All categories

3 years ago

Solve 2cos2x + cosx − 1 = 0 for x over the interval [0, 2pi ).

Mathematics

1 answer:

Galina-37 [17]3 years ago

4 0

2cos^2x+cosx-1 = 0

2cos^2x + 2cosx - cosx - 1 = 0

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

2cosx(cosx + 1) - 1(cosx + 1) = 0

(cosx + 1)(2cosx - 1) = 0

cosx+1 = 0 or 2cosx-1 = 0

cosx+1 = 0 gives cosx = -1, x = PI

2cosx-1 = 0 gives cosx = 1/2, x = PI/3 or x = 5PI/3

answer: x = PI/3 or x = PI or x = 5PI/3

You might be interested in

4y - 7 = 5x2 - x + 2 + 3y

zalisa [80]

Answer:

y = 9 + -1x + 5x2

Step-by-step explanation:

Simplifying

4y + -7 = 5x2 + -1x + 2 + 3y

Reorder the terms:

-7 + 4y = 5x2 + -1x + 2 + 3y

Reorder the terms:

-7 + 4y = 2 + -1x + 5x2 + 3y

Solving

-7 + 4y = 2 + -1x + 5x2 + 3y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-3y' to each side of the equation.

-7 + 4y + -3y = 2 + -1x + 5x2 + 3y + -3y

Combine like terms: 4y + -3y = 1y

-7 + 1y = 2 + -1x + 5x2 + 3y + -3y

Combine like terms: 3y + -3y = 0

-7 + 1y = 2 + -1x + 5x2 + 0

-7 + 1y = 2 + -1x + 5x2

Add '7' to each side of the equation.

-7 + 7 + 1y = 2 + -1x + 7 + 5x2

Combine like terms: -7 + 7 = 0

0 + 1y = 2 + -1x + 7 + 5x2

1y = 2 + -1x + 7 + 5x2

Reorder the terms:

1y = 2 + 7 + -1x + 5x2

Combine like terms: 2 + 7 = 9

1y = 9 + -1x + 5x2

Divide each side by '1'.

y = 9 + -1x + 5x2

Simplifying

y = 9 + -1x + 5x2

6 0

3 years ago

SMART PPL PLEASE HELP ,Explain how you know the expression represents the area of shaded part of the rectangle.

MrRa [10]

Answer:

6(m-2)

Step-by-step explanation:

Alright. Let's start by finding the length of this shaded area. The full length of the rectangle is 'm', and the part that is not shaded has a length of '2', so if we subtract the full length and the non-shaded length, we will get the shaded part's length. This is 'm-2'. The width/height we already know...it is 6, so-

Answer is: 6(m-2)

5 0

3 years ago

Read 2 more answers

Quadrilateral ABCD is a rhombus. What is the value of p?

Sveta_85 [38]

Answer:

yes becuse id theres 4 letters it can be a parallogram

3 0

3 years ago

Which ones are parallel?

amid [387]

The answer is : a||b

3 0

3 years ago

Read 2 more answers

graph the solution to the following system of inequalities y<-2x+7, y greater than or equal to 2x - 3

Alex777 [14]

Answer:

See attached diagram

Step-by-step explanation:

Graph the solution of the inequality $y$ First, draw the dotted line $y=-2x+7$ (dotted because the sign of the inequality is <). Then determine wich part of the coordinate plane should be shaded. Since the origin's coordinates satisfy the inequality, then this point should belong to the region (red part on the diagram).

Graph the solution of the inequality $y\ge 2x-3.$ First, draw the solid line $y=2x-3$ (solid because the sign of the inequality is ≥). Then determine wich part of the coordinate plane should be shaded. Since the origin's coordinates satisfy the inequality, then this point should belong to the region (blue part on the diagram).

The intersection of both regions is the solution of the system of two inequalities.

6 0

3 years ago