Trigonometric Equations

Solve the equation over the interval [0°, 360°)

cos(theta) = -1/2

Answers

Answer 1

Answer:

[tex]\frac{2\pi }{3};\frac{4\pi }{3}.[/tex]

Step-by-step explanation:

1) cos(θ)=-0.5;

theta=±2π/3+2πn, where n∈Z;

2) if θ∈[0;360], then

[tex]\theta=\frac{2\pi }{3}; \frac{4\pi }{3}.[/tex]


Related Questions


Can someone solve this question to me.i will mark brainliest. :)

Answers

Answer:

Parent Function:  [tex]y=\sqrt{x}[/tex]Horizontal shift: right 3 unitsVertical shift: up 3 unitsReflection about the x-axis: noneVertical strech: streched

Step-by-step explanation:

assume that [tex]y=\sqrt{x}[/tex] is [tex]f(x)=\sqrt{x}[/tex] and [tex]y=\sqrt{-2x+6}+3[/tex] is

[tex]g(x)=\sqrt{-2x+6}+3\\ f(x)=\sqrt{x} \\g(x)=\sqrt{-2x+6}+3[/tex]

The transformation from the first equation to the second equation can be found by finding a,h and k for each equation.

[tex]y=a\sqrt{x-h}+k[/tex]

factor a 1 out of the absolute value to make the coefficient of x equal to 1

[tex]y=\sqrt{x}[/tex]

factor a 2 out of the absolute value to make the coefficient of x equal to 1

[tex]y=\sqrt{2}\sqrt{x-3}+3[/tex]

find a, h and k for [tex]y=\sqrt{2}\sqrt{x-3}+3[/tex]

[tex]a=1.41421356\\ h=3\\k=3[/tex]

the horizontal shift depends on the value of h when [tex]h > 0[/tex], the horizontal shift is described as:

[tex]g(x)=f(x+h)[/tex] - the graph is shifted to the left h units

[tex]g(x)=f(x-h)\\[/tex] - the graph is shifted to the right h units

the vertical shift depends on the value of k

What is the factorization of the trinomial below?

-x^2 - 2x + 48

A. -1(x - 8)(x + 6)

B. -1(x + 8)(x - 6)

C. (x + 6)(x - 8)

D. (x - 6)(x + 8)

Answers

Answer:

The answer to this question is A

"The sum of a number and 20 is multiplied by 6 and the result is 26."

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Consider the number as x

let's solve ~

[tex]\qquad \sf  \dashrightarrow \:6(x + 20) = 26[/tex]

[tex]\qquad \sf  \dashrightarrow \:6x + 120 = 26[/tex]

[tex]\qquad \sf  \dashrightarrow \:6x = - 120 + 26[/tex]

[tex]\qquad \sf  \dashrightarrow \:6x = -94[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = - 94 \div 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{ - 47}{3} [/tex]

・ .━━━━━━━†━━━━━━━━━.・

Answer:

[tex](x + 20) 6 = 26[/tex]

[tex]6x + 120 = 26[/tex]

[tex]6x = 26 - 120[/tex]

[tex]6x = - 94[/tex]

[tex] \displaystyle \: x = \frac{ - 94}{6} [/tex]

[tex] \displaystyle{x = \frac{ - 47}{3} }[/tex]

[tex]\red {\rule{35pt}{2pt}} \green{ \rule{35pt}{2pt}}\orange{ \rule{35pt}{2pt}}\pink{ \rule{35pt}{2pt}}\blue{ \rule{35pt}{2pt}}\purple{ \rule{35pt}{2pt}}\red{ \rule{35pt}{2pt}}[/tex]

[tex] \bold{ \displaystyle{x = - \frac{47}{3} }}[/tex]

i really need help with this question i received a wrong answer i don't have as many points to spend this time if you want 50 points you can go to my previous question to answer there if you want

Answers

Answer:

Step-by-step explanation:

let the eq. be

y=a(x-2)(x-4)+b

x=0,y=-2

-2=a(0-2)(0-4)+b

-2=8a+b

when x=6,y=-2

-2=a(6-2)(6-4)+b

-2=8a+b

when x=8,y=-6

-6=a(8-2)(8-4)+b

-6=24a+b

16a=-4

a=-1/4

-2=-2+b

b=0

y=-1/4(x-2)(x-4)

y=-1/4(x^2-6x+8)

y=-1/4x^2+3/2x -2

when x=1

y=-1/4(1-2)(1-4)

y=-3/4

Find the volume of the prism.

Answers

Answer:

I'm guessing it is 12000

Step-by-step explanation:

let me now if it is wrong

[tex] \Large\tt{ANSWER}[/tex]

[tex]\LARGE \tt{12000 \: cm^3 }[/tex]

[tex]\Large \tt{SOLUTION}[/tex]

Formula of Rectangular Prism

Volume = Length × Width × Height

Volume = Length × Width × HeightVolume = 60 cm ×20 cm × 10 cm[tex]\Large \tt{12000 \: cm^3 }[/tex]

For More Information, Visit this Link.

→ What is Volume:

brainly.ph/question/6286323

Tom and Blair live the same
distance from their school.
Marcia lives 2 blocks from the
school, but 7 blocks from Blair.
She lives 1 block closer to the
school than she does to Tom.
They all live on the same street
as the school. How far apart do
Tom and Blair live?

Answers

Answer:

Step-by-step explanation:

We can think of this problem like a triangle that Tom, Blair, and Marcia live in.

This triangle is a right triangle.

the opposite is 3, the hypotenuse is 7, and the adjacent side is unknown.

Solving for the adjacent side will give us the distance that Tom and Blair live from each other

a^2 +b^2 = c^2

3^2 + b^2= 7^2

Now we solve for B

7^2 =49

3^3=9

9+b^2=49

Now we subtract

49-9=40

9+40=49

The square root of 40 is 6.3246

Now we check our work

3^2 +6.32^2=7^2

9+ 40 =49

The answer is, tom and Blair live approximately 6.3246 blocks from each other

Hope this helps!

please answer this question​

Answers

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Before answering the given question, you should know the difference between polygon and regular polygon.

Polygon :- It is closed figure constitute of straight line having different measurements and also having varies angles. Regular polygon :- It is also a closed figure constitute of straight lines which having equal measuresment and all the angles of the given polygon are equal .

There are different types of polygon based on the sides :-

A polygon having 3 sided called triangle ,having 4 sides called quadrilateral ,having 5 sides pentagon and so on.

Let's Begin :-

I have thought to make a 4 side polygon that is quadrilateral.

Steps of construction :-

Step - 1 :- Draw a 5 cm line AB horizontally Step - 2 :- Then , From a point B, Draw a Vertical line of 5 cm and named it BC Step - 3 :- Then, From a point C, Draw a horizontal line of 5 cm and named it CD Step - 4 :- Now, join the line AD Step - 5 :- Measure all the angles form by the 4 sides of the quadrilateral.

Result :- All the angles are equal that is 90° each.

Conclusion :- The above figure is square as it is having equal sides and angles.

Now, we have to find the sum of the angles of the polygon :-

Here,

All angles are equal in measure 90°

Therefore,

The sum of the angles of the given polygon

[tex]\sf{ = 90{\degree} + 90{\degree} + 90{\degree} + 90{\degree} }[/tex]

[tex]\sf{ = 180{\degree} + 90{\degree} + 90{\degree} }[/tex]

[tex]\sf{ = 270{\degree} + 90{\degree} }[/tex]

[tex]\sf{ = 360{\degree} }[/tex]

Hence, The sum of the angles of the above polygon is 360° .

i need help please its due today

Answers

It would be 11/15 (11 over 15)


On a recent math assignment consisting of 32 problems, Wendy had 5 application problems, and the
rest involved only computation. What percent of the problems were only computation?

Answers

Answer:

84.375%

Step-by-step explanation:

Total no. of computation problem=32-5=27

Total no. problems in the assignment=32

=) per%= 27/32×100%=84.375%

PLS MARK ME AS BRAINLIEST

what is the definition of an average?

Answers

-------------------------------------------------------------------------------------------------------------

Answer:

Average: a calculated "central" value of a set of numbers

-------------------------------------------------------------------------------------------------------------

How to find it in the average:

Add all of the numbers given, then divide by the number of digits.

-------------------------------------------------------------------------------------------------------------

Example:

Question 1. ) Find the average of the digits.

10, 12, 7, 9, 14, 8, 5, 19

Step 1. Add all of the numbers - 70

Step 2. Count how many different numbers there are - 8

Step 3. Take your first answer and your second and divide them

Step 4. 70 ÷ 8 = 8.75 So 8.75 would be the average

-------------------------------------------------------------------------------------------------------------

a number expressing the central or typical value in a set of data, in particular the mode, median

The Greyhound bus going to Michigan leaves the station every 20 minutes. Another bus going to Arkansas leaves the station every 40 minutes. If it is 10:40 a.m., what will be the first time both Greyhound buses leave the station at the same time?

Answers

The Greyhound bus going to Michigan leaves the station every 20 minutes.

it's 10:40

so next departure on 10:60 => 11:00 then 11:20 then 11:40...

Another bus going to Arkansas leaves the station every 40 minutes.

it is 10:40

so next departure on 11:20 then 12:00

=> 11:20

Natalie has 112 boxes she left 105 five boxes and she found 20 boxes how much dose she have?

Answers

Answer:

27 boxes.

Step-by-step explanation:

This situation can be represented by the equation:

(112 - 105) + 20 = ?

First we subtract 105 from 112:

112 - 105= 7

Now add 20.

7 + 20 = 27

Natalie has 27 boxes now.

If y varies inversely as x, and y=16 when x=4, find y when x=10

Answers

Answer:

40

Step-by-step explanation:

you have to multiply x by 4 to get y when x=4 and y=16. so if x=10, then you have to multiply what x is (10) by 4 because there is a common ratio.

hope this helps!! please give brainliest!!!!!!

Graham carves a block of wood shaped like a cube with a square pyramid on top. How much paint will Graham need to paint the toy? Enter your answer in the box.

Answers

Divide the box into two parts for easy way answer

For cube:-

Side=a=12cm

TSA

6a²6(12)²6(144)864cm^2

Cancel one side area

TSA=864-144=720cm^2

For triangular pyramid:-

Area of one base

0.5(Base)(Height)0.5(12)(15)6(15)90cm^2

Area of four sides=90(4)=360cm^2

Total surface area:-

720+3601080cm^2

Answer:

1080 cm^2

Step-by-step explanation:

∴ Given:

Graham carves a block of wood shaped like a cube with a square pyramid on top.

∴To Find:

How much paint will Graham need to paint the toy?

∴Solve:

Base on the given:

[tex]S=5a^2+4ah\cdot\frac{1}{2}[/tex]

= [tex]5\cdot12^2+4\cdot12\cdot15\cdot\frac{1}{2}[/tex]

[tex]=1080cm^2[/tex]

Hence [tex]1080cm^2[/tex] of paint is needed.

~lenvy~

Which equation does not represent a quadratic function?

Y = (x + 3)^2

y = 3x^2

y = 6x^2 - 1

y = x + 5

Answers

[tex]\text{A quadratic function is in the form of } ~ f(x)=ax^2 +bx+c.\\\\\\y=x+5 ~ \text{is linear so it is not in a form of quadratic function.}[/tex]

Darron wants to send a package to his mother for her birthday. At Box-r-us, they have boxes that come in three different lengths, four different widths and five different heights. At ship to go they have have boxes that comes in six different lengths two different widths and seven different heights. The number of boxes that box r us has is ——— ship to go

Answers

Answer:

less than

Step-by-step explanation:

At Box-r-us, they have 3*4*5=60 different boxes.

At Ship to go they have 6*2*7=84 different boxes

Therefore the number of boxes that box r us has is less than the number of boxes that Ship to go has.

A thief steals an atm card and must randomly guess the correct five-digit pin code from a 8​-key keypad. repetition of digits is allowed. what is the probability of a correct guess on the first​ try?

Answers

Answer:

The probability of a correct guess on the first try is 0.024%.

Since a thief steals an atm card and must randomly guess the correct four -digit pin code from a 8 -key keypad, and repetition of digits is allowed, to determine what is the probability of a correct guess on the first try the following calculation must be performed:

8 x 8 x 8 x 8 = X

8 ^ 4 = X

4096 = X

1/4096 = X

0.000244140625 = X

0.000244140625 x 100 = 0.024%

Therefore, the probability of a correct guess on the first try is 0.024%

Step-by-step explanation:

I need help with this question!

Answers

Answer:

B

Step-by-step explanation:

Six times a number increased by 4 is no less than 50.
Which inequality represents this statement?
1: 6x+4≤50
2: 6x+4<50
3: 6x+4≥50
4: 6x+4>50

Answers

Answer:

3.

Step-by-step explanation:

For this question, you just have to pick apart what "no less than" means. If I say I can have no less than 2 apples to eat, that's me saying that that's the minimum number I can have, but 2 apples is also still fine. In this case, that minimum is 50 but we can still have over 50. So, 6x+4 can be greater than or equal to 50.

What is the equation of a hyperbola with a = 1 and c = 9? Assume that the transverse axis is horizontal.

Answers

Answer:

Step-by-step explanation:

The general formula for a horizontal hyperbola :

[tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} } =1[/tex]

Given: a = 1 we know a² = 1 ,and that c = 9 so we know c² = 9² = 81

We also know that the relation between a, b, c for a hyperbola is c²= a²+b²

c²= a²+b², substitute what we know

81 = 1 +b², subtract 1 from both sides of the equation

80 = b²

The equation of our hyperbola is:

[tex]\frac{x^{2} }{1 } -\frac{y^{2} }{80 } =1[/tex]  or  [tex]x^{2} -\frac{y^{2} }{80} =1[/tex]

Roberto's science grade is calculated using a weighted average. Quizzes are worth 25%, homework is worth 10%, unit tests are worth 30%, and labs are worth 35%.

Roberto earned an average of 94% on his quizzes, 99% on his homework, 92% on his unit tests, and 94% on his labs.

What is Roberto's final science grade?

93.3%

93.9%

94.8%

95.3%

Answers

Answer:

Final grade:  93.9%

Step-by-step explanation:

The weights are as follows:  0.25, 0.10, 0.30 and 0.35.  Note that these add up to the whole, that is, to 1.00.

Then the final grade is:

0.25(94) + 0.10(99) + 0.30(92) + 0.35(94) = 93.9

Can u help me? thank you ​

Answers

Answer:

x =10

Step-by-step explanation:

30:12 is a 2.5 ratio so the smaller one is 2.5x smaller so 25/x = 2.5 or 25/2.5 = x = 10

What does using the degrees of freedom in a sample correct for? possible bias between the alternative and null hypotheses possible bias between the sample and the population possible bias between the standard deviation and variance possible bias between the standard deviation and the mean

Answers

In Statistics and mathematics, the degrees of freedom in a sample are used to correct: A. possible bias between the alternative and null hypotheses.

What is a null hypothesis?

A null hypothesis ([tex]H_0[/tex]) can be defined as the opposite of an alternate hypothesis ([tex]H_a[/tex]), and it asserts that two (2) possibilities are the same.

In In Statistics and mathematics, the test statistics of a given sample is calculated with this formula:

[tex]Z=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

x is the sample mean.u is the mean.is the standard deviation.n is the sample size.

Also, the degrees of freedom in a sample are used to correct a possible bias that exists between the alternative and null hypotheses.

Read more on null hypothesis here: https://brainly.com/question/14913351

If 3 sweaters cost $25.95, how much would 6 sweaters cost?

Answers

Answer:

If 3 sweaters cost $25.95, then 6 sweaters must cost $95.69.

Step-by-step explanation:

Im sorry if this answer isnt correct.

If we randomly select 2 students at a time and record their drinking habits, what is the probability that both students drink

Answers

Answer:

1 liter

Step-by-step explanation:

x2by 100%8hdofux27675 868*uhf

High-efficiency particulate air (HEPA) filters are designed to remove which sized particles from the environment? 0.1 microns or smaller a) b) 0.3 microns or larger O c) 0.1 microns or larger d) 0.3 microns or smaller

Answers

Answer:

  (b)  0.3 microns or larger

Step-by-step explanation:

A particle of size 0.3 microns is judged to be the most penetrating particle size. So, a rating for the filtering of those particles will be a worst-case rating. For particles of any other size, the filter will perform better than for 0.3 micron particles. HEPA filters are rated based on their performance with particles ...

  0.3 microns or larger

If x = 12 cm, what is the volume of the prism?

cm3

Answers

Answer:

4320

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Shirley has 5 novels and 5 comic books in her bag.
Three of her books are in Japanese, 2 of which are
comic books. The rest of her books are in English.
If a book is chosen at random from her bag, find
the probability of choosing
(((i) a book in Japanese))))-question

Answers

Answer:

3/10

Step-by-step explanation=

Total amount of books in her bag = 10

Total amount of Japanese books in bag = 3

So you have a 3 out of 10 chance of choosing a Japanese book

Also, this problem was trying to confuse you with all the extra wording

Here is the important information in bold

Shirley has 5 novels and 5 comic books in her bag.

Three of her books are in Japanese, 2 of which are

comic books. The rest of her books are in English.

If a book is chosen at random from her bag, find

the probability of choosing

(((i) a book in Japanese))))-question

The length of a rectangular garden is 4 more than three times the width. If the perimeter of the garden 104 feet, what are the dimensions of the garden.

Write your system of equations:
Answer the question being asked:

Answers

Answer:

12 ft by 40 ft

Step-by-step explanation:

Let L represent the length and W the width.  Then L = 3W + 4.

The perimeter formula is P = 2L + 2W or P = 2(L + W).

Substituting 104 ft for P, we get 104 ft = 2(L + W), which reduces to

52 ft = L + W, or 52 ft = 3W + 4 + W.

Therefore, 52 ft = 4W + 4.  

Solving this for W, we get 48 ft = 4W, or W = 12 ft.

Then, because L = 3W + 4, L = 3(12 ft) + 4 = 40 ft = L

The dimensions of the garden are 12 ft by 40 ft.

please help please help please

Answers

light and heat

Step-by-step explanation:

all stars in general produce light and heat

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