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andreyandreev [35.5K]

3 years ago

14

Find the volume of the resulting solid if the region under the curve y = 10/(x2 + 3x + 2) from x = 0 to x = 1 is rotated about t

he x-axis and the y-axis.

1 answer:

alexgriva [62]3 years ago

5 0

Answer:

Step-by-step explanation:

Check attachment for solution

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How do I solve: 2 sin (2x) - 2 sin x + 2√3 cos x - √3 = 0

ziro4ka [17]

Answer:

$\displaystyle x = \frac{\pi}{3} +k\, \pi$ or $\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi$ , where $k$ is an integer.

There are three such angles between $0$ and $2\pi$ : $\displaystyle \frac{\pi}{3}$ , $\displaystyle \frac{2\, \pi}{3}$ , and $\displaystyle \frac{4\,\pi}{3}$ .

Step-by-step explanation:

By the double angle identity of sines:

$\sin(2\, x) = 2\, \sin x \cdot \cos x$ .

Rewrite the original equation with this identity:

$2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0$ .

Note, that $2\, (2\, \sin x \cdot \cos x)$ and $(-2\, \sin x)$ share the common factor $(2\, \sin x)$ . On the other hand, $2\sqrt{3}\, \cos x$ and $(-\sqrt{3})$ share the common factor $\sqrt[3}$ . Combine these terms pairwise using the two common factors:

$(2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0$ .

Note the new common factor $(2\, \cos x - 1)$ . Therefore:

$\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0$ .

This equation holds as long as either $\left(2\, \sin x + \sqrt{3}\right)$ or $(2\, \cos x - 1)$ is zero. Let $k$ be an integer. Accordingly:

$\displaystyle \sin x = -\frac{\sqrt{3}}{2}$ , which corresponds to $\displaystyle x = -\frac{\pi}{3} + 2\, k\, \pi$ and $\displaystyle x = -\frac{2\, \pi}{3} + 2\, k\, \pi$ .
$\displaystyle \cos x = \frac{1}{2}$ , which corresponds to $\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi$ and $\displaystyle x = -\frac{\pi}{3} + 2\, k \, \pi$ .

Any $x$ that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

$\displaystyle x = \frac{\pi}{3} + k \, \pi$ (from $\displaystyle x = -\frac{2\,\pi}{3} + 2\, k\, \pi$ and $\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi$ , combined,) as well as
$\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi$ .

7 0

3 years ago

The manager at a concert venue keeps track of the number of adult tickets and student tickets sold each day and the total money

poizon [28]

Answer: the number of adult and student tickets sold are (45, 29)

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of student tickets that were sold.

On Wednesday, a total of 74 tickets were sold. This means that

x + y = 74

x = 74 - y- - - - - - - - - - - - - - 1

If adult tickets are sold for $15 and student tickets are sold for $11 and the money collected was $994, it means that

15x + 11y = 994- - - - - - - - - - - - - - 2

Substituting equation 1 into equation 2, it becomes

15(74 - y) + 11y = 994

1110 - 15y + 11y = 994

- 15y + 11y = 994 - 1110

- 4y = - 116

y = - 116/ - 4

y = 29

Substituting y = 29 into equation 1, it becomes

x = 74 - 29 = 45

6 0

3 years ago

I really need help, please dont put something silly.

Brut [27]

Answer:

1) 2.92405063291 (put it in the correct amount of significant figures)

2) 6.4688 (put it in the correct amount of significant figures)

Step-by-step explanation:

i dont know how many significant figures to put it into but theres the full answers

7 0

3 years ago

The first one please

hoa [83]

One of the would be getting 6 biscuits and the other would be getting 3.<span />

3 0

3 years ago

Need help is it correct or incorrect for all of them

gulaghasi [49]

Answer:A is correctly scientifically notated

B is incorrect

C is correctly notated

D is correct. 10 to the zero power simply means “1”

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers