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sertanlavr [38]
3 years ago
7

Quiz 3

Mathematics
1 answer:
andrezito [222]3 years ago
4 0
It is 2x+8!!!!!!! I’m pretty sure
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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
Which is an equation of the line with slope –3 and passes through (2, –1)
Savatey [412]

using the formula:

y = mx +b

Using the given slope and coordinate points we get:

-1 = -3(2) + b

-1 = -6 + b

add 6 to each side

5 = b

y = -3x + 5

which is the same as:

3x + y = 5 ...answer choice a

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2 years ago
Whats 1.64 as a mixed number in simplest form
raketka [301]
It is 1 16/25

Hope it helps ;-)
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942 ÷ 7 = ? A. 134 R4 B. 136 C. 134 R2 D. 133 R1
zimovet [89]

Answer:


Step-by-step explanation:

134

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The graph below shows the solution to which system of inequalities? ​
solong [7]

Answer:

C

Step-by-step explanation:

The graph shows it clearly.

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