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3 years ago

The inequality below compares two rational numbers. -8/18 > -17/27

Mathematics

1 answer:

astraxan [27]3 years ago

6 0

Answer:

I have provided it below

Step-by-step explanation:

- 8/18 > - 17/27

- 0.444444 > 0.62963

So this inequality is TRUE

Hope this helps!!

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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

Help with this algebra problem? 12y+6=6y+12?

Anika [276]

First, combine like terms.
12y+6=6y+12 turns into
12y-6y=12-6, which is
6y=6. Now divide both sides by 6.
y=1

now do a quick check (cause that's always a good idea).
12(1)+6=6(1)+12
12+6=6+12
18=18 ; )

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3 years ago

the angle of elevation of a jet plane from a point P on the ground is 60 degree after a flight of 15 seconds the angle of elevat

Nana76 [90]

Answer:

200m/s

Step-by-step explanation:

Please see the attached pictures for full solution.

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3 years ago

What is the solution to the equation 2x + 4 = 23x?

Cerrena [4.2K]

Answer:

x=4/21

Step-by-step explanation:

2x+4=23x

-2x -2x

4=21x

4/21=x

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3 years ago

I kind of don’t get this could someone explain and answer this question I would really appreciate :)

amm1812

Answer:

its the fourth one

sts3ps oe

3 0

3 years ago

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