1/5 this is the closest answer i can think of
The maximum volume of the box is 40√(10/27) cu in.
Here we see that volume is to be maximized
The surface area of the box is 40 sq in
Since the top lid is open, the surface area will be
lb + 2lh + 2bh = 40
Now, the length is equal to the breadth.
Let them be x in
Hence,
x² + 2xh + 2xh = 40
or, 4xh = 40 - x²
or, h = 10/x - x/4
Let f(x) = volume of the box
= lbh
Hence,
f(x) = x²(10/x - x/4)
= 10x - x³/4
differentiating with respect to x and equating it to 0 gives us
f'(x) = 10 - 3x²/4 = 0
or, 3x²/4 = 10
or, x² = 40/3
Hence x will be equal to 2√(10/3)
Now to check whether this value of x will give us the max volume, we will find
f"(2√(10/3))
f"(x) = -3x/2
hence,
f"(2√(10/3)) = -3√(10/3)
Since the above value is negative, volume is maximum for x = 2√(10/3)
Hence volume
= 10 X 2√(10/3) - [2√(10/3)]³/4
= 2√(10/3) [10 - 10/3]
= 2√(10/3) X 20/3
= 40√(10/27) cu in
To learn more about Maximization visit
brainly.com/question/14682292
#SPJ4
Complete Question
(Image Attached)
What's the question? there isn't enough info to help.
Answer:


Step-by-step explanation:
Given two points on the line (0, 16) and (3, 40), an equation for the line can be written using the slope-intercept line equation which takes the format
.
Where,

b = y-intercept or the point at which the line cuts the y-axis.
Let's find slope (m) using the slope formula:
Let,





Find b. Substitute the values of x = 0, y = 16, and m = 8 in the slope-intercept formula to find b.





Plug in the values of m and b into the slope-intercept formula to get the equation of the line.


Let's use the equation to find x when y = 112.

Substitute y = 112 in the equation



Divide both sides by 8

