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andreyandreev [35.5K]
3 years ago
6

What is 675 divided by 12 long division...lol I’m TIRED.help...

Mathematics
1 answer:
irina1246 [14]3 years ago
6 0

Your answer tired person is: 56.25

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The width of the rectangle is 1/3 of the length. Find the length and width of the rectangle.
adell [148]

Answer:

1.333333333

Step-by-step explanation:

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A candy company makes boxes of chocolates. Each box has 32 chocolates total. Of those 32 chocolates 14 of them have nuts. If the
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Answer: 266

Step-by-step explanation: This is a ratio problem. If there are 14 chocolates with nuts out of every 32 chocolates, you can use this as a ratio and set it up as a proportion.

(1) 14 chocolates w/ nuts / 32 chocolates = n chocolates / 608 chocolates

(2) Solve for n: 8,512 = 32n; n = 266

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3 years ago
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1/6
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3 years ago
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You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the
Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

3 0
3 years ago
The figure à shown on ancient coin which was once used in china.the coin is in the shape of a circle of radius 3cm with a square
lianna [129]

Answer:

(1) 2π - x² = 0 (2) x = 2.5 cm (3) perimeter = 10 cm

Step-by-step explanation:

(1)The area of the circular coin without the inner square removed is πr² where r = 3 cm is the radius of the coin. So, the area of the coin without the inner square removed is πr² = π(3 cm)² = 9π cm²

The area of the square of x sides removed from its center is x².

The area A of the each face of the coin is thus A = 9π - x²

Since the area of each face of the coin A = 7π cm²,

then

7π = 9π - x²

9π - 7π - x² = 0

2π - x² = 0

(2) Solve the equation 2π - x² = 0

2π - x² = 0

x² = 2π

x = ±√(2π)

x = ± 2.51 cm

Since x cannot be negative, we take the positive answer.

So, x = 2.51 cm

≅ 2.5 cm

(3) Find the perimeter of the square

The perimeter of the square, p is given by p = 4x

p = 4 × 2.51 cm

= 10.04 cm

≅ 10 cm

8 0
3 years ago
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