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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Answer:
Step-by-step explanation:ygvt fvbygtfr5nBHY$nujmk,mjnhbygtf
Answer:
40 feet represents the height of the tree ⇒ H
Step-by-step explanation:
Let us solve the question using the proportional
∵ A tree casts a shadow 64 feet long
∴ L = 64 feet
∵ At the same time, a girl 5 feet tall standing near the tree
∴ H = 5 feet
∵ She casts a shadow that is 8 feet long
∴ L = 8 feet
The ratios between the shadows and the heights of the tree and the girl are proportional
∵ =
→ Substitute their values in the equivalent ratios
∴ =
→ By using cross multiplication
∴ H × 8 = 5 × 64
∴ 8H = 320
→ Divide both sides by 8
∴ H = 40 feet
∴ 40 feet represents the height of the tree
Answer:
x = 18
Step-by-step explanation:
To write a proportion, we need to write down the data we have.
Shorter side of rectangle 1 = 6
Longer side of rectangle 1 = 13
Shorter side of rectangle 2 = x
Longer side of rectangle 2 = 39.
A proportion representing this would be:
Solving this proportion for x, we would have:
Therefore, the shorter side of the second rectangle is 18.
Answer:
1/18
Step-by-step explanation: