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3 years ago

Which of the answers are correct? Select all that apply.

Mathematics

1 answer:

Leona [35]3 years ago

8 0

Answer:A, b and also c

Step-by-step explanation:

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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

Solve 2x + 5x - 11 = -46

irga5000 [103]

Answer:

Step-by-step explanation:

7x-11=-46

(7x-11)+11=-46+11

X = -5

5 0

3 years ago

Which of the following best shows the associative property of multiplication?

Marizza181 [45]

Answer:

(4 × 3) × 6 = 4 × (3 × 6) shows the Associative Property of Multiplication.

8 0

3 years ago

Read 2 more answers

32-oz container of yogurt for $2.56

LekaFEV [45]

What’s the question?

5 0

3 years ago

Find the geometric mean between each pair of numbers. sq root 49 and sq root841

vodomira [7]

Answer:

The geometric mean between each pair of numbers $\bold{\sqrt{49} \text { and } \sqrt{841} \text { is } 14.24}$

Solution:

The Geometric mean between two numbers a and b is given as Geometric mean = $\bold{\sqrt{ab}}$ --- eqn 1

The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root for the numbers.

From question, given that two numbers are $\sqrt{49} and \sqrt{841}$

Hence we can say “a” = $\sqrt{49}$ =7

Similarly “b” = $\sqrt{841}$ = 29

We have to find the geometric mean between “7” and “29”

By using equation 1,

Geometric mean between 7 and 29 = $\sqrt{7 \times 29} = \sqrt{203}$ = 14.24

Hence the geometric mean between $\sqrt{49} \text { and } \sqrt{841} \text { is } 14.24$

8 0

3 years ago