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solniwko [45]
2 years ago
12

Help please! asap!

Mathematics
1 answer:
aliya0001 [1]2 years ago
8 0

Answer: 50% or 1/2

Step-by-step explanation:

number of possible combos:

1+1, 1+2, 1+3, 1+4, 1+5, 1+6

2+1, 2+2, 2+3, 2+4, 2+5, 2+6

3+1, 3+2, 3+3, 3+4, 3+5, 3+6

4+1, 4+2, 4+3, 4+4, 4+5, 4+6

5+1, 5+2, 5+3, 5+4, 5+5, 5+6

6+1, 6+2, 6+3, 6+4, 6+5, 6+6

number of even sums within combos:

1+1, 1+3, 1+5

2+2, 2+4, 2+6

3+1, 3+3, 3+5

4+2, 4+4, 4+6

5+1, 5+3, 5+5

6+2, 6+4, 6+6

<u>TOTAL combos:</u>

36

<u>TOTAL even sums:</u>

18

so that means 18/36 or 1/2 of the possible combinations has a sum of an even number.

sorry it’s not a table but I literally worked it out while answering so that’s all my work

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Answer:

The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Given  

                cos( 3x - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

                  cos( 3x - \frac{\pi }{3} )  = cos (\frac{\pi }{6} )

                      3x - \frac{\pi }{3}  =  \frac{\pi }{6}

                      3x - \frac{\pi }{3  } + \frac{\pi }{3}   =  \frac{\pi }{6} + \frac{\pi }{3}

                      3x = \frac{2\pi +\pi }{6} = \frac{3\pi }{6} = \frac{\pi }{2}

                     x = \frac{\pi }{6}

<u><em>Step(ii)</em></u>:-

The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

<u><em>verification </em></u>:-

      cos( 3x - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

put  x = \frac{\pi }{6}

    cos( 3(\frac{\pi }{6})  - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

    cos (\frac{\pi }{6} ) = \frac{\sqrt{3} }{2} \\\\\frac{\sqrt{3} }{2} =  \frac{\sqrt{3} }{2}

Both are equal

∴The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

                     

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