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2 years ago

Solve and graph 2cos(2x) = x radians

Mathematics

1 answer:

AleksandrR [38]2 years ago

8 0

The solutions of the equation 2cos(2x) = x are (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)

<h3>How to solve the equation?</h3>

The equation is given as:

2cos(2x) = x

Split the equation as follows:

y = 2cos(2x)

y = x

Next, we plot the graph of y = 2cos(2x) and y = x (see attachment)

From the attached graph, y = 2cos(2x) and y = x intersect at the following points

(x, y) = (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)

Hence, the solutions of the equation 2cos(2x) = x are (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)

Read more about trigonometry equations at:

brainly.com/question/8120556

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A coin, having probability p of landing heads, is continually flipped until at least one head and one tail have been flipped. (a

Natali [406]

Answer:

(a)

The probability that you stop at the fifth flip would be

$p^4 (1-p) + (1-p)^4 p$

(b)

The expected numbers of flips needed would be

$\sum\limits_{n=1}^{\infty} n p(1-p)^{n-1} = 1/p$

Therefore, suppose that $p = 0.5$ , then the expected number of flips needed would be 1/0.5 = 2.

Step-by-step explanation:

(a)

Case 1

Imagine that you throw your coin and you get only heads, then you would stop when you get the first tail. So the probability that you stop at the fifth flip would be

$p^4 (1-p)$

Case 2

Imagine that you throw your coin and you get only tails, then you would stop when you get the first head. So the probability that you stop at the fifth flip would be

$(1-p)^4p$

Therefore the probability that you stop at the fifth flip would be

$p^4 (1-p) + (1-p)^4 p$

(b)

The expected numbers of flips needed would be

$\sum\limits_{n=1}^{\infty} n p(1-p)^{n-1} = 1/p$

Therefore, suppose that $p = 0.5$ , then the expected number of flips needed would be 1/0.5 = 2.

7 0

2 years ago

Choose any method to find the gcf of 40 16 and 24

Juli2301 [7.4K]

The GCF of 40 16 and 24 is 8

<h3>How to determine the GCF of 40 16 and 24?</h3>

The numbers are given as:

40 16 and 24

Start by listing out the factors of the numbers:

This is done as follows:

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Then the greatest common factor in the above list is 8.

Hence, the GCF of 40 16 and 24 is 8