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yanalaym [24]
3 years ago
7

Solve 2sin x + sqrt3 = 0

Mathematics
1 answer:
Natasha2012 [34]3 years ago
5 0
Subtract sqrt 3 to isolate 2sin x
Divide by 2 to isolate sin x
Take the arcsin of each side to isolate x
Thinking of a 30-60-90 triangle, we know that x sqrt 3 is opposite 60° and 2x acts as the hypotenuse, thus it will be some variation of 60°.
 In order to produce a negative result, x must be -60° (-π/3)
It is worth noting that this is a restricted value. Any addition/subtraction of 2π from this answer will produce the same result, thus your full answer is the above plus or minus 2kπ where k ∈ Z (k is an interger)

2\sin x+\sqrt{3}=0\\\\2\sin x=-\sqrt{3}\\\\\sin x=-\frac{\sqrt{3}}2\\\\\sin^{-1}(\frac{\sqrt{3}}2)=x\\\\\boxed{x=-\frac{\pi}3\pm2k\pi,\ k\in \mathbb{Z}}\ (-\frac{\pi}3=-60\°)




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6 0
3 years ago
A 3.5‘ x 5.5‘ nearest place in a wooden frame what is the area of the frame
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The area of the frame would be 19.25’
8 0
3 years ago
Nimisha wants to draw a wheel like the one shown. Each shaded part of the wheel should be one-third of each unshaded part. What
ivolga24 [154]

Answer:

Each shade has a 22.5 degree angle from the middle

Each unshaded has a 67.5 degree angle from the middle.

Step-by-step explanation:

You can solve this by making each unshaded part equal to x and each shaded part equal 1/3x it is a circle so it has to equal 360 so you end up with:

x + 1/3x + x + 1/3x + x + 1/3x + x + 1/3x = 360

Combine Like terms:

16/3x = 360

Multiply both sides by the opposite:

(3/16) (16/3x) = (360) (3/16)

x=135/2 or x=67.5

Then you can plug 67.5 in for x:

1/3x ---> 1/3(67.5) = 22.5

3 0
3 years ago
Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 mph faster than Charlene. They meet in
Thepotemich [5.8K]

Answer:

34 mph.    

Step-by-step explanation:

Let x be speed of Charlene, then speed of Paul will be x+16 as we are given that Paul is driving 16 mph faster than Charlene.

Let y be distance covered by Charlene, then distance covered by Paul will be 420-y.  

Now we will use formula \text{Speed}=\frac{\text{Distance}}{\text{Time}}. Upon using our given information we will get two equation and two unknowns as:  

x+16=\frac{420-y}{5}...(1)

x=\frac{y}{5}...(2)

Upon substituting x=\frac{y}{5} in 1st equation we will get,

\frac{y}{5}+16=\frac{420-y}{5}

Upon multiplying both sides of our equation by 5 we will get,

5(\frac{y}{5}+16)=420-y

5\times\frac{y}{5}+5\times 16=420-y    

y+80=420-y

y+80+y=420-y+y

2y+80=420

2y=420-80

2y=340

y=\frac{340}{2}  

y=170      

Upon substituting y=170 in 2nd equation we will get,

x=\frac{170}{5}

x=34

Therefore, Charlene's speed is 34 miles per hour.


6 0
3 years ago
What is a triangular prism? Guy please answer this question it's me ?
IRISSAK [1]

Answer:

A prism is a polyhedron A prism is a 3-dimensional shape with two identical shapes facing each other. These identical shapes are called “bases”. The bases can be a triangle, square, rectangle or any other polygon.

Step-by-step explanation:

i hope this will help you

5 0
3 years ago
Read 2 more answers
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