Over the interval [0, 2), what are the solutions to sin(2x) = 2cos(x)? Check all that apply,

Answers

Answer 1

Answer:

pi/2 and 3pi/2

Step-by-step explanation:

on edge

Answer 2

The required solutions to sin(2x) = 2cos(x) are the following as :  [tex]\:x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].

What are Trigonometric functions?

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The equation of trigonometry functions is given in the question:

sin(2x) = 2cos(x)

We have to determine the solution to the given trigonometry equation

As per the question, we have

⇒ sin(2x) = 2cos(x)

Rewrite the above trigonometry equation,

⇒ sin(2x) - 2cos(x) = 0

⇒ 2sin(x)cos(x) - 2cos(x) = 0

Common factor out from the equation,

⇒ 2cos(x)[sin(x) - 1] = 0

Solving each part separately

2cos(x) = 0 and sin(x) - 1 = 0

cos(x) = 0 and sin(x) = 1

[tex]\:x=\frac{\pi }{2}+2\pi n, and \:x=\frac{3\pi }{2}+2\pi n[/tex].

Thus, the required solutions to sin(2x) = 2cos(x) are the following:  [tex]\:x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].

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Related Questions

A square has a perimeter of 72 cm what is the length of each side

Answers

Answer:

each side is 12 cm

Step-by-step explanation:

This is a simple equation, since a square is equal an all 4 sides, all you have to do it divide 72 by 4 to get your answer.

May I have brainliest please? :)

2. What is the place value of the 5 in 3562? ​

Answers

Answer:

Hundreds Place

Step-by-step explanation:

The 5 is in the hundreds place.

Hope this helps :D

3 is the thousands place

5 is the hundreds place

6 is the tens place

2 is the ones place

You tell me the answer.

Which ordered pair would form a proportional relationship with the point graphed below?

(10.-20)
(-30, 20)
(-10,5)
(35, -20

Answers

The third option but can also be the first option, The would proportionate properly.

Consider the equation 1.5x+4.5y=18. Where does the graph intersect the y-axis? *

Answers

Answer:

intersect y axis at  (0,4)

Step-by-step explanation:

lemme know if u need work

Jen paid 26 cents for a mini bag of candy.She bought 4 bags of candy for herself and a friend.How much will she pay for the candy?

Answers

Answer: 1.04 I think

Step-by-step explanation:

Answer:

1.04

Step-by-step explanation:

26x4=104 and I put the decimal point in.

HELP I GIVE BRAINLIEST

Answers

Answer:

The answer is 15/19

Step-by-step explanation:

Both 60 and 76 are divisible by 4:

60/4 = 15 and 76/4 = 19

Final answer; 15/19

On a map , 1 inch represents 10 feet . How many inches would represent 35 feet .

Answers

Answer:

3 and a half inches or 3.50 inches

Step-by-step explanation:

if ten feet is 1 inch 30 feet would be 3 inches, 5 feet would make a half a inch since 10 feets divided by 2 is 5. one inch divided by 2 is 0.50 inches (or a half)

there for the answer is 3 and a half inches

because 1 inch represents 10 feet, that would equal to 3 inches, and then half of an inch 3.5 inches

y-4=-x+7 in standard form.​

Answers

Answer:

Step-by-step explanation:

x + y = 11

Geometry please help!!!!!!!?

Answers

It’s 8 because YX = 8 and VW is the same length as YX. So VW=8

Answer:

It is same as the length of YX =8 inches so the length of VW=8 inches

Question 1 (1 point)
(05.01)
The graph of a system of equations will intersect at more than 1 point. (1 point)

a
Always

b
Sometimes

c
Never

Answers

Answer: Sometimes

Step-by-step explanation:

A system of equations can intersect at no points; this is when the lines are parallel, which means they have the same slope and different y-intercept.

A system of equations can intersect at one point; this is when the lines have different slopes.

A system of equations can intersect in infinitely many points; this is when the graphs overlay one another, which means they are graphs of the same line.  The two equations would equal the same thing.

Sometimes is the answer

Do you guys know this.

Answers

Answer:

0.77

Step-by-step explanation:

You solve the inner first, then move to the outer.

Plug in x = 20 for g(x) = [tex]\frac{2x+2}{x-6}[/tex]. It should give you [tex]\frac{42}{14}[/tex], which simplifies to 3.

You then need to solve f(x) with the given value from g(x), which is 3.

Plug in x = 3 for the equation [tex]\sqrt{0.4x^2-x}[/tex], and you should get [tex]\sqrt{0.6}[/tex].

The answer is roughly 0.77.

A radius of 8.5m what is the area

Answers

Answer:

22/7 * 8.5 * 8.5 = answer

Answer:

Step-by-step explanation:

A = π r² ≈ 3.14 × (8.5)² = 226.865 m²

Solve the formula 5x + 2y = 19 for y

Answers

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[tex]5x + 2y = 19[/tex]

Subtract sides 5x

[tex] - 5x + 5x + 2y = - 5x + 19[/tex]

[tex]2y = - 5x + 19[/tex]

Divide sides by 2

[tex] \frac{2y}{2} = \frac{ - 5x + 19}{2} \\ [/tex]

[tex]y = \frac{ - 5x}{2} + \frac{19}{2} \\ [/tex]

[tex]y = - \frac{5}{2} x + \frac{19}{2} \\ [/tex]

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The solution of the equation 5x + 2y = 19 for the value of y is y = (-5 / 2)x + ( 19 / 2).

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression is 5x + 2y = 19. The value of y will be calculated as:-

5x + 2y = 19

2y = 19 - 5x

y = ( 19 / 2 ) - ( 5x / 2 )

Therefore,  the solution of the equation 5x + 2y = 19 for the value of y is y = (-5 / 2)x + ( 19 / 2).

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What number divided by−3 gives 12 as the result?
​​

Answers

Answer:

-36

Step-by-step explanation:

x / (-3) = 12

x = 12*(-3)

x = -36

rationalise the denominator and simplify

Answers

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Step-by-step explanation:

[tex] \bf \underline{Given-} \\ [/tex]

[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ [/tex]

[tex] \bf \underline{What\: to\: do-} \\ [/tex]

To rationalise the denominator

[tex] \bf \underline{Solution-} \\ [/tex]

[tex]\textsf{We have,}[/tex]

[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ [/tex]

[tex]\textsf{The denominator is 5+2√3. Multiplying the numerator and denominator by 7-4√3,}\\[/tex]

[tex]\textsf{we get,}\\[/tex]

[tex] ⟹\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ [/tex]

[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3}) } \\ \\ [/tex]

[tex]\textsf{⬤ Applying Algebraic Identity

(a+b)(a-b) = a² - b² to the denominator}\\[/tex]

[tex]\textsf{We get,}\\[/tex]

[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 {)}^{2} - (4 \sqrt{3} {)}^{2} } \\ \\ [/tex]

[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 8 \sqrt{3 \times 3} }{49 - 48} \\ \\ [/tex]

[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 24 }{1} \\ \\ [/tex]

[tex]⟹(35 - 24) - 6 \sqrt{3} \\ \\ [/tex]

[tex]⟹11 - 6 \sqrt{3} \: \: \: \tt \red{ Ans}. \\ \\ [/tex]

[tex] \bf \underline{Hence \:the \:denominator\: is\: rationalised.}\\[/tex]

For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a mean score of 500 with a standard deviation of 100. Assume that the SAT scores are normally distributed. What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be
(a) more than 675?
b) between 450 and 675?

Answers

Answer:

The probability that a randomly selected high school senior's score on mathematics part of SAT will be

(a) more than 675 is 0.0401

(b)between 450 and 675 is 0.6514

Step-by-step explanation:

Mean of Sat =[tex]\mu = 500[/tex]

Standard deviation = [tex]\sigma = 100[/tex]

We will use z score over here

 What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be

(a) more than 675?

P(X>675)

[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}[/tex]

Z=1.75

P(X>675)=1-P(X<675)=1-0.9599=0.0401

b)between 450 and 675?

P(450<X<675)

At x = 675

[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}[/tex]

Z=1.75

At x = 450

[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{450-500}{100}[/tex]

Z=-0.5

P(450<X<675)=0.9599-0.3085=0.6514

Hence the probability that a randomly selected high school senior's score on mathematics part of SAT will be

(a) more than 675 is 0.0401

(b)between 450 and 675 is 0.6514

Margaret is making strawberry milkshakes for the kids party. The recipe calls for 1/3 of a cup of strawberry syrup to make 8 milkshakes. How many cups of Strawberry syrup are needed to make 48 milkshakes?
A.) 3
B.)2
C.)16
D.) 8

Answers

Answer:

B. The answer is 2 cups.

12‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $20per foot, and the fencing for the east and west sides costs $10 per foot. If I have a budget of $200 for the project, what are the dimensions of the garden with the largest area I can enclose? HINT [See Example 2.]
ft (smaller value) ? ft (larger value)
ft2

Answers

Answer:

Length = [tex]5\ \text{ft}[/tex]

Breadth = [tex]5\ \text{ft}[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the length of the garden

and [tex]y[/tex] be the width of the garden

From the details of the cost in the question we get

[tex]20x+2\times (10y)=200\\\Rightarrow 20x+20y=200\\\Rightarrow x+y=\dfrac{200}{20}\\\Rightarrow x+y=10\\\Rightarrow y=10-x[/tex]

Now area of the garden is

[tex]A=xy\\\Rightarrow A=x(10-x)\\\Rightarrow A=10x-x^2[/tex]

Differentiating with respect to x we get

[tex]\dfrac{dA}{dx}=10-2x[/tex]

Equating with 0

[tex]0=10-2x\\\Rightarrow x=\dfrac{-10}{-2}\\\Rightarrow x=5[/tex]

Double derivative of the area is

[tex]\dfrac{d^2A}{dx^2}=-2<0[/tex]

So, area is maximum at [tex]x=5[/tex]

[tex]y=10-x=10-5\\\Rightarrow y=5[/tex]

So, the length and breadth of the rectangle is [tex]5\ \text{ft}[/tex].

A recipe uses 150g butter, 500g sugar, and 100g currants to make 18 small cakes?
a. how many of each ingredient will be needed to make 6 dozen cakes
b. how many whole cakes could be made with 1kg of butter

Answers

Answer:

a. The following will be needed to make 6 dozen cakes:

Number of grams of butter needed = 600g

Number of grams of sugar needed = 2,000g

Number of grams of currants needed = 400g

b. The number whole that cakes could be made with 1kg of butter is still 18 whole cakes.

Step-by-step explanation:

a. how many of each ingredient will be needed to make 6 dozen cakes

This can be calculated as follows:

One dozen = 12

Number of small cakes in 6 dozen cakes = 6 * 12 = 72 small cakes

Number of 18 small cakes that can be obtained from 72 small cakes = 72 / 18 = 4

Therefore, we multiply each ingredient by 4 to obtain the number oof each ingredient that will be needed to make 6 dozen cakes as follows:

Number of grams of butter needed = 150 * 4 = 600g

Number of grams of sugar needed = 500 * 4 = 2,000g

Number of grams of currants needed = 100 * 4 = 400g

b. how many whole cakes could be made with 1kg of butter

Ordinary in terms of measurement, we have:

1kg = 1,000g

Since it is not indicated in the question that additional grams of other ingredients are made available, only 150g butter will be used out of the 1,000g butter made available together with already available 500g sugar and 100g currants to make just 18 cakes. This implies that no additional whole cakes will be made to add to the current 18 small cakes that is being made. Additional whole cakes would only be made when additional grants of sugar and currants are made available.

Therefore, the number whole that cakes could be made with 1kg of butter is still 18 small cakes.

evaluate 103 × 97 without directly multiplying​

Answers

Answer:

9991

Step-by-step explanation:

103 × 97

(100 +3) (50+47)

get two number which you can add to get the value in the question

n then expand

100(50+47) +3(50+47)

5000+4700+150+141

9991

Sierra, an Event Planner for Hilton, has group medical insurance with an annual premium of $8,245. Her employer pays 74%. If she is paid semi monthly, a) what is her portion of the annual premium? b) her medical insurance deduction per pay period?

Answers

9514 1404 393

Answer:

$2,143.70$89.32

Step-by-step explanation:

If 74% is paid by Hilton, then Sierra pays 26% of $8245 per year. Her annual share is ...

  0.26 × $8245 = $2143.70 . . . Sierra's share

__

Then the deduction in each of her 24 pay periods is ...

  $2143.70/24 = $89.32 . . . per pay period

Samir usually drink 3 cups of coffee in the morning how many liters of coffee does he drink round

Answers

Answer:

0.709765 liters

Step-by-step explanation:

A garden is in the shape of a rectangle 90 m by 60 m.
Flowers are grown in 40% of the garden.
The rest of the garden is grass.
Work out the area of the garden that is grass.

Answers

Answer:

3240 sq meters

Step-by-step explanation:

Area of garden = 90*60= 5400 square meters.

Flowers grown on = 40%

So, grass grown on = (100 -40)% = 60%

60% of 5400 = 0.6*5400 = 3,240.

So, the area of the garden that is grass = 3,240 square meters

3,240 meters

The area is 90*60m which is 5,400m.

60% of the garden is grass (1-0.4=.6)

60% of 5,400 = 3,240 meters

Is 4/10 closer to 0, 1, 1/2

Answers

Answer:

1/2

Step-by-step explanation:

Divide the denominator in half

10/2 = 5

4 is close to 5 so 4/10 is close to 1/2

Answer:

4/10 is closer to 1/2.

Think of a pie. There are 10 slices total, but only 4 slices remain, because I ate them all! Do you think that 4 out of 10 slices would be closer to a whole pie or half a pie? It would be closer half a pie.

Further explanation:

If you were to round the number 44 to the closest ten, it would be 40. If you were to round 47 to he nearest ten, it would be 50. If you were to round 45 to the nearest ten, it would also be 50. I hope this helps!

Half (1/2) is the answer.

HURRY!! At the snack bar, hot dogs cost $4 each and bottled water costs $2 each:

Answers

Answer: (2,1) (1,3)

Step-by-step explanation: Assume that the number of hot dogs is X and the number of water bottles is y.

Rewrite −x−6 with a positive exponent. Assume x is not equal to zero.

Answers

Answer:

= -1/x^6

Explanation:

Using the concept negative rule of exponents.

-x^-6 = -1/x^6

Question 2 options: A consumer advocate group selects a random sample of 205 snack foods and finds that 174 of them contain more fat grams than what is indicated in the snack's nutritional information. Create a 90% confidence interval for the population proportion for snack foods that contain more fat grams that what is indicated in the snack's nutritional information.

Answers

Answer:

156 snack foods.

Step-by-step explanation:

205 - 174 = 31

To find 90% of 174, multiply 174 by 0.90.

174 x 0.90 = 156

The answer is 156 snack foods.

Mr. Jones got four seats on the school's trip to Grand
Canyon for his students. In how many different ways Mr.
Jones can select a group of four from his class of 36?

Answers

Answer:

D. 58,905

Step-by-step explanation:

Number of seats available for Mr. Jones had for the trip = 4

Number of students in his class = 36

Number of ways he can select a group of 4 out of 36 students from his class is calculated as follows:

[tex] C \binom{36}{4} = \frac{36!}{(36 - 4)! * 4!)} [/tex]

[tex] = \frac{36!}{(32! * 4!)} = 58,905 [/tex]

find the slope and the y-intercept of 7x = 2y-4

Answers

Answer:

Slope: [tex]\frac{7}{2}[/tex]

Y-intercept: (0, 2)

Step-by-step explanation:

7x = 2y - 4

-2y = -7x - 4

y = [tex]\frac{-7}{-2}[/tex] x - [tex]\frac{4}{-2}[/tex]

y = [tex]\frac{7}{2}[/tex] x + 2

The slope is always the coefficient of x and the y-intercept is always the constant. It looks like (0, constant) when written in y-int form.

Answer:

slope (m) is 7/2 (aka 3.5) and y-int is (0,2)

Step-by-step explanation:

I don't really have an explanation, basically rearrange the problem so that to y is on the left but it would be 2y so divide the right side by two. I an explain further in depth if needed

archilles ordered a pizza with 16 slices every hour he ate half of the remaining slice

Answers

Answer:

so there is 8 slice left

Step-by-step explanation:

Other Questions
There are several different models that represent compounds. One type of model is shown.A large black sphere connected to 4 small blue spheres by 4 grey sticks. What type of model is shown?a structural formulaa chemical formulaa space-filling modela ball-and-stick model PLEASE HELP ME ??!!!!! Help pleaseeeeeeeeeeewe HELP ME PLZZ I NEED HELP WITH THIS!! Read the paragraph.I have been a nurse for twenty years. In that time, I have seen a great number of patients suffer because they did not have health insurance. One of the worst cases was a young mother of two who was diagnosed with early stage skin cancer. Because she could not afford treatment, the cancer spread from her skin to other parts of her body. By the time I saw her for the first time, the cancer had reached her brain, and she could no longer be helped. This sort of thing should not happen to anyone. A strong universal health care system could prevent instances like this from occurring.Which rhetorical appeal is used in the text, One of the worst cases was a young mother of two who was diagnosed with early stage skin cancer?logos, an appeal based on logicethos, an appeal based on the authors characterpathos, an appeal based on emotionno rhetorical appeal is used Consider this equation.7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)Mia solved the equation and determined that m = 2. Is she correct? Select the correct text in the passage.Read the excerpt from The Story of My Life by Helen Keller. Choose the text that describes Helens perspective of being touched.At first, when my teacher told me about a new thing I asked very few questions. My ideas were vague, and my vocabulary was inadequate; but as my knowledge of things grew, and I learned more and more words, my field of inquiry broadened, and I would return again and again to the same subject, eager for further information. Sometimes a new word revived an image that some earlier experience had engraved on my brain.I remember the morning that I first asked the meaning of the word, "love." This was before I knew many words. I had found a few early violets in the garden and brought them to my teacher. She tried to kiss me: but at that time I did not like to have any one kiss me except my mother. Miss Sullivan put her arm gently round me and spelled into my hand, "I love Helen."A: At first, when my teacher told me about a new thing I asked very few questionsB: I learned more and more words, my field of inquiry broadened, and I would return again and again to the same subject,C: I remember the morning that I first asked the meaning of the word, "love."D: She tried to kiss me: but at that time I did not like to have any one kiss me except my mother. Solve the equation y = ax b for the variable x. Solve this equation.23x15x=x1 short note on where do we use electronics in daily life Members of the Assembly of New York serve ____-year terms. I need some help with this The area of a circle is 36 [tex]\pi[/tex]cm?.What is the radius of this circle? Which angles are corresponding angles? why are correctional officers held to high standard of ethics according to this segment ? How important is the setting to the story? - The story's characters can only be found in one place around the world. - The same story could be told anywhere in the world. - India's geography is the only place where rhinoceroses live in the world. - India, as a country, gives the story distinctiveness that is at the heart of the story. (The Most Dangerous Game): Rainsford struggles with an internal conflict while he is in the jungle. Rainsford versus ____A. religious aspirationsB. A hopeful futureC. Self sufficiencyD. Hunting as a sport With more than 33 species, more species of bats live in Texas than anywhere else in the United States. If Texas contains fewer than 3% of the species of bats in the world, how many species of bats are there worldwide? what the slope of (15,9) (-10,3) 6. They were like two peas in a pod.Simile or Metaphor?