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11111nata11111 [884]
3 years ago
11

What is the domain of this function?

Mathematics
1 answer:
muminat3 years ago
8 0

It's Letter C. 1 3 and 5

that's the domain

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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
PLEASE HELP I WILL MAKE YOUR ANSWER THE BRAINLIEST perimeter of the parallelogram
marysya [2.9K]

Answer: i think the awnser is 48

Step-by-step explanation:

8+8=16 16+16+16=48

5 0
2 years ago
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What’s the range of these temperatures -15, -6, 22, 10, -11
Nadya [2.5K]

range = largest - smallest

    = 22 - (-15)

   = 22 + 15

   = 37

6 0
3 years ago
trey is selling candy bars to raise money for his basketball team. the team receives $1.25 for each candy . he has already sold
zlopas [31]

Answer:

He has earned $31.25 for his basketball team.

Step-by-step explanation:

25 * 1.25 = 31.25

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Equilateral triangle X Y W has degree angles of 60 degrees. Point D extends from side X W. Angle D X Y is 120 degrees. Triangle
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Answer:

80

Step-by-step explanation:

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