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2 years ago

You roll a die and pick a marble at the same time.

Mathematics

1 answer:

Ede4ka [16]2 years ago

4 0

4/18
With a six-sided die and 3 marbles there are 18 different outcomes.
(6 numbers • 3 marbles = 18 outcomes)
1/2 of the die is even (2,4,6) so that’s already a 3/6 chance of getting an even number. But since there is only one red marble there is a 1/3 chance of picking it. 3+1=4. 4/18

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Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2

Oxana [17]

Answer:

The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Step-by-step explanation:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$

Multiply and Divide by $2cos(\frac{\pi }{14})$

= $\frac{2sin(\frac{\pi }{14})cos(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})}{2cos(\frac{\pi }{14})}$

⇒ Let $\frac{\pi }{14}$ = Ф and 7Ф = $\frac{\pi }{2}$

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ ∵cos7Ф = 0

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ ∵sin7Ф = 1

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Keywords: prove, sinФ, cosФ

Learn more about trigonometric functions from brainly.com/question/7331447

#learnwithBrainly

4 0

3 years ago

I need help for #1 (an explanation would be great too).

Ivan

Answer:

±6i√2

Step-by-step explanation:

Recall that the square root of a negative number is imaginary, which is shown by the use of "i."

Examples: √4 = ±2; √4 = i√4 = ±i2

Then √72 = ±√36√2 = ±6√2, and

√(-72) = ± i√36√2 = ±6i√2

Note that this is identical to the result shown in the problem: √(36·2·(-1) )

5 0

3 years ago

Vikki [24]

Similar triangles have corresponding sides with proportional lengths.

AB/BC = DE/EF

5/9 = 7.5/EF

5(EF) = 9 * 7.5

5(EF) = 67.5

EF = 13.5

4 0

2 years ago

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MrRa [10]

Answer:

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2 years ago

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Find the area of the figure.

Feliz [49]

Look up "Everything You Need To Know About Math In One Big Fat Notebook pdf." It's the best thing I've ever been given, I have it with me in math class all the time and I've aced every test.

6 0

3 years ago