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Alenkinab [10]
3 years ago
13

1. (2 points) Solve each equation and write the answer on the line

Mathematics
1 answer:
FromTheMoon [43]3 years ago
4 0
Hello there! So, by looking at the numbers, there are eighteen tens being compared to 21 * (5 + 5). Eighteen tens is equivalent to 180, because tens = 10, and 18 * 10 is 180. To solve 21 * (5 + 5), we first add what's in the parenthesis. 5 + 5 is 10. 21 * 10 is 210. And as we see, 180 < 210, because the one in the hundreds place is less than the two in the hundreds place. The answer is eighteen tens < 21 * (5 + 5).
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What number is 2/10 of 20
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Answer:

2/10 * 20 = 4.

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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.

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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