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2 years ago

Knowing that sin 30 = 1/2 what is a

Mathematics

2 answers:

Aleksandr [31]2 years ago

6 0

Answer:

B. 18

Step-by-step explanation:

We have been given a diagram of a right triangle and we are asked to find the value of a.

Since we know that Sine relates the opposite with hypotenuse of a right triangle.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

Upon substituting our given values we will get,

$sin(30^o)=\frac{9}{a}$

Upon substituting $sin(30^o)=\frac{1}{2}$ in above equation we will get,

$\frac{1}{2}=\frac{9}{a}$

Now let us cross multiply our equation to solve for a.

$1\cdot a=9\cdot 2$

$a=18$

Therefore, the value of a is 18 and option B is the correct choice.

natulia [17]2 years ago

4 0

$sin30^o=\frac{9}{a}\\\frac{9}{a}=\frac{1}{2}\\a=2\cdot9\\a=18$

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Which pairs of angles in the figure below are vertical angles?

ch4aika [34]

Answer: Option A and Option C.

Step-by-step explanation:

For this exercise it is important to know the definition of "Vertical Angles".

When two lines intersect or cross, there are a pair of angles that share the same vertex and they are opposite each other. This pair of angles are known as "Vertical angles".

By definition, Vertical angles are congruent, which means that the have the equal measure.

In this case, you can observe in the picture provided in the exercise that the line TI and the line WN intersect each other at the point S.

You can identify that the pair of angles that are opposite to each other and share the same vertex are the shown below:

$\angle ISN$ and $\angle TSW$

$\angle TSN$ and $\angle ISW$

6 0

2 years ago

QUICK! 75 POINTS !!Select all that are part of the solution set of csc(x) > 1 and over 0 ≤ x ≤ 2π.

Vladimir79 [104]

Answer:

$\frac{\pi}{4}$

$\frac{5\pi}{6}$

Step-by-step explanation:

The answer uses the unit circle and that sine and cosecant are reciprocals.

The first choice doesn't even fit the criteria that $x$ is between $0$ and $2\pi$ (inclusive of both endpoints) because of the $x=\frac{-7\pi}{6}$ .

Let's check the second choice.

$\csc(\frac{\pi}{4})=\frac{2}{\sqrt{2}} \text{ since } \sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$ .

$\csc(\frac{\pi}{4})>1 \text{ since } \frac{2}{\sqrt{2}}>1$

$\csc(\frac{\pi}{2})=1 \text{ since } \sin(\frac{\pi}{2})=1$ which means $\csc(\frac{\pi}{2})=1$ which is not greater than 1.

So we can eliminate second choice.

Let's look at the third.

$\csc(\frac{5\pi}{6})=2 \text{ since } \sin(\frac{5\pi}{6})=\frac{1}{2}$ which means $\csc(\frac{5\pi}{6})>1$ .

$\csc(\pi)$ isn't defined because $\sin(\pi)=0$ .

So we are eliminating 3rd choice now.

Let's look at the fourth choice.

$\csc(\frac{7\pi}{6})=-2 \text{ since } \sin(\frac{7\pi}{6})=\frac{-1}{2}$ which means $\csc(\frac{7\pi}{6})$ and not greater than 1.

I was looking at the rows as if they were choices.

Let me break up my choices.

So we said $x=-\frac{7\pi}{6}$ doesn't work because it is not included in the inequality $0\le x \le 2\pi$ .

How about $x=0$ ? This leads to $\csc(0)$ which doesn't exist because $\sin(0)=0$ .

So neither of the first two choices on the first row.

Let's look at the second row again.

We said $\frac{\pi}{4}$ worked but not $\frac{\pi}{2}$

Let's look at the choices on the third row.

We said $\frac{5\pi}{6}$ worked but not $x=\pi$

Let's look at at the last choice.

We said it gave something less than 1 so this choice doesn't work.

6 0

1 year ago

Read 2 more answers

You are visiting your friend Fabio's house. You find that, as a joke, he filled his swimming pool with Kool-Aid, which dissolved

Rzqust [24]

Answer:

The amount of work required to remove all of the water by pumping it over the side = 3.12 × 10⁶ lbs.ft

Step-by-step explanation:

Work done in moving anything from point A to point B = Fx

For this setup,

If we take an elemental vertical height, dx, The volume would be A.dx

where A = Cross sectional Area = πr² = π(18)² = 1017.88 ft²

dV = 1017.88 dx

The elemental force on that part will be

dF = ρg dV

ρg = 63.8 lbs/ft³

dF = 63.8 × 1017.88 dx = 64940.5 dx

F = ∫dF = 64940.5 dx

W = Fx = (∫dF)x = ∫ 64940.5x dx = 64940.5 ∫ xdx

We'll be integrating from (11 - 6) ft to 11 ft because that's the total height it'll be pumped through

W = 64940.5 (x²/2)¹¹₅ = 64940.5((11² - 5²)/2) = 3.12 × 10⁶ lbs.ft

4 0

2 years ago

Luke’s soccer team won 12 games and lost 5 games. Select all the expressions that show the ratio of wins to losses. Asap plz

almond37 [142]

Answer:

We don't have any options to choose from, but here are some general ones:

12:5

12 / 5

41% of games Luke lost.

59% of games Luke won.

Step-by-step explanation:

4 0

2 years ago

A carnival sold 135 bottles of juice in one day. They sold 1/3 of the bottles in the first hour and 2/5 of the bottles in the se

vazorg [7]

1/3x135=45 bottles the first hour
135-45=90 bottles left after first hour
2/5x90=36 bottles the second hour
45+36=81 bottles altogether

7 0

2 years ago