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stealth61 [152]
2 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]2 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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kotykmax [81]
<span>D. lie in the same plane.
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The definition of capillarity is that points are considered as co-planar when these points are on the same plane, so it is obvious that the answer D is true because this statement is the definition of capillarity. This is shown in Figure 1.

</span><span>A. lie on the same line.
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If four points lie on the same line then there will be a plane that contains this line, therefore the definition is fulfilled. This is shown in Figure 2.

</span><em>Finally, the correct answers are A. and D.</em>

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Answer:

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What is the length of line segment KJ?
Karolina [17]

Please consider the attached file.

We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.

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