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Naddik [55]
3 years ago
12

Please help and show steps so i could figure out how to do it , will give branliest!

Mathematics
1 answer:
erastova [34]3 years ago
3 0

Answer:

8

Step-by-step explanation:

1. 3b - 2 (1 - b) / a - 2

2. 3(2) - 2 (1 - 2) / 3 - 2

3. 6 - 2 (-1) / 1

4. 6 + 2 / 1

5. 8 / 1

6. 8

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Jorge is asked to build a box in the shape of a rectangular prism. The maximum girth of the box is 20 cm. What is the width of t
MariettaO [177]

Answer:

The width of the box is 6.7 cm

The maximum volume is 148.1 cm³

Step-by-step explanation:

The given parameters of the box Jorge is asked to build are;

The maximum girth of the box = 20 cm

The nature of the sides of the box = 2 square sides and 4 rectangular sides

The side length of square side of the box = w

The length of the rectangular side of the box = l

Therefore, we have;

The girth = 2·w + 2·l = 20 cm

∴ w + l = 20/2 = 10

w + l = 10

l = 10 - w

The volume of the box, V = Area of square side × Length of rectangular side

∴ V = w × w × l = w × w × (10 - w)

V = 10·w² - w³

At the maximum volume, we have;

dV/dw = d(10·w² - w³)/dw = 0

∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0

2×10·w - 3·w² = 20·w - 3·w² = 0

20·w - 3·w² = 0 at the maximum volume

w·(20 - 3·w) = 0

∴ w = 0 or w = 20/3 = 6.\overline 6

Given that 6.\overline 6 > 0, we have;

At the maximum volume, the width of the block, w = 6.\overline 6 cm ≈ 6.7 cm

The maximum volume, V_{max}, is therefore given when w = 6.\overline 6 cm = 20/3 cm  as follows;

V = 10·w² - w³

V_{max} = 10·(20/3)² - (20/3)³ = 4000/27 = 148.\overline {148}

The maximum volume, V_{max} = 148.\overline {148} cm³ ≈ 148.1 cm³

Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)

The width of the box is;

6.7 cm

The maximum volume is;

148.1 cm³

5 0
3 years ago
To find 19 + (11+37), Lennie added 19 and 11. Then he added 37 to the sum. What property did he use ?
Ad libitum [116K]

19 + (11+37) = (19 + 11) + 37

Associative property of addition

3 0
3 years ago
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What are the solutions to the quadratic equation x^2 + 8x - 8 = 0?
Elanso [62]

Answer:

x=−4+2√6 or x=−4−2√6

E is the answer

4 0
2 years ago
What’s the solution of 2 plus 2
egoroff_w [7]

Answer: 4

Step-by-step explanation: 2 + 2 = 4

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Dorji thought of a number. He first multiplied the number by 3 and then subtracted 12
jeyben [28]

Answer

The answer is 24

Step-by-step explanation

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