Solve 2cos^2x + cosx − 1 = 0 for x over the interval [0, 2 pi ).

Answers

Answer 1

Answer: $2cos^(2)(x) + cos(x)-1 = 0$

This could also be written as, where $a = cos(x)$

$2a^(2) + a - 1 = 0$

This would factorize to give:

$(2a-1)(a+1)=0$

So we can factorize our original expression:

$2cos^(2)(x) + cos(x)-1 = 0 \n \n (2cosx - 1)(cosx+1) = 0$

We can then solve for $x$ as we would with a normal quadratic:

$2cosx -1 =0 \n \n cosx = (1)/(2) \n \n x = cos^(-1)( (1)/(2) ) \n \n x = ( \pi )/(3), (5 \pi )/(3)$

And also:

$cos(x)+1 = 0 \n \n cos(x)= -1 \n \n x = cos^(-1)(1) \n \n x = 0, 2 \pi$

So our values for $x$ are:

$x =0, ( \pi )/(3), (5 \pi )/(3), 2 \pi$

As: $0 \leq x\ \textless \ 2 \pi$

Our final solutions for $x$ are:

$x = \boxed{0, ( \pi )/(3), (5 \pi )/(3)}$

Answer 2

Answer:

The solutions to the equation 2cos²(x) + cos(x) - 1 = 0 over the interval [0, 2π) are x = π/3, 5π/3, and π.

We have,

To solve the equation 2cos²(x) + cos(x) - 1 = 0 over the interval [0, 2π), we can use a substitution technique.

Let's substitute cos(x) with a variable, say, u.

The equation becomes:

2u^2 + u - 1 = 0.

Now, we can factorize the quadratic equation:

(2u - 1)(u + 1) = 0.

Setting each factor equal to zero, we have:

2u - 1 = 0 or u + 1 = 0.

Solving these equations separately, we find:

2u = 1 or u = -1.

For 2u = 1, we get u = 1/2. Taking the inverse cosine of 1/2,

We have cos(x) = 1/2.

For u = -1, we get u = -1. Taking the inverse cosine of -1, we have cos(x) = -1.

Now, we need to determine the solutions for x within the given interval [0, 2π).

For cos(x) = 1/2, the solutions within the interval are x = π/3 and x = 5π/3.

For cos(x) = -1, the solution within the interval is x = π.

Therefore,

The solutions to the equation 2cos²(x) + cos(x) - 1 = 0 over the interval [0, 2π) are x = π/3, 5π/3, and π.

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Evaluate the expression for the given value of the variable(s). 5a+5b;a=-6b=-5

A. 19 B. 17 C. -11 D. 21

Answers

The given expression is 5a+5b The given values of a and b are a=-6 ,b=-5

Substituting the values of a and b in the expression we have :

5a+5b= 5(-6)+5(-5)

= -30 -25 ( when a positive and a negative number is multiplied the result is a negative number)

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The answer to the expression 5a+5b when a=-6 anf b=5 is -55.

[The given options are not correct.]

The answer to what you have there is -55 using order of operations. 5 times -6 is -30. 5 times -5 is -25. add. You get -55.

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28° + x-4°+2x=180°

Answers

Answer:

x = 52

Step-by-step explanation:

28 + x - 4 + 2x = 180

Simplify the left side

3x + 24 = 180

Subtract 24 from each side

3x = 156

Divide each side by 3

x = 52

This is a probability question:A committee of six is to review the value of discipline in education. The committee is to be chosen randomly from 3 interest teachers, a student council of 6 students and 5 interested parents. What are the following probabilities?
a)no students are on the committee
b) The committee is made up only of students
c) There will be at least one teacher on the committee.

Answers

Im pretty sure it is b

2x = 36 solve the equation

Answers

Answer: x = 18

Step-by-step explanation:

divide the whole equation by 2 to single out x, so then 36/2 = 18

2x/2 =36/2 which is equal to x=18

How many more ways can 10 juniors running for the positions of president, vice president, secretary, treasurer be selected when compared to 12 sophomores running for 5 identical positions of class representative's?

Answers

10 juniors are running for 4 positions.
There are ten people who can get into the first spot
Nine people for the second
8 people for the third
7 for the fourth
10x9x8x7= 5040 different ways.

For the sophomores: 12x11x10x9x8= 95040
However, the positions are identical which means that the order doesn't matter. (There's a difference between A getting postion 1, B for 2, C for 3, D for 4 and B for 1, A for 2, C for 3, D for 4)

There are 5 identical positions, therefore we divide this by 5! (5x4x3x2x1)= 120
95040/120= 792
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A kite, flying 50 feet high in the air is attached by a string to a stake in the sand. How long is the string to the nearest tenth of a foot?a) 50.0 feet
b) 70.7 feet
c) 86.6 feet
d) 100.0 feet ...?

Answers

Height of the kite from the ground = 50 feet
Angle at which the kite is flying = 45 degrees
Let us assume the length of the string = x feet
Then
x = 50 * (square root 2)
= 50 * 1.414
= 70.7 feet
From the above deduction, it can be concluded that the correct option among all the options that are given in the question is the second option or option "b".

Answer:

the answer is b) 70.7 feet

Step-by-step explanation:

thank you for amazing answers on the board.

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