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sergij07 [2.7K]
3 years ago
12

Which of the following is a solution to sin x/2 = sqrt3/2 ?

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
3 0

Answer:

A. 60 degrees

Step-by-step explanation:

Solution to sin(x/2)=(\sqrt{3}/2)

By looking at this equation, I can identify that the answer must be within the first quadrant since the numerator and denominator are both positive.

Since it is in the first quadrant, the range of the value of the answer must be between 0 degrees less than or equal to x less than or equal to 90 degrees.

I can also identify that this is a 30, 60, 90 degree triangle because it has a \sqrt{3} and 2 as the numerator and denominator; in this case this tells us that we are dealing with a 30, 60, 90 degree triangle because that is the only triangle with those 2 respective sides.

Once identifying those two pieces of information, we can then determine the answer.

Since sin is equal Opposite/Hypotenuse, we can then substitute the sides of the triangle (\sqrt{3}, 2) to find the angle (unknown).

So the equation would look like this,

Sinx/2=\sqrt{3}/2 (\sqrt{3} representing the opposite side of the angle; 2 representing the Hypotenuse of the triangle)

We can then conclude that 60 degrees is the unknown angle, due to the nature of a 30 60 90 degree triangle.

*Use the attachment for reference

Therefore, the answer, 60 degrees, is a solution to the equation "sin(x/2)=(\sqrt{3}/2)"

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A spinner is divided into many different color sectors. Some sectors are larger than others. The spinner was spun 300 times. The
Furkat [3]
Solutions 

We know that <span>a spinner was divided into many different color sectors. Some sectors are larger than others. The spinner was spun 300 times. The results were tallied up and were written in a table. 

</span><span>Red:93

Blue:59

Green:105

Yellow:43
</span>
The spinner landed the highest on green. To find <span>the probability that the next spin will land on green we have add all the numbers and simplify them.  

93 + 59 + 105 + 43 = 300 

Out of 300 the spinner landed to green 105 times. We have the fraction 105/300. 

105/300 can be reduced. To reduce the fraction we need to the GCF of 105 and 300. The GCF is 15. 

</span>We can reduce the fraction by dividing the numerator and denominator by the GCF = 15. 

105 ÷ 15 = 7 

300 ÷ 15 = 20 

Our new fraction is 7/20 

The <span>probability that the next spin will land on green is 7/20. 
</span>≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
<span>
To get the answer to part (B) we have to add the results of red and green then simplify. 

93 + 105 = 198 

The fraction is 198/300. </span><span>198/300 can be reduced. To reduce the fraction we need to the GCF of 105 and 300. The GCF is 6. 

</span>We can reduce the fraction by dividing <span>the numerator and denominator by the GCF = 6.

</span>198 ÷ 6 = 33

300 ÷ 6 = 50<span>

The new fraction is 33/50 

</span>The probability that the next spin will land on either green or red is <span>33/50. 
</span>
Hope this helps 
4 0
3 years ago
If 4 is 1/4 what is the whole
nevsk [136]

Answer:16/1

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Ryan is making small meat loaves. Each small meat loaf uses 3/4 pound of meat. How much meat does Ryan need to make 8 small meat
taurus [48]
Ryan will need 6 pounds of meatloaf. If you want to know how I got my answer, my work along with the answer will be shown below:

3/4 pound=1 small meatloaf

*Multiply 3/4 pound by 8 because he wants to make 8 small meat loaves, or just add 3/4+3/4+3/4+3/4+3/4+3/4+3/4+3/4*.

#1 way (recommended): 3/4*8/1=24/4....=6 pounds
#2 way: 3/4+3/4=6/4+3/4=9/4+3/4=12/4+3/4=15/4+3/4=18/4+3/4=21/4+3/4=24/4=6 pounds

I hope this helps! Let me know if you still need help!


3 0
3 years ago
How do you write 1.92 x 10 0
nordsb [41]
Im guessing your saying how do you write 1.92 x 10 when you multiply you dont need to line up your decimals but it would lookm something like this:
1.92
x 10

and if it was 1.92 and 10.0 it would look like this

1.92
x 10.0

the deimals dont line up because you are multipling but if you were adding or subtrcating then you would have to line it up but not in this case

4 0
3 years ago
I need help with this:What is the value of y? Enter your answer in the box. y =
lina2011 [118]

Answer:

y=5 degrees

Step-by-step explanation:

It is an isosceles triangle so that means that there are two angles that equal 75, so that means the third side with 4y + 10 is equal to 30 degrees.

4y+10=30

4y=20

y=5 degrees

3 0
3 years ago
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