3 cos 2x + Sinx = 1 for
0° ≤x ≤ 360​

Answers

Answer 1

Answer:

x = 41.81°, 138.19°, 210°, 330°

Explanation:

3cos(2x) + sin(x) = 1

subtract one from both sides

→ 3cos(2x) + sin(x) − 1 = 0

rewrite using trigonometry identities

→ 2 + sin(x) − 6sin²(x) = 0

solve x by substitution

f(x) = 2 + sin(x) − 6sin²(x)

= 2 + 4sin(x) - 3sin(x) − 6sin²(x)

= −2sinx(3sinx −2) − (3sinx−2)

= (3sinx −2)(−2sinx−1)

= −(3sinx −2)(2sinx+1)

f(x) = 2 + sin(x) − 6sin²(x) = 0

= −(3sinx −2)(2sinx+1) = 0

(3sinx −2) = 0 (2sinx+1) = 0

→sinx = 2/3 →sinx = −1/2

x = 41.81°, 138.19° x = 210°, 330°

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Related Questions

Find the missing length in the right triangle.


Answers

Answer:

10 ft

Step-by-step explanation:

By using the pythagorean theorem, we know that leg1 squared plus leg2 squared is equal to hypotenuse squared.

[tex]6^2+8^2=?^2\\36+64=?^2\\100=?^2\\10=?[/tex]

Answer: 10ft

Step-by-step explanation:

Pythagorean Theorem- In a right triangle, a²+b²=c² where: (image attached)

a=6ft ; b=8ft

6ft²= 36ft ; 8ft²= 64ft

36+64=100ft

√100= 10ft

A painter leans a ladder up against a wall. The ladder is 25 feet long and the wall is 15 feet high. How far from the wall is the base of the ladder?

Answers

Answer:

12 feet

Step-by-step explanation:

The ladder is 12 feet up the wall.

The ladder forms a right triangle with the wall and the ground. You want to use Pythagorean theorem to solve the problem. a2+b2 = c2

Use the Pythagorean Theorem (a2+b2=c2) where b=9 and c=15. Solve for a.

(hope this helps can i plz have brainlist :D hehe)

After two six-sided dice are rolled, what is the probability that the dice faces add up to either a 4 or 6?
0.222
0.139
0.167
0.083

Answers

Answer:

0.222

Step-by-step explanation:

out of 36 outcomes you have 8 possible outcomes for a '4' or '6':

1,5

5,1

3,3

2,4

4,2

2,2

1,3

3,1

8/36 = 2/9 = .2 repeating

The probability that the dice faces add up to either 4 or 6 is 0.222.

What is Probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Here, After two six sided dice are rolled,

Hence, Total outcomes = 36

So, Probability of getting sum 4 that is,  {(1, 3), (2, 2), (3, 1)};

P = 3/36    

And, Probability of getting sum 6 = 5/36

Hence, Total Probability of getting sum either 4 or 6 = 3/ 36 + 5/36

                                                                         = 8/36

                                                                         = 2/9

                                                                         = 0.222

Thus, the probability that the dice faces add up to either 4 or 6 is 0.222.

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to find the value of r, Stephen rewrites 3r - 18 = 27 as 3(r - 6) = 3(9). How could this help Stephen reason the value of r? Explain your reasoning.

PLZ HELP ASAP

Answers

Answer: See explanation

Step-by-step explanation:

We are informed that Stephen rewrites 3r - 18 = 27 as 3(r - 6) = 3(9). This is quite thoughtful of Stephen and it's an easier way to solve the question.

In this case, 3 is a common factor to 3r, 18 and 27. Therefore, we will then have: 3(r - 6) = 3(9).

Since 3 is a common base to both, we are more concerned with the values inside the brackets. This will be:

r-6 = 9

r = 9 + 6

r = 15

Check: 3r - 18

3(15) - 18 = 45 - 18 = 27

Match the following.

1. equilateral triangle
2. rectangle
3. circle circumference
4. trapezoid
5. parallelogram
6. triangle
7. regular polygon
8. circle area

Answers

1. A = 1/4s squared, square root of 3

2. A = bh

3. A = pi(r) squared

4. A = 1/2 h (b1+ b2)

5. C = pi(d)

6. A = base x altitude

7. A = 1/2(ap)

8. A = 1/2(bh)

- regular polygon

- trapezoid

- rectangle

- parallelogram

- circle circumference

- equilateral triangle

- circle area

Answer:

Answers are below.

Step-by-step explanation:

1.  Equilateral triangle - A = 1/4 s^2 √3

2. Rectangle - A = bh

3. Circle circumference - C = πd

4. Trapezoid - A = 1/2 h (b1 + b2)

5. Parallelogram - A = base x altitude

6. Triangle - A = 1/2 bh

7. Regular polygon - A = 1/2 ap

8. Circle area - A = πr^2

Hope this helps.  

A quadrilateral had two angles thst measure 260degrees amd 50 degrees. The other two angles are in a ratio of 2:3. What are the measures of those two angles.

Answers

Step-by-step explanation:

Here's another solution.

360-275-20=65

ratio 3:10

3x+10x=65

13x=65

x=5

5*3=15° and 5*10=50°

15° and 50° are the other two angles

Mr. Morales owns a tour bus company and just received the news that fuel prices are going to increase by 125% it is currently $3.40 per gallon what will the cost per cost per gallon after the increase

Answers

Answer:

Step-by-step explanation:

Your answer

Let me think. 125 %,,,. So 1.25* 3.4= 4.25

New price = 7.65

Mark it as Brainlist answer. Follow me.

b. A 50A by 35ft residential
garden produces 1975
servings of food over the
course of a year. How many
servings of food per square
foot is this?

Answers

Answer:

1.13 food per square feet

Step-by-step explanation:

Given

Dimension: 50ft by 35ft

Servings = 1975

Required

Determine the amount per servings

First, we calculate the area.

[tex]Area = 50ft * 35ft[/tex]

[tex]Area = 1750ft^2[/tex]

Next, we calculate the amount per square foot.

This is:

[tex]Rate = \frac{Serivings}{Area}[/tex]

This gives;

[tex]Rate = \frac{1975}{1750}[/tex]

[tex]Rate = 1.13[/tex]

WILL GIVE BRAINLIEST!!!!
3. The nth term of a Sequence is given by an =
n/n+2
If the Domain of the Sequence is {1,2,3,4,5} choose the correct range of the Sequence

Answers

Answer:

answer b :) i hope this helps

Tina found $4.75 at the bottom of her purse and added it to her wallet. She later bought milk and eggs for $6,55 and had
$5.43 left in her wallet
Tina wants to know how much money she had in her wallet before adding the amount she found in her purse (%). Choose ALL
equations in which x correctly represents the amount in her wallet before adding the amount she found,
A)
$6,55 - x + $4.75 - $5.43
B)
x + $4.75 - $6,55 - $5.43
C)
$5.43 -
$6.55 - $1.75 -
Eliminate
D)
$4.75 - $6.55 - $5.43 - X
E)
$5,43 - x + $4.75 - $6.55

Answers

Step-by-step explanation:

step 1. x + 4.75 - 6.55 = 5.43

step 2. looks like b is the only answer.

Answer:

i need help wit this

Step-by-step explanation:

The question below give me used to determine h, The high in feet of a model rocket t seconds after it is launched from a roof that is 48 feet in height.

H=-16t^2+128t+48

Which equation reveals the maximum height reached by the model rocket?

Choices/answers^^

Answers

Answer: the answer is B.

Step-by-step explanation:

The correct equation which reveals the maximum height reached by the model rocket is,

h = - 16 (t + 4)² - 304

What is Quadratic equation?

An equation of order 2 in highest variable is called a Quadratic equation.

Given that;

The equation is,

H = -16t² + 128t + 48

Now, The equation which reveals the maximum height reached by the model rocket is find as;

H = -16t² + 128t + 48

h = -16(t² + 8t) + 48

h = -16 (t² + 8t) + 256 - 256 + 48

h = -16 (t² + 8t + 16) + 256 + 48

h = -16 (t + 4)² + 304

Thus, The correct equation which reveals the maximum height reached by the model rocket is,

h = - 16 (t + 4)² - 304

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a Toyota Yaris goes 15 km on one litre of petrol how much petrol will it need to get to paga from bawku,120km​

Answers

Answer:

8 litre

Step-by-step explanation:

very simple 120÷15=8

hope it helps you

please mark me as brainlist

(10x-4) + ( -7 + x )

Answers

The answer is 11(x-1)
answer is 11(x-1) if its factoring. simplifying would be 11x-11

What is the equation, in point-slope form, of the line passing through the point (5, -3) with a slope of 1/7?

y + 3 = (x - 5)
y - 3 = (x + 5)
y - 3 = 7(x + 5)
y + 3 = 7(x - 5)

Answers

Answer:

Step-by-step explanation:

None of the choices has a slope of 1/7

b) A triangle-based prism
12.7 cm
8 cm
9 cm
9 cm
Volume:
Surface Area:
What is the volume and surface area

Answers

Answer:

Step-by-step explanation:

9²+9²=162

√162 ≈12.7

so base is a right angled triangle with sides 12.7,9,9

area of base and top=2×1/2×9×9=81 cm²

area of sides=(9+9+12.7)×8

=30.7×8=245.6 cm ²

total surface are =81+245.6=326.6 cm²

volume=1/2 ×9×9×8=324 cm³

There are 6 thirds in 2 wholes. How many thirds are there in 6 wholes?

Answers

Answer:

there's 18 thirds in 6 wholes

Heidi’s older sister needs to take either Chemistry (C), Geometry (G), or Physics (P) this year. She can take the class during any one of six periods (1 through 6). Is there more than one way to draw a tree diagram to model this situation? Explain.

Answers

Answer:

Yes. You can make a tree diagram with each subject at the top and the periods as the branches or with the periods at the top and each subject as a branch. Both ways provide the same number of​ outcomes, 18

Step-by-step explanation:

No, there is only one way to draw a tree diagram to model this situation.

What is Combination?

An arrangement of objects where the order in which the objects are selected does not matter.

No, there is only one way to draw a tree diagram to model this situation. The reason for this is that the choices for the classes and periods are mutually exclusive and exhaustive.

Starting with the first branch, there are three possible classes (C, G, or P) that the sister can take.

From each of these branches, there are six possible periods (1 through 6) that the sister can take the class.

Therefore, the tree diagram will have 3 branches at the top level, each with 6 branches at the next level, for a total of 18 possible outcomes.

If we try to draw a different tree diagram, we will end up with the same possible outcomes, just with a different arrangement of the branches.

Hence, there is only one way to draw a tree diagram to model this situation.

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what is the prudct of 7\9 and 6

Answers

Answer:

378

Step-by-step explanation:

9 × 7 × 6 = 378

pls mark brainliest, if not, its ok :)

Answer:

14/3, or 4.6^bar

Step-by-step explanation:

first you'd just divide 7 by 9, resulting in [tex]\frac{7}{9}[/tex], or 0.7^bar.

Then you'd multiply either by 6, resulting in the answers above. Fractions are easier than infinite numbers, so if you're able to do that, I'd suggest you do so.

Hope this helped!

18 Which expression below is equivalent to -3x + 5(x + 2)? Circle the
correct answer.
A 2x + 2
B.
-x+ 2
C 2x + 10
D
- 8x + 10
Kaitlin chose A as the correct answer. How did she get that answer?

Answers

Answer:

C

Step-by-step explanation:

First, use the distributive property to open the parentheses:

-3x + 5x + 10

2x + 10

The correct answer is C

Kaitlin forgot to use the distributive property on both the x and 2.  

Hope this helps!

find the value of x.

Answers

Answer:

x = 120 degress

Step-by-step explanation:

I can help with more, I have the answers.

what is 9+10x6x[7x7]+8x6x6x6x7x8

Answers

Answer:

99717

Step-by-step explanation:

Use PEMDAS

P stands for parenthesis so you do 7 x 7 first. It equals 49. E stands for exponents but there aren't no exponents. M stands for multiplying so you multiply 10 x 6 = 60. Then 60 x 49 = 2940. 8 x 6 = 48. 48 times 6 is 288. 288 x 6 is 1728. 1728 x 7 is 12096. 12096 x 8 is 96768. The A in PEMDAS is addition. 9+2940 equals 2949. 2949 + 96768  = 99717.

Bags of sugar come in 3 sizes.

Small bag: A 175 g bag costs 55p.
Medium bag: A 525 g bag costs £1.76.
Large bag: A 1.15 kg bag costs £3.51.

Find the cost per gram for each bag of sugar.
Round your answers to 3dp.

Answers

Answer:

The cost per gram for each bag is:

Small bag: 0.00314 £

Medium bag: 0.00335 £    

Large bag: 0.00305 £  

Step-by-step explanation:

Small bag:

If 175 g cost 0.55 £, 1 g will be:

[tex] \frac{1g*0.55 \£}{175\: g} = 0.00314 \£[/tex]

Medium bag:

If 525 g cost  £ 1.76, 1g will be:

[tex] \frac{1g*1.76 \£}{525\: g} = 0.00335 \£[/tex]    

Large bag:  

If 1150 g cost  £ 3.51, 1g will be:

[tex] \frac{1g*3.51 \£}{1150\: g} = 0.00305 \£[/tex]        

   

I hope it helps you!

         

I feel like I’m wrong and if I am can someone correct me? Thank you!

Answers

No that’s right believe in your self

5y+3y????????????????????​

Answers

Answer:

8y

Step-by-step explanation:

It's really simple! Because both of the variables are the same, You can just add it!

Hope this helps ^^

Why is sum of yi.ui zero

Answers

Answer:

Q

=

n

i

=

1

(

Yi

(

β

0

+

β

1

X

i))

2

I NEED THE ANSWERS PLZ

Answers

Answer:

1. 32

2. 4.7

3. 3

Step-by-step explanation:

4*8=32

6.5-1.8= 4.7

18/6=3 or 18 divided by 6 = 3

4x; x=8 answer is 32

Find tan e
53
45
8
28
A. B.
Ο Ο
D.
< PREVIOUS

Answers

TAN: 45/28

SIN: 45/53

COS: 28/53

sin(x°) = opposite/hypotenuse

cos(x°) = adjacent/hypotenuse

tan(x°) = opposite/adjacent

x is any degree measure.

Hence option C (45/28) is correct

What are trigonometric rations?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec) are the six trigonometric ratios (sec). Trigonometry is the branch of mathematics concerned with the sides and angles of a right-angled triangle in geometry. As a result, trig ratios are assessed in terms of sides and angles.

How to solve ?

Given θ

∴tan θ=[tex]\frac{Perpendicular}{Base}[/tex]

=45/28

= option c

Hence option C (45/28) is correct

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Find the Area Please​

Answers

12x8=96
This should be the correct answer

javier walks from his home at point k to the internet cafe at point 0. if the school at point w is exactly halfway between javier's house and the internet cafe, how far does javier walk?

Answers

Answer:

actually need the numericals but attached

Step-by-step explanation:

if we take it as 1 km then it would be

home to cafe = 1 km

cafe to school =

[tex] \frac{1}{2} [/tex]

so it will be 1 + 1/2 that is

[tex]1 \frac{1}{2} km[/tex]

ok mark me as brainlist

Poru
1. It is a relationship that compares two or more quantities
A. quantity
B ratio
C. fraction
D. colon​

Answers

The answer is B


Because it has 2 or more quantities for different units for a measure. Hope this helps have a nice day :)
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