1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stealth61 [152]
3 years ago
7

Consider the expression 2√3 cos(x)csc(x)+4cos(x)-3csc(x)-2 √ 3 This expression can be represented as the product of the factors.

.. _____ and _____
By equating the expression to zero we get the solutions over the interval [0,2pi] as
A: (pi/6, pi/3, 2pi/3 and 11pi/6)
B: (5pi/6, 7pi/3, and 5pi/3)
C: (pi/6, 4pi/3, 5pi/3, and 11pi/6)
D: (pi/3, 2pi/3, 5pi/6, and 7pi/6)
Mathematics
1 answer:
Alla [95]3 years ago
8 0

Answer with explanation:

The given expression is:

 2 \sqrt{3}\cos x * \csc x+4 \cos x-3 \csc x-2\sqrt{3}\\\\=2 \cos x*(\sqrt{3}*\csc x+2)-\sqrt{3}*(\sqrt{3}*\csc x+2)\\\\\rightarrow (2\cos x -\sqrt{3})*(\sqrt{3}*\csc x+2)\\\\\rightarrow (2\cos x -\sqrt{3})*(\sqrt{3}*\csc x+2)=0\\\\(2\cos x -\sqrt{3})=0 \wedge (\sqrt{3}*\csc x+2)=0

  \cos x=\frac{\sqrt{3}}{2} \wedge \csc x=\frac{-2}{\sqrt{3}}\\\\x=\frac{\pi}{6},2\pi-\frac{\pi}{6}\\\\x=\frac{\pi}{6},\frac{11\pi}{6} \wedge x=\pi+\frac{\pi}{3} ,2\pi-\frac{\pi}{3}\\\\x=\frac{4\pi}{3},\frac{5\pi}{3}\\\\x={\frac{\pi}{6},\frac{11\pi}{6},\frac{4\pi}{3},\frac{5\pi}{3}}

Option C

You might be interested in
The sum of a number x and 5 equals 14
pav-90 [236]

Answer:

x=9

Step-by-step explanation:

Since x+5=14, then you would subtract 5 from 14. 14-5=9. So that means x equals 9.

3 0
3 years ago
Read 2 more answers
Is 0.6 60 and 6 equal?
quester [9]

Answer:

Yesss

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times
rusak2 [61]

Answer:

x=30\\y=68\\z=82

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

y+z=5x

The third angle is 14 more than the second

z=y+14

And remember that the sum of these three angles must be equal to 180.

x+y+z=180

Let's take these equations

y+z=5x\\z=y+14\\x+y+z=180

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

x+y+z=180\\x+(y+z)=180\\x+(5x)=180

Distribute the + sign

x+5x=180

Combine like terms;

6x=180

Divide by 6.

x=\frac{180}{6}\\ x=30

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example z=y+14

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

x+y+z=180\\30+y+(y+14)=180

Distribute the + sign and Combine like terms;

30+y+y+14=180\\44+2y=180\\

Subtract 44 to isolate 2y.

2y=180-44\\2y=136

Now divide by 2.

y=\frac{136}{2}\\ y=68

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82

5 0
3 years ago
Points showing equivalent relics on the coordinate planeten
koban [17]

Answer:

<em>Answer: (8,12) Third option</em>

Step-by-step explanation:

<u>Equivalent Ratios</u>

Nardia plotted some points showing equivalent ratios. The points shown in the graph are: (2,3), (4,6), (10,15)

The ratios of the points in the form y:x are:

\frac{3}{2}

\frac{6}{4}=\frac{3}{2}

\frac{15}{10}=\frac{3}{2}

Note all the ratios are equivalent.

From the ordered pairs provided in the choices, only one of them has the same ratio y:x.

Point (12,8) has a ratio:

\frac{12}{8}=\frac{3}{2}

Answer: (8,12) Third option

3 0
3 years ago
For
sdas [7]
5(x − 4)^2

5(x - 4)(x - 4)

5(x^2 - 8x + 16)

5x^2 - 40x + 80

Did you follow?
6 0
3 years ago
Other questions:
  • What is equivalent 75/100
    8·2 answers
  • What is the answer to this problem?<br>8x + 7 - 4x + 1= 20
    15·1 answer
  • At a sporting event, the price for 3 cheeseburgers and 2 cups of lemonade is $14 and the price for 2 cheeseburgers and 4 cups of
    7·2 answers
  • Dean saved 15$ to buy baseball cards. Each pack of baseball cards costs 6$. How many packs can dean buy
    14·1 answer
  • In 17, 874,000 what is the value of 1
    10·1 answer
  • Which of the two triangles has the greatest area?
    8·1 answer
  • Plz answer correctly for me<br><br><br> THANK YOU
    9·1 answer
  • Casey ran out of time while taking a multiple-choice test and plans to guess on the last 101010 questions. Each question has 555
    14·2 answers
  • -4-8 and 3-(-1)<br> thats it
    11·2 answers
  • 1.8*10^-3/6*10^8 write your answer in scientific notation
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!