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elixir [45]
3 years ago
8

What is tm2×2&hhrhejejrh​

Mathematics
1 answer:
timama [110]3 years ago
6 0

Answer:

what??? what do you mean

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Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE
AVprozaik [17]

Answer:

D

Step-by-step explanation:

We are given that:

\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}

Using double angle identities:

\displaystyle  \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence:

<h2>\displaystyle  \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}</h2>

Simplify:

\displaystyle  \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}

Evaluate:

\displaystyle  \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}

So, our answer is D.

7 0
3 years ago
Why is the formula for the area of a triangle one half the area for a rectangle
Naya [18.7K]
The area of a triangle is one half the area for a rectangle because the triangle is half of a rectangle with equal base and height
8 0
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2(4x+3)=7x+5<br><br> (SHOW WORK)<br><br><br><br><br> REPOST
coldgirl [10]

Answer: the answer is -1

Step-by-step explanation:

8 0
2 years ago
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Which of these number is irrational?<br><br> a) 9.6<br> b) √45 <br> c) 3/8<br> d) 3.4 x 10 ⁵
bearhunter [10]

Answer:

I think (D)

Step-by-step explanation:

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Solve for x: - 4 + x &gt; 5
Rufina [12.5K]

Answer:

x>9 this is the correct answer

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