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3 years ago

What is the domain of the function shown in the graph below?

Mathematics

2 answers:

tigry1 [53]3 years ago

6 0

Answer:

All except one interval [-2,8]

Step-by-step explanation:

Notice that the function, wich an hyperbola, has a vertical asymptote in both -2 and 8 and there is nothing between this two values.

So we will exclude what's between them out of the domain.

Natali [406]3 years ago

5 0

All values except [-2,7]

the graph isn't proper, but it's obvious what the answer would be.

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I'm have some issues with the problem shown in the screenshot and would love some help.

KiRa [710]

The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.

Maximum volume of the box is approximately 1048.6 in.³

<h3>How can the dimensions and volume of the box be calculated?</h3>

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let x represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, V, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

$\frac{d V }{dx} = \frac{d( 4 \cdot \: {x}^{3} - 106 \cdot \: {x}^{2} + 630\cdot \: {x} ) }{dx} = 0$

Which gives;

$\frac{d V }{dx} =12\cdot \: {x}^{2} - 212\cdot \: {x} + 630 = 0$

6•x² - 106•x + 315 = 0

$x = \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6}$

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

Width ≈ 18 - 2×4.55 in. = 8.89 in.

Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.

Height = x ≈ 4.55 in.

The maximum volume of the box, V ≈ 1048.6 in.³

Learn more about differentiation and integration here:

brainly.com/question/13058734

#SPJ1

7 0

2 years ago

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Elan Coil [88]

Answer:

see explanation

Step-by-step explanation:

The diagrams show triangular figures

The first figure has 1 dot

The second has 1 + 2 = 3 dots

The third has 3 + 3 = 6 dots

The fourth has 6 + 4 = 10 dots

Note the pattern is + 2 , + 3, + 4

Thus the fifth pattern is 10 + 5 = 15 dots

5 0

3 years ago

There are 112 seats in the school auditorium there are 7 seats in each row there are 70 people seated filling up full rows of se

irina [24]

6 rows
112/7=16
70/7=10
16-10=6

3 0

4 years ago

Choose the correct correspondence RT

Marizza181 [45]

$RT$ corresponds to TR. correct option b.

Step-by-step explanation:

In the given parallelogram or rectangle , we have a diagonal RT . We need to find which side is in correspondence with side/Diagonal RT of parallelogram URST .

Side TU:

In triangle UTR , we see that TR is hypotenuse and is the longest side among UR & TU . So , TR can never be equal in length to UR & TU . So there's no correspondence of Side TU with RT.

Side TR:

Since, direction of sides are not mentioned here , we can say that TR & RT is parallel & equal to each other . So , TR is in correspondence with side/Diagonal RT of parallelogram URST .

Side UR:

In triangle UTR , we see that TR is hypotenuse and is the longest side among UR & TU . So , TR can never be equal in length to UR & TU . So there's no correspondence of Side UR with RT.

4 0

4 years ago

sandra has 4 math test this marking period. she recieved 90%, 87%. and 92% on the first three. what is the minimum score she nee

Butoxors [25]

She would need to get a 90% or more.

6 0

3 years ago