which of the following are solutions to the equation 2cos2x-1=0

Which Of The Following Are Solutions To The Equation 2cos2x-1=0

Answers

Answer 1

Answer:

x = π/4 and 5π/4

Step-by-step explanation:

Given the expression;

2cos²x - 1 = 0

2cos²x = 0+1

2cos²x = 1

cos²x = 1/2

cos x = ±√1/2

cos x = ±0.7071

x = arccos(±0.7071)

x = ±45 degrees

Convert to radians

Sence 180° = π rad

45°  = x

x = 45π/180

x = π/4

If x = -45°

Since cos is negative in the 3rd quadrant

x = 180 + 45

x = 225°

x = 225π/180

x = 45π/36

x = 5π/4


Related Questions

A metal smith is mixing two molten metals

Answers

Answer:

I think the answer is going to be A (15)(0.75) and 0.7(15 – x) + 0.9x, I hope this helps!! :)

Step-by-step explanation:

PLS HELP SOON WILL MARK BRAINLYEST

A railroad tunnel is shaped like a semi-ellipse, as shown below. A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis. The height of the tunnel at the center is 35 ft, and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse.

Answers

According to the question

b= 35 and (8,21) lies on the ellipse

After calculation we get a= 10

equation for the ellipse.

[tex] \frac{ {x}^{2} }{100} + \frac{ {y}^{2} }{1225} = 1[/tex]

What is the vertex of the parabola?
y - 3 = 1/2 (x + 5)²
( __ , __ )

Answers

Answer:

(-5,31/2)

Step-by-step explanation:

open bracket

y=1/2x^2+5x+28

compare with y=ax2+bx+c

use formula (-b/2a,4ac-b2/4a)

Marcel and Floyd are playing games at an arcade. Marcel has $8.25 and is only playing $0.25 games. Floyd has $9.75 and is only playing $0.75 games. Jorge wants to find the number of games after which Marcel and Floyd will have the same amount of money remaining. Jorge’s work is shown below.

Answers

Answer:

3 games

Step-by-step explanation:

8.
Out of total population of 50,000, only 28,000 read Newspaper and 23,000 read
magazines while 4,000 read both. How many of them do not read any paper ?​

Answers

the answer is in the picture

PLEASE HELP ITS EASY BUT LIKE yh

Answers

Answer:

40  I told u

Step-by-step explanation:

right angles are 90 degrees

Answer :

x +25 +25 =90 degrees

x +50 =90 degrees

x = 90 -50

x = 40 degrees

On a coordinate plane, line D F goes through points (negative 1, negative 3) and (2, 3). Point G is at (negative 4, negative 4).

Answers

The line passes through the y-axis at point (0,4).

Step-by-step explanation:

On a coordinate plane, line DF goes through points (-1,-3) and (2,3).

So, the slope of the line DF is \frac{- 3 - 3}{- 1 - 2} = 2

−1−2

−3−3

=2

Then the straight line which is parallel to DF will be given by

y = 2x + c.

Where, c is any constant and we have to evaluate it if this line passes through the point (-4,-4).

So, - 4 = 2(- 4) + c

⇒ c = 4

So, the straight line which is parallel to DF and passes through the point (-4,-4) is y = 2x + 4.

Now, putting x = 0, we get, y = 4.

Therefore, the line passes through the y-axis at point (0,4). (Answer)

Answer:

The answer would be D

Step-by-step explanation:

Which is the ratio of triangles and to hearts
there is 22 hearts and
11 triangles

Answers

Answer:

triangles : hearts = 11 : 22 = = 11 : 2(11) = 1 : 2

If you put it in fraction form it's [tex]\frac{triangles}{hearts} =\frac{11}{22} =\frac{11}{2(11)}=\frac{1}{2}[/tex].

a man invested 800.00in a bank at a simple interest rate of 5% per annum .Find his total amou year​

Answers

Answer:

£840

Step-by-step explanation:

800 × 1.05 = 840

(1.05 Is the decimal multiplier = (100% + 5%)/100)

When the angle of elevation of the sun is
42°, fnd the length of the shadow, to the
nearest foot, cast by a tree 60 feet tall.

Answers

Answer:

The shadow length is 67

Step-by-step explanation:

solution shown in the picture

the area of a rectangular bathroom mirror is 20 square feet. it is 2 feet tall. how wide is it?

Answers

Area = length x width

Fill in the given information

20 = 2 x width

Solve for width by dividing both sides by 2

Width =20/2

Width = 10 feet

Answer:

It is 10 feet wide

Step-by-step explanation:

The area of a rectangle is:

A = Length x width

So if we have the area, finding the width means diving the area by the given length.

In this case, the area of the rectangle is 20 square feet and the length is 2 feet:

20/2 = 10

Therefore the missing width is 10 feet

Which expression has a solution of 11, if m = 1?

m - 11
11 + m
14 - m
m + 10

Answers

Answer:

m+10 has the solution of 11

Find the H.C.F. of the following numbers using division method
(a) 24, 40

Answers

Answer:

Ok

Thank you for

your time

After substituting, what is the first step when evaluating vegy 4 2 when x 6?
O Multiply 3 by 5
O Add 5 and 3
Subtract 4.2 from 5
Add 3 and 4.2 hurry I'm being timedd!!!

Answers

Answer:

Multiply 3 by 5

Step-by-step explanation:

After substituting, what is the first step when evaluating x+3x-4.2 when x=5

Given:

x + 3x - 4.2

when x = 5

Substitute x = 5 into the expression

x + 3x - 4.2

= 5 + 3(5) - 4.2

= 5 + 15 - 4.2

= 20 - 4.2

= 16.8

x + 3x - 4.2, when x = 5 is 16.8

After substituting, the first step when evaluating x + 3x - 4.2 when x = 5 is Multiply 3 by 5

I don't get this can somone help me please ​

Answers

Answer:

f = m+h

Step-by-step explanation:

just add h to both sides of the equation to isolate f.

Hope this helps!

I need help ASAP!

List the fractions and decimals in order least to greatest.

Question1. 2.3 , 2 4/5 , 2.6

Question 2. 0.5 , 3/16 , 0.75 , 5/48


Who ever helped me thank you :D

Answers

Answer:

Q1: 2.3, 2.6, 2 4/5

Q2: 5/48, 3/16, 0.5, 0.75

Step-by-step explanation:

that should be correct sorry if im wrong

Answer: The answer is already completed

Step-by-step explanation:

is Catholic Schools bad?​

Answers

Answer:

Not really。。

Step-by-step explanation:

this school had remained excellent。students grduating from these school have higher ACT scores

25. Kendra owns a toy store. She charges $8.00 for two puzzles and a piece of candy. She charges (1 poi
$4.50 for one puzzle and a piece of candy. How much does each puzzle cost?
O $3.50
O $4.50
O $1.00
$2.25

Answers

Given:

Kendra charges $8.00 for two puzzles and a piece of candy.

She charges $4.50 for one puzzle and a piece of candy.

To find:

The cost of each puzzle.

Solution:

Let x be the cost of a puzzle and y be the cost of piece of candy.

Kendra charges $8.00 for two puzzles and a piece of candy.

[tex]2x+y=8[/tex]               ...(i)

She charges $4.50 for one puzzle and a piece of candy.

[tex]x+y=4.50[/tex]             ...(ii)

Subtracting (ii) from (i), we get

[tex]2x+y-(x+y)=8-4.50[/tex]

[tex]2x+y-x-y=3.50[/tex]

[tex]x=3.50[/tex]

The cost of puzzle is $3.50. Therefore, the correct option is A.

The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer. What is the probability that the sample mean would differ from the true mean by more than 1.1 dollars if a sample of 38 5-gallon pails is randomly selected? Round your answer to four decimal places.

Answers

Answer:

Probability[(X - μ) < 1.1] = 0.6046

Step-by-step explanation:

Given:

σ² = 64

Mean μ = 34

Find:

Probability[(X - μ) < 1.1]

Computation:

Standard deviation σ = √σ²

Standard deviation σ = √64

Standard deviation σ = 8

Probability[(X - μ) < 1.1] = Probability[-1.1 < (X - μ) < 1.1]

Probability[(X - μ) < 1.1] = Probability[-1.1/(8/√38) < (X - μ) < 1.1/(8/√38)]

Using z table

Probability[(X - μ) < 1.1] = 0.6046

Find the TWO integers whos product is -12 and whose sum is 1

Answers

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Answer:

Step-by-step explanation:

If the product of 2 integers is -12, then that equation looks like this:

xy = -12

If the sum of those same 2 integers in 1, then that equation looks like this:

x + y = 1

Let's solve the second equation for x and plug it into the first equation. Solving the second equation for x gives us

x = 1 - y and plug that into the first equation in place of x to get:

(1 - y)y = -12 and

[tex]y-y^2=-12[/tex] Now move everything over to one side and factor to find y:

[tex]-y^2+y+12=0[/tex] and the 2 values for y are

y = -3 and y = 4. Let's see what happens when we solve for x.

If xy = -12 and y is -3:

x(-3) = -12 so

x = 4

If xy = -12 and y is4:

x(4) = -12 so

x = -3

So it looks like the 2 integers are -3 and 4

Write in the form a to the power of k, where a is a prime number and k is rational
[tex]\sqrt[4]{27}[/tex]

Answers

The answer is 3 to the 3/4 power.

Multiply the following rational expressions and simplify the result

Answers

Answer:

Step-by-step explanation:

We have to solve the given expression,

[tex]\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}[/tex]

[tex]\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}[/tex] = [tex]\frac{-y(-9+33y+3y^3)}{100-49y^2}.\frac{7y^2+17y+10}{14y(y+2)}[/tex]

                                   = [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{7y^2+10y+7y+10}{14y(y+2)}[/tex]

                                   = [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{y(7y+10)+1(7y+10)}{14y(y+2)}[/tex]

                                   = [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{(y+1)(7y+10)}{14y(y+2)}[/tex]

                                   = [tex]\frac{-3y(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14y(y+2)}[/tex]

                                   = [tex]\frac{-3(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14(y+2)}[/tex]

                                   = [tex]\frac{3(3-11y-y^3)(y+1)}{(10-7y)(14(y+2)}[/tex]

A farmer wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $4 a yard, but the farmer needs to use special fencing which cost $5 a yard on the south side of a plot. If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing.

Answers

Hello,

Let's assume x the length of the north's wall

and y the length of west side .

Area:x*y=600  ==> y=600/x

Cost: 2*y*4+5*x=8y+5x= 4800/x+5x

Minimize cost: (4800/x+5x)'=0

-4800/x²+5=0

x²=4800/5

x²=960

[tex]x=8\sqrt{15} \\\\y=5\sqrt{15} \\[/tex]

How many years will it take $2,000 to grow to $3,300 if it is invested at 4.75% compounded​ continuously?

Answers

Answer:

10.54263764

Step-by-step explanation:

[tex]3300=2000e^{.0475t}\\\\1.65=e^{.0475t}\\\ln(1.65)=.0475t\\.500775288=.0475t\\t=10.54263764[/tex]

Answer:

It will take about 10.5 years for the investment to reach $3,300.

Step-by-step explanation:

Continuous compound is given by:

[tex]\displaystyle A=Pe^{rt}[/tex]

Where P is the principal, e is Euler's number, r is the rate, and t is the time (in this case in years).

Since our principal is $2,000 at a rate of 4.75% or 0.0475, our equation is:

[tex]\displaystyle A=2000e^{0.0475t}[/tex]

We want to find the number of years it will take for our investment to reach $3,300. So, substitute 3300 for A and solve for t:

[tex]3300=2000e^{0.0475t}[/tex]

Divide both sides by 2000:

[tex]\displaystyle e^{0.0475t}=\frac{33}{20}[/tex]

We can take the natural log of both sides:

[tex]\displaystyle 0.0475t=\ln\left(\frac{33}{20}\right)[/tex]

Therefore:

[tex]\displaystyle t=\frac{1}{0.0475}\ln\left(\frac{33}{20}\right)\approx 10.54\text{ years}[/tex]

It will take about 10.5 years for the investment to reach $3,300.

What is the midpoint of the segment with endpoints(-4, -
2) and (2, 6)?

Answers

Answer:

(-1,2)

Step-by-step explanation:

hope you find this useful!

https://ncalculators.com/geometry/mid-points-calculator.htm

Be sure to show your work and solve for h:
6 + h + 8 = 24

Answers

Answer:

10

Step-by-step explanation:

6 + h + 8 = 24

h + 6 + 8 = 24

h + 14 = 24

h = 24 - 14

h = 10

An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, and 50.06. Calculate the sample mean and sample standard deviation.

Answers

Answer:

Mean = 43.969

Standard deviation = 12.341

Step-by-step explanation:

Given the data :

36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, 50.06

The sample mean :

Σx / n = 351.75 / 8 = 43.969

Sample standard deviation :

√Σ(x - mean)²/n-1

√[(36.45-43.969)² + (67.90-43.969)² + (38.77-43.969)² + (42.18-43.969)² + (26.72-43.969)² + (50.77-43.969)² + (38.9-43.969)² + (50.06-43.969)² ] / ((8 - 1)

Standard deviation = 12.341

(-6)^-1 multiply by x = 27^-1. find x

Answers

i’m guessing the question is written as (-6)^-1x=27^-1

to get rid of a negative exponent, you use the reciprocal of the number.

so (-6)^-1 would be 1/-6
27^-1 would be 1/27

rewrite is as

(1/-6)x = 1/27

multiply both sides by reciprocal or 1/-6 to cancel it and make x by itself

it’s would be x = 1/27(-6)

multiply

x = -6/27

simplify

the final answer is x=-2/9

Find the first five terms of the sequence described.

Answers

Answer:

I dont think i dont know this but its 10?

Find the slope of the line that passes through (6, 4) and (4, 1).

Answers

Answer:

[tex]1.5[/tex]

Step-by-step explanation:

[tex](6 \: \: \: \: \: 4)(4 \: \: \: \: \: 1) \\ m = \frac{y1 - y2}{x1 - x2} \\ = \frac{4 - 1}{6 - 2} \\ = \frac{3}{2} \\ = 1.5[/tex]

hope this helps you.

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