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
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Complete Question
(Image Attached)
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2) and to the left of the line is shaded.
<h3>What are the characteristics of the graph of the inequality?</h3>
Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.
Characteristics of the graph of the inequality-
- Open circle-When the value of the variable is equal to the given number, then the graph of the inequality has an open circle.
- Closed circle-When the value of the variable is not equal to the given number, then the graph of the inequality has a closed circle.
- The ray will move to the right-When the, value of the variable is greater than the number, then the ray will move to the right.
- The ray will move to the left-When the value of the variable is less than the number, then the ray will move to the left.
The linear inequality given in the problem is,
The graph of this line is attached below. Here, for the greater than sign, every thing on the left of the graph is shaded, and the line will be dotted because of inequality as shown in the attached image.
Hence, on a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2) and to the left of the line is shaded.
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Answer:
3ab
Step-by-step explanation:
Answer: D. x=72
Step-by-step explanation:
With the equation x/8-6=3 we can start solving by first moving the "-6"
x/8-6(<u>+6)</u>=3(+6)
x/8=9 <-- Rewrite equation after adding "6" to both sides
x/8(*8)=9(*8) <--- Multiply both sides by 8
x=72 <-- After multiplying, solution is found
