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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

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Solve for x<br> 30x=(60)(ЧО)
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3 years ago
A librarian has 4 identical copies of Hamlet, 3 identical copies of Macbeth, 2 identical copies of Romeo and Juliet, and one cop
lesantik [10]

Answer:

The number of distinct arrangements is <em>12600</em><em>.</em>

Step-by-step explanation:

This is a permutation type of question and therefore the number of distinguishable permutations is:

n!/(n₁! n₂! n₃! ... nₓ!)

where

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In this case

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  • n₂ is the identical copies of Macbeth
  • n₃ is the identical copies of Romeo and Juliet
  • nₓ = n₄ is the one copy of Midsummer's Night Dream

Therefore,

<em>Number of distinct arrangements =  10!/(4! × 3! × 2! × 1!)</em>

<em>                                                         = </em><em>12600 ways</em>

<em />

Thus, the number of distinct arrangements is <em>12600</em><em>.</em>

4 0
3 years ago
(7x-3) ( 11y+5) what’s the value of x
timofeeve [1]

Answer:

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7x = 63

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if you need to find for y

11y + 5 = 60

11y = 55

   y = 5

Step-by-step explanation:

plz mark brainest

7 0
3 years ago
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