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zloy xaker [14]
3 years ago
9

How do you find percent decrease?

Mathematics
1 answer:
snow_lady [41]3 years ago
5 0
I think thats how ur welcome

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by
a_sh-v [17]

Answer:

Dimension of the box is 16.1\times 7.1\times 2.45

The volume of the box is 280.05 in³.

Step-by-step explanation:          

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is L=21-2h

The width of the box is W=12-2h

The volume of the box is V=L\times W\times H

V=(21-2h)\times (12-2h)\times h

V=(21-2h)\times (12h-2h^2)

V=252h-42h^2-24h^2+4h^3

V=4h^3-66h^2+252h

To maximize the volume we find derivative of volume and put it to zero.

V'=12h^2-132h+252

0=12h^2-132h+252

Solving by quadratic formula,

h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}

h=\frac{132\pm72.99}{24}

h=2.45,8.54

Now, substitute the value of h in the volume,

V=4h^3-66h^2+252h

When, h=2.45

V=4(2.45)^3-66(2.45)^2+252(2.45)

V\approx 280.05

When, h=8.54

V=4(8.54)^3-66(8.54)^2+252(8.54)

V\approx -170.06

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is L=21-2(2.45)=16.1

The width of the box is W=12-2(2.45)=7.1

So, Dimension of the box is 16.1\times 7.1\times 2.45

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A group pre-orders 12 tickets for a sightseeing tour, even though they don't have the money to pay for them yet. Each ticket cos
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404 is the answer. if you add them all together
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The edge of a cube was found to be 15 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maxim
Artyom0805 [142]

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Step-by-step explanation:

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Simplify 10 divided by 7 divided by 8 and put it in a fraction please :)
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Step-by-step explanation:

3 0
2 years ago
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Joey wants to build a rectangular garden. He plans to use a side of a river for one side of the garden, he will not place fencin
jonny [76]

We let x and y be the measures of the sides of the rectangular garden. The perimeter subtracted with the other side should be equal to 92.

<span>                                                       2x + y = 92</span>

The value of y in terms of x is equal to,

<span>                                            y = 92 – 2x</span>

The area is the product of the two sides,

<span>                                                                        A = xy</span>

Substituting,

<span>                                                            A = x (92 – 2x) = 92x – 2x2</span>

Solving for the derivative and equating to zero,

<span>                                                            0 = 92 – 4x  ; x = 23</span>

Therefore, the area of the garden is,

<span>                                                            A = 23(92 – 2(23)) = 1058 yard<span>2</span></span>

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3 years ago
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