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Mars2501 [29]
2 years ago
8

Plz g0ive me solution

Mathematics
1 answer:
Serga [27]2 years ago
8 0

Answer:

separate the x from the numbers it will make the equation easier

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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
Graph the proportional relationship, y = 5x.
kap26 [50]

Answer:

Hope the graph below helps.

Step-by-step explanation:

5 0
2 years ago
A rectangular basketball court has perimeter of 232 feet. The length of the court is 32 feet greater that the width. What is the
Leviafan [203]

Answer: width = 42, length = 74

Step-by-step explanation: 42 + 32 = 74

42 + 42 + 74 + 74 = 232

6 0
3 years ago
What is the name of the song 50 points and brainliest.
solong [7]

Answer:

Butterflies

Step-by-step explanation:

Thanks

6 0
3 years ago
Please help me out here! :D
zimovet [89]

I see no reason for the aluminum foil to have lost any volume, matter, mass , etc.

If all pieces are retrieved for measuring. - &

If a clean cut was achieved- and the blade used to cut did not impede upon the proceedings by also being variable, then I reiterate that there should be no difference in volume, matter, mass, etc.

7 0
3 years ago
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