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marissa [1.9K]
4 years ago
10

Evaluate cot870°. 1. - sqrt3 2. -1/sqrt3 3. 1/sqrt3 4. sqrt3

Mathematics
1 answer:
ivolga24 [154]4 years ago
3 0

ANSWER

-\sqrt{3}

EXPLANATION

The given angle is 870°.

870°-360°-360°=150°

This means that:

870° is coterminal with 150°, hence its terminal side is in the second quadrant.

It makes an acute angle of 30° with the x-axis.

Note that cotangent is negative in the second quadrant,

Hence,

\cot(870 \degree)  =  \cot(150 \degree)  =  -  \cot(30 \degree)  =  -  \frac{1}{ \tan(30 \degree) }  =  - \sqrt{3}

The first option is correct.

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Answer:

a. f(2)=24  

Step-by-step explanation:

Given function:

f(x)=3x^2+9x-6

To find f(2)

Solution:

In order to find f(2),we need to plugin input=2 i.e. the value of x=2 in the function and find the output by evaluating.

Plugging in x=2 in the given function.

f(2)=3(2)^2+9(2)-6

Evaluating.

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f(2)=12+18-6

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The answer will be that out of 36 boys 24 speak french and 12 speak german and out of 24 girls 16 speak french and 8 speak german.

<h3>What is the frequency tree?</h3>

In the question we have that there are 60 students in total out of which 36 are boys:

So number of the girls will be = 60-36=24

Now if 2/3 of the boys speak french the number of the boys who speak french will be = (2÷3)x36=24

Now the number of the boys who speak german will be =36-24=12

Now since 40 students study french so we have the number of the boys who speak french is 24. so the number if the girls who speak french will be =40-24=16

Since there are 24 girls in total and out of them 16 speak french so the remaining girls speak german=24-16=8

Hence answer will be that out of 36 boys 24 speak french and 12 speak german and out of 24 girls 16 speak french and 8 speak german.

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According to the question, the correct graph is D.

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