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3 years ago

Given sin thata = 2/5 and 0° < thata < 90°. find sin 2 thata

Mathematics

1 answer:

Andrej [43]3 years ago

5 0

Recall the double angle identity:

$\sin2\theta=2\sin\theta\cos\theta$

With $\theta$ measuring between 0º and 90º, we know $\cos\theta>0$ . So from the Pythagorean identity, we get

$\sin^2\theta+\cos^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\dfrac{\sqrt{21}}5$

Then

$\sin2\theta=2\dfrac25\dfrac{\sqrt{21}}5=\dfrac{4\sqrt{21}}{25}$

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Solve this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7

ratelena [41]

Answer:

Solving this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7 we get x=2 and y=-3

Solution set = {2,-3}

Step-by-step explanation:

We need to solve this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7

let:

$3x-2y=12--eq(1)\\x+3y=-7 --eq(2)$

Finding value of x from equation 2 and putting in eq(1)

$From \ eq(2)\\x+3y=-7\\x=-7-3y$

Putting value of x in eq(1)

$3x-2y=12\\Put \ x=-7-3y\\3(-7-3y)-2y=12\\Solving\\-21-9y-2y=12\\-11y=12+21\\-11y=33\\y=\frac{33}{-11}\\y=-3$

So, we get y=-3

Now put value of y in equation 2 to find value of x

$x+3y=-7\\x+3(-3)=-7\\x-9=-7\\x=-7+9\\x=2$

So, we get value of x =2

So, solving this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7 we get x=2 and y=-3

Solution set = {2,-3}

4 0

2 years ago

Subtract 3 — (—3) <br> answer idk

nikklg [1K]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Which inequality in standard form represents the<br> shaded region?

Lubov Fominskaja [6]

The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)

<h3>What inequality represents the figure</h3>

In accordance with the figure, we have an inequation of the form y ≥ f(x). Now we proceed to find the <em>quadratic</em> equation of the parabola:

f(x) = a · (x + 1) · (x - 9)

- 125 = a · (4 + 1) · (4 - 9)

- 125 = a · 5 · (- 5)

- 125 = - 25 · a

a = - 5

f(x) = 5 · (x + 1) · (x - 9)

f(x) = 5 · (x² - 8 · x - 9)

f(x) = 5 · x² - 40 · x - 45

The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)

To learn more on inequalities: brainly.com/question/17675534

#SPJ1

5 0

2 years ago

Quiz

Tasya [4]

Answer:

1603

Step-by-step explanation:

3^3*4^3-5^3

__________

3*3*3=9*3=27

4*4*4=16*4=64

5*5*5=25*5=125

(27*64)-125

1728-125

1603

7 0

3 years ago

Read 2 more answers

Answer with work pls

viktelen [127]

Answer:

50 students

Step-by-step explanation:

Hello!

To solve this question, we would first need to look at the data. In this data, there are people who chose their favorite sport, and the number of people who chose that response. In order to solve the problem, we would have to find the ratio of how many people choose baseball over the other sports.

By this, we can add the number of students together. 30+10+5+15=60. Out of those 60 students, only 5 people chose baseball.

Since the ratio of the people who chose baseball is 5/60 (meaning that it is a 5/60 % chance someone would pick this sport), we would need to find the amount of people assumed to pick baseball in 600 student survey.

We can make a relationship with these two numbers.

$\frac{5}{60} =\frac{x}{600}$ , since the ratio of the students who chose baseball remain the same.

You can see that the ratio on the denominators just add a zero on the bottom, so the top should add 0 as well, to get 50 for x, what we needed.

You can also solve that relationship by cross multiplication.

5(600)=x(60

3000=60x

50=x

Regardless, the answer is 50 students who would choose baseball in a 600 persons survey.

5 0

2 years ago

Given sin thata = 2/5 and 0° < thata < 90°. find sin 2 thata​

Given sin thata = 2/5 and 0° < thata < 90°. find sin 2 thata