Find the value of x in this polygon. x =

If 180°<α<270°, cos ⁡α= −8/17, 270°<β<360°, and sin β= −4/5, what is sin⁡(α+β)?

mars1129 [50]

Answer:

$\sin(\alpha+\beta) = -0.153$

Step-by-step explanation:

Let determine the angles behind each trigonometric expression:

$\cos \alpha = -\frac{8}{17}$

$\alpha = \cos^{-1}\left(-\frac{8}{17} \right)$

Given that $180^{\circ}< \alpha < 270^{\circ}$ , the value of $\alpha$ is:

$\alpha \approx 241.928^{\circ}$

$\sin \beta = -\frac{4}{5}$

$\beta = \sin^{-1}\left(-\frac{4}{5} \right)$

Given that $270^{\circ}< \beta$ , the value of $\beta$ is:

$\beta \approx 306.870^{\circ}$

The sine function of the sum of angles can be determined by the following identity:

$\sin(\alpha + \beta)=\sin \alpha \cdot \cos \beta + \sin \beta \cdot \cos \alpha$

If $\alpha \approx 241.928^{\circ}$ and $\beta \approx 306.870^{\circ}$ , then:

$\sin (241.928^{\circ}+306.870^{\circ}) = (\sin 241.928^{\circ}) \cdot (\cos 306.870^{\circ}) + (\sin 306.870^{\circ})\cdot (\cos 241.928^{\circ})$ $\sin(241.928^{\circ}+306.870^{\circ}) = -0.153$

7 0

4 years ago

Lori works as a cartoonist for a teen magazine.The time she spent sketching is given by the equation m=12s, where mis the number

Vera_Pavlovna [14]

Answer:

Lori spends 9 minutes on sketching $\frac{3}{4}$ th of a sketch.

Step-by-step explanation:

Given equation:

$m=12\ s$

where $m\rightarrow$ number of minutes Lori spends on sketching

and $s\rightarrow$ number of sketches Lori makes.

We need to calculate the time spent by Lori in sketching $\frac{3}{4}$ of a sketch.

So we know the value of $s=\frac{3}{4}$ as $s$ represents number of sketches and in this situation Lori has sketched only a fraction of a painting.

So we plugin $s=\frac{3}{4}$ in the equation and calculate $m$ which is time spent by Lori sketching $\frac{3}{4}$ th of a sketch.

$m=12\ \frac{3}{4}$

$m=\frac{36}{4}$

∴ $m=9$ minutes (Answer)

∴ Lori spends 9 minutes on sketching $\frac{3}{4}$ th of a sketch.

5 0

3 years ago

Help me please please!!!!!!!!

Alenkasestr [34]

I’m pretty sure the answer is C

3 0

3 years ago

The drama club members at Millie’s middle school are selling tickets to the school play. Millie wants to determine the average n

ki77a [65]

Answer:

The first sampling method is Convenient Sampling. It is biased sampling and it is not representative of a random sample.

The second sampling method is Systematic Sampling. If this method of sampling is drawn from the population, it is an efficiently randomized sampling method.

Let us review the given answers.

1. Both samples should be exactly the same.

INCORRECT

2. Neither sample will be representative.

Because the second sampling method can be random, this answer is

INCORRECT.

3. The first sampling method, ..., is the most representative,

INCORRECT

4. The second sampling method, ..., is the most representative.

CORRECT

Step-by-step explanation:

Hope that helps

3 0

3 years ago

Sal has already finished 5/9 of the 45 math problems he was assigned. If each math problem took him 3/5 of a minute to finish an

Oliga [24]

Step-by-step explanation:

plz refer the attachment

6 0

3 years ago

Find the value of x in this polygon.x =