer:
If the line passes through the orgin
Step-by-step explanation:
3y + 9x = 12
3y = -9x + 12
y = -3x + 4
If you want function notation you can replace y with f(x)
f(x) = -3x + 4
