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lakkis [162]
3 years ago
8

how three different fractional number representations of a rational number are related to determining the sign of of quotient of

two integers
Mathematics
1 answer:
lakkis [162]3 years ago
6 0
Someone help i need this answer to!!
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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
Good morning everyone :)​
Triss [41]

Answer:

Good Morning

:)

Step-by-step explanation:

5 0
2 years ago
Mona stopped at a gas station where the price per gallon was $2.80. She spent $14 to fill up her car. What equation would repres
alina1380 [7]

Answer:

A.) 5 x 2.80 B.) 100

Step-by-step explanation:

14/2.80=5 which is how many gallons

5 x 20 = 100 for the miles

8 0
3 years ago
Read 2 more answers
Suppose the function y = 30,000(1.06)x models the annual profit for a small business x years after 2000. Find the profit at the
goldfiish [28.3K]
From 2000 to 2011, there are 11 years. From the given function, we can calculate the profit for a small business at the end of 2011 by substituting 11 to the x of the given equation. 
                                         y = (30,000)(1.06)(11)
                                         y = 349,800
Thus, the profit at the end of 2011 is approximately $349,800. 
4 0
3 years ago
Solve the inequality:<br> 5 (2h+8) &lt; 60
sashaice [31]

Answer:

5 (2h+8) < 60

10h+40<60

10h<20

h<2

Your Welcome

BIFFY OUT!!!

5 0
3 years ago
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