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zloy xaker [14]
3 years ago
12

Box A has a volume of 24 cubic meters. Box B is similar to Box A. To create Box B, Box A's dimensions were multiplied by 4. What

is the volume of Box B?
Mathematics
1 answer:
Paraphin [41]3 years ago
4 0

Answer: 1536\ m^3

Step-by-step explanation:

Given

Box A has a volume of 24\ m^3

Box B is similar to box A such that box A dimension is multiplied by 4 to get the box B

So, each length is 4 times the box A and volume is the cube of the side.

Thus, the volume of box B is 4\times 4\times 4 the volume of box A

The volume of box B is  

=4\times 4\times 4\times 24\\=1536\ m^3

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Using differential calculus, maximize the volume of a box made of cardboard (top is open) as shown in Figure A. 15, subject to t
lana [24]

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)

3 0
1 year ago
Write an equation in slope-intercept form of the line.
alexira [117]

Answer:

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Step-by-step explanation:

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3 years ago
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Mandarinka [93]
Round 1 player 1 because 12 is the greatest number
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3 years ago
What is the estimated number to 204878
noname [10]
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4 0
3 years ago
Y = 3x - 8<br>y = 4 - X​
mihalych1998 [28]

Answer:

Step-by-step explanation:

Using substitution method.

y = 3x - 8  -------(i)

y = 4 - x -------- (ii)

Substitute y = 3x-8 in equation (ii)

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4x = 4 + 8

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