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julsineya [31]
2 years ago
8

Find all exact solutions on [0, 2π). (Enter your answers as a comma-separated list.)

Mathematics
1 answer:
nalin [4]2 years ago
7 0

Answer:

0, \dfrac{\pi}{6}, \dfrac{5\pi}{6},  \pi

Step-by-step explanation:

Given the equation:

sin(x)-2sin(x) tan(x)=0

To find:

The solutions of given equation in the range [0, 2\pi) i.e. 0 can be in the answer but 2\pi can not be there in the answer.

Solution:

Taking tan(x) common, we get:

tan(x) (1-2sin(x))=0

The solutions can be given as:

tan(x) = 0 OR 1-2sin(x) = 0

Let us solve both the equations one by one:

First equation:

tan(x) = 0\\ \Rightarrow x=0, \pi

Second equation:

1-2sin(x) = 0\\\Rightarrow 2sinx=1\\\Rightarrow sinx=\dfrac{1}{2}\\\Rightarrow x = \dfrac{\pi}{6}, \dfrac{5\pi}{6}

Therefore, the answers as a comma separated list are:

0, \dfrac{\pi}{6}, \dfrac{5\pi}{6},  \pi

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PLZ HELP QUICK-------------->
sveticcg [70]
<h2>>>> Answer <<<</h2>

Let's check which polynomial is divisible by ( x - 1 ) using hit , trial and error method .

A ( x ) = 3x³ + 2x² - x

The word " divisible " itself says that " it is a factor "

Using factor theorem ;

Let;

=> x - 1 = 0

=> x = 1

Substitute the value of x in p ( x )

p ( 1 ) =

3 ( 1 )³ + 2 ( 1 )² - 1

3 ( 1 ) + 2 ( 1 ) - 1

3 + 2 - 1

5 - 1

4

This implies ;

A ( x ) is not divisible by ( x - 1 )

Similarly,

B ( x ) = 5x³ - 4x² - x

B ( 1 ) =

5 ( 1 )³ - 4 ( 1 )² - 1

5 ( 1 ) - 4 ( 1 ) - 1

5 - 4 - 1

5 - 5

0

This implies ;

B ( x ) is divisible by ( x - 1 )

Similarly,

C ( x ) = 2x³ - 3x² + 2x - 1

C ( 1 ) =

2 ( 1 )³ - 3 ( 1 )² + 2 ( 1 ) - 1

2 ( 1 ) - 3 ( 1 ) + 2 - 1

2 - 3 + 2 - 1

4 - 4

0

This implies ;

C ( x ) is divisible by ( x - 1 )

Similarly,

D ( x ) = x³ + 2x² + 3x + 2

D ( 1 ) =

( 1 )³ + 2 ( 1 )² + 3 ( 1 ) + 2

1 + 2 + 3 + 2

8

This implies ;

D ( x ) is not divisible by ( x - 1 )

<h2>Therefore ; </h2>

<h3>B ( x ) & C ( x ) are divisible by ( x - 1 ) </h3>
6 0
3 years ago
In how many ways can 15 basketball players be listed in a program?
Viktor [21]
The answer is 15 !

Explanation:
You have 15 slots, each of which will hold one of the names of the players. You need to fill the first slot with some name.
7 0
3 years ago
Read 2 more answers
Need help again please...
Greeley [361]
40 - 4 = 36

average = 36/9 = 4

answer
average number of members who joined the math club is 4 per month

5 0
3 years ago
Can someone please help me with this math problem:)
Dennis_Churaev [7]

Answer:

x = 20

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

\frac{x}{12} = \frac{15}{9} ( cross- multiply )

9x = 180 ( divide both sides by 9 )

x = 20

5 0
3 years ago
Read 2 more answers
Please help and explain how to solve these! Thanks
spin [16.1K]
2. C
Slope = 40/8 = 5
Slope of graph c = 5/1 = 5

3. D
Slope = 9/3 = 3
Slope of graph d = 81/27 = 3
3 0
3 years ago
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