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Step-by-step explanation:
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Solve for x:sinx+sin2x+sin3x=cosx+cos2x+cos3x in the interval 0≤x≤2π.
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We write the given equation as
(sinx+sin3x)+sin2x=(cosx+cos3x)+cos2x
or 2sin2xcosx+sin2x=2cos2xcosx+cos2x
or sin2x(2cosx+1)=cos2x(2cosx+1)
or (sin2x−cos2x)(2cosx+1)=0
∴sin2x−cos2x=0 or 2cosx+1=0
If sin2x−cos2x=0, then tan2x=1,
Hence 2x=nπ+π/4
or x=(4n+1)
8
π
.(1)
If 2cosx+1=0, then cosx=−1/2 (2)
∴x=2nπ±
3
2π
or x=
3
6n±2
π
We seek values of x in the interval 0≤x≤2π
In this interval (1) gives
x=π/8,5π/8,9π/8,13π/8. (n=0,1,2,3)
and (2) gives x=2π/3,4π/3. (for n=0,1)
Thus we get the answer
x=π/8,5π/8,2π/3,9π/8,4π/3,13π/8.
Related Questions
the quotient of 8 and y
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Answer:
"The quotient of 8 and y" is written as the following algebraic expression:
8÷y
find the value of x
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In the given problem, x represents the exterior angle, while the m < 65° and m < 48° are the non-adjacent interior angles.
To find the value of x:
65° + 48° = x
113° = x
Therefore, the value of x = 113°
30. You can work at most 25 hours next week. You need to earn at least $85 to cover your gas and food
expenses. Your babysitting job pays $7.50 per hour and your math tutoring job pays $6 per hour.
a) Define your variables.
b) Write two inequalities that represent the constraints of the scenario.
Answers
Sooo my math teacher who’s a pain in the behind was the only one gave us homework while we’re out for and extended 1 day so if you would please help me bc I have to go back and turn this in tomorrow, please and thank you :/ (just 8-16)
Answers
Answer:ok??/????????
Step-by-step explanation:Whaaaaat?????
Matt's pool table is 3 feet wide and 9 feet long. Matt wants to replace the felt on the pool table. The felt costs $4.00 per square foot. How much would it cost in total to replace the felt on the pool table?
Answers
Answer:
$108
Step-by-step explanation:
3X9= 27square foot. Then you multiply 27 by 4, which equals $108
PRE- CALC MATH HELP
100 Points and Brainlist.
if PDF doesn't work Follow the link in my comments
Follow the link for question
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i cant see the pdf???????????????
[tex]10\times 5\times 13=?[/tex]
Answers
Answer:
[tex] = > 10 \times 5 \times 13[/tex]
[tex] = > 50 \times 13[/tex]
[tex] = > 650[/tex]
Given that ∠ADC≅∠BCD, AC⊥CD and BD⊥CD, which of the following proves that △ACD≅△BDC?
Answers
Answer:
1. ∠ADC≅∠BCD (Given)
2. AC¯¯¯¯¯⊥CD¯¯¯¯¯; BD¯¯¯¯¯⊥CD¯¯¯¯¯ (Given
)3. ∠ACD and ∠BDC are right angles(Def. of ⊥)
4. ∠ACD≅∠BDC (Rt. ∠≅Thm.)
5. CD¯¯¯¯¯≅CD¯¯¯¯¯ (Reflex. Prop. of ≅)
6. △ACD≅△BCD (ASA Steps 1, 5, 4)
△ACD and △BCD are Congruent triangles because Two angles are the same, as is a corresponding side.
What is of congruent triangle?Congruent triangles have comparable sides and angles that are equal. The symbol "≅" represents congruence.The three sides are all the same (SSS: side, side, side)Two angles are the same, as is a corresponding side (ASA: angle, side, angle)We know that two triangles are congruent if all of their sides are the same— thus side, side, side (SAS: side, angle, side). We also know they are congruent if we have a side, an angle between the sides, and another congruent side—so side, angle, side.1. ∠ADC≅∠BCD (Given)
2. AC⊥CD; BD⊥CD (Given
3. ∠ACD and ∠BDC are right angles(Def. of ⊥)
4. ∠ACD≅∠BDC (Rt. ∠≅Thm.)
5. CD≅CD (Reflex. Prop. of ≅)
6. △ACD≅△BCD
To learn more about Congruent triangles refer,
https://brainly.com/question/2938476
#SPJ2
solves the equation
8x-2 =3(x-9)
Answers
8x-2=3(x-9)
Answer:
-5.2
Step-by-step explanation:
Maybe can I have some help?
Answers
8.8d + 9.65 = –3.01 + 7.2d + 1.46
d= -14 right ?
Answers
Answer:
d=-7
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Answer:
d=-23.934375
Step-by-step explanation:
i need to find the slope and the value of A B
Answers
Answer:
the slope is 2 and a=8 b=6
Step-by-step explanation:
A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. The 95% confidence interval for the true mean number of pushups that can be done is _____.
Answers
Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).
For this problem, we have the standard deviation for the sample, thus, the t-distribution is used.
The sample mean is of 15, thus [tex]\overline{x} = 15[/tex].The sample standard deviation is of 9, thus [tex]s = 9[/tex].The sample size is of 10, thus [tex]n = 10[/tex].First, we find the number of degrees of freedom, which is the one less than the sample size, thus df = 9.
Then, looking at the t-table or using a calculator, we find the critical value for a 95% confidence interval, with 9 df, thus t = 2.2622.
The margin of error is of:
[tex]M = t\frac{s}{n}[/tex]
Then:
[tex]M = 2.2622\frac{9}{\sqrt{10}} = 6[/tex]
The confidence interval is:
[tex]\overline{x} \pm M[/tex]
Then
[tex]\overline{x} - M = 15 - 6 = 9[/tex]
[tex]\overline{x} + M = 15 + 6 = 21[/tex]
The confidence interval is (9, 21).
A similar problem is given at https://brainly.com/question/25157574
Pat's English class is located in the same quadrant as the gym. Which of the following could be the coordinates of the English classroom? (4 points) ASAP
(2, 5)
(−2, 5)
(−2, −5)
(2, −5)
Answers
Answer its (-2,5)
if its on q2
A store had 2 BLUE chairs for $22.78 or 6 RED chairs for $67.80.
Type in the rate for each color of chairs below. blue $_______ Red $_______
Which color chair has a lower unit price? ________
Answers
Answer:
Blue chairs
Step-by-step explanation:
To get the unit rate of red chairs, you simply divide 22.78/2, which equals $11.39
So the unit rate of RED chairs is $11.39
To get the unit rate of the blue chairs, you simply divide 67.80/6 which equals $11.30
So the unit rate of BLUE chairs is $11.30
Unit rate is simply the cost of one item (in this case chairs) the unit rate stays the same. If we flipped the operation on blue chairs and did 11.30*6, it equals $67.80. The same goes for the red chairs, if we did 11.39*2 it equals $22.78.
Hope this helps!
HELP PLEASE!!!!!!!!!
Answers
9514 1404 393
Answer:
A) W'(-4, 2), ...
Step-by-step explanation:
Put the values of x and y in the translation relation to see what the translated point's coordinates are.
(x, y) ⇒ (x -7, y +4)
W(3, -2) ⇒ W'(3 -7, -2 +4) = W'(-4, 2) . . . . . . . . matches only choice A
please show the work but thanks !!!
Answers
Solve √3x+4−2=3
The square root covers the 4 but not the -2
Answers
[tex] \sqrt{3} x + 4 - 2 = 3 \\ = > \sqrt{3} x = 3 - 4 + 2 \\ = > \sqrt{3} x = 1 \\ = > x = \frac{1}{ \sqrt{3} } \\rationalising \: \: \: the \: \: \: denominator \\ = > x = \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ = > x = \frac{ \sqrt{3} }{3} \\ [/tex]
Answer:[tex] \frac{ \sqrt{3} }{3} [/tex]
Answer: x = 7
Step-by-step explanation:
[tex]\sqrt{3x+4}=3+2[/tex]
[tex]\sqrt{3x+4}=5[/tex]
[tex]3x+4 =25[/tex]
[tex]3x = 21[/tex]
[tex]x=7[/tex]
Please give me a brainliest answer
if i fill the 42 L tank in my car and take a 360km trip. If my car consumes gasoline at a rate of 8 L per 100km how muck farther can i go before i run out of gasoline.
Answers
Using the principle of proportional relationship, the 42 L of gas can go for a further 165 km
Consumption rate = 8L for 100 km
Km per Litre :
8L = 100km
1 L = m
8m = 100
m = (100 ÷ 8)
= 12.5 kilometer per Litre
Number of kilometers for 42 L
12.5 km = 1 L
m = 42 L
Cross multiply
m = 12.5 × 42
m = 525 km
The difference in the distance = 525 - 360 = 165 km
Therefore, the gas can go for a further 165 km
Learn more : https://brainly.com/question/18112348
Help me for 75 points.
Answers
Answer:
2.6% = 0.026
142% = 71/50
34% = 17/50
Help me find x please!!!
Answers
Answer:
Step-by-step explanation:
2) 133 + a = 180 {Linear pair}
a = 180 - 133
a = 47
a +b = 180 {linear pair}
47 + b = 180
b = 180 - 47
b = 133
x = b + 30 {Exterior angle property}
x = 133 +30
x = 163
3) m + 35+ 35 = 180 {Angle sum property of triangle}
m + 70 = 180
m = 180 - 70
m = 110
z = 35 {alternate interior angles are congruent}
x = m + z
x = 110 + 35
x = 145
proportional escape room puzzle two
Answers
Answer:
Step-by-step explanation:
Is there a question to it?
Number of College Faculty The number of faculty listed for a variety of private colleges that offer only bachelor’s degrees is listed below. Use these data to construct a frequency distribution with 7 classes, a histogram, a frequency polygon, and an ogive. Discuss the shape of this distribution. What proportion of schools have 180 or more faculty?
Answers
Answer: Number of College Faculty The number of faculty listed for a variety of private colleges which offer only bachelor’s degrees is listed below. Use these data to construct a frequency distribution with 7 classes, a histogram, a frequency polygon, and an ogive. Discuss the shape of this distribution. What proportion of schools have 180 or more faculty? 165 221 218 206 138 135 224 204 70 210 207 154 155 82 120 116 176 162 225 214 93 389 77 135 221 161 128 310 Source
What is the graph of the function f(x) = the quantity of x squared minus 7 x plus 12, all over x minus 3 ? (1 point);
Answers
Answer:
pic is answer
Step-by-step explanation:
If you have a collection of 20 items, how many different groups of 8 can you create?
Answers
Answer:
you can create 2 groups of 8 and you will have a group of 4 left
Step-by-step explanation:
I need some help with this thank you!
Answers
Answer:
9
Step-by-step explanation:
2^28(3^-2/2^3)^4 x 1/(3^-5 x 2^8 x 6^0)^2
2^28(3^-2/2^3)^4 x 1/(3^-5 x 2^8 x 1)^2
2^28(3^-2/2^3)^4 x 243^2/256^2
2^28 x 1/2^12 x 3^8 x 243^2/256^2
243^2 x 1 x 2^28/256^2 x 3^8 x 2^12
2^28 x 243^2/2^12 x 3^8 x 256^2
2^16 x 243^2/3^8 x 256^2
2^16 x 3^10/2^16 x 3^8
=3^2
=9
Given that a = 4 and b = 6, find the value of a+b
Answers
Answer:
10
Step-by-step explanation:
We know that a = 4 and b = 6, and we are trying to find the answer to both of them added, so to get a + b, we can substitue the values of a and b by their numbers. So,
a + b
Is the same as
4 + 6, which equals 10.
Therefore, the value of a+b is 10
Hope this helps :)
RAMPS Rodney is rolling marbles down a ramp. Every second that passes, he measures how far the marbles travel. He records the information in the table shown below.
Make a conjecture about how far the marble will roll in the fifth second.
Answers
Using the principle of common difference , we can observe that the distance moved per roll increases by a constant amount of centimeters . Hence, the distance moved in the 5th roll is 180 cm
Setting up a proportional relationship :
Second = S Distance = dThe common difference between each roll can be obtained thus :
d2 - d1 = d3 - d2 = d4 - d3
60 - 20 = 100 - 60 = 140 - 100
40 = 40 = 40
Hence, the common difference = 40
The distance obtained on the fifth roll :
d(5) = d(4) + common difference
d(5) = 140 + 40
d(5) = 180
Therefore, the distance obtained on the fifth roll is 180 cm
Learn more :https://brainly.com/question/18796573
Consider the system of equations.
5x + 2y = 12
5x – 2y = 28
What is the solution to the system of equations? Show work using substitution or elimination to support your answer.
A (4, -4)
B (-4, 4)
C (5, -6.5)
D (4, 16)
Answers
Answer:
A. (4, -4)
Step-by-step explanation:
Equation form x = 4, y = −4
Answer:
Option A
Step-by-step explanation:
5x + 2 y = 12 -----------(I)
5x - 2y = 28 ------------(II)
Add equation (I) & (II). So, y will be eliminated and we will get the value of x
(I) 5x + 2y = 12
(II) 5x -2y = 28 {Now add}
10x = 40
x = 40/10
x = 4
Plugin x = 4 in equation (I)
5*4 + 2y = 12
20 + 2y = 12
2y = 12 - 20
2y = -8
y = -8/2
y = -4
What’s the mean, variance and standard deviation
Answers
Answer:
Step-by-step explanation:
binomial distritubtion
mean= n*p
.23*300= 69
variance= n*p*(1-p)
.23*300*(1-.23)=53.1
standard deviation= sqrt(variance)
sqrt(53.13)= 7.3
