find all solutions in the interval [0,2pi).
2sin^2(x)=sin(x)
Answers
[tex]2\sin^2 x =\sin x \\\\\implies 2 \sin^2 x - \sin x=0\\\\\implies \sin x(2 \sin x -1) =0\\\\\implies \sin x = 0~~\text{or}~~ 2 \sin x -1 =0\\\\\implies \sin x = 0~~ \text{or}~ ~ \sin x = \dfrac 12\\\\\text{For}~~ \sin x = 0\\\\x=n\pi \\\\\text{In the interval,}~~[0, 2\pi)\\\\x=0, \pi\\\\\text{For}~~ \sin x = \dfrac 12\\\\x=n\pi+(-1)^n \dfrac{\pi}6 \\\\\text{In the interval,}~~[0, 2\pi)\\\\x=\dfrac{\pi}6,~ \dfrac{5\pi}6\\\\\text{Hence,}~ x = 0,~\pi,~ \dfrac{\pi}6, ~\dfrac{5 \pi}6[/tex]
Answer:
[tex]x=0, \dfrac{\pi}{6},\dfrac{5\pi}{6},\pi \:\sf(for\:the\:given\:interval)[/tex]
Step-by-step explanation:
given interval [0, 2π) = 0 ≤ x < 2π
[tex]2\sin^2(x)=\sin(x)[/tex]
subtract sin(x) from both sides:
[tex]\implies 2\sin^2(x)-\sin(x)=0[/tex]
factor:
[tex]\implies \sin(x)[2\sin(x)-1]=0[/tex]
[tex]\sin(x)=0[/tex]
[tex]\implies x=0 \pm2 \pi n, \pi \pm2 \pi n[/tex]
[tex]\implies x=0, \pi \:\sf(for\:the\:given\:interval)[/tex]
[tex]2\sin(x)-1=0[/tex]
[tex]\implies \sin(x)=\dfrac12[/tex]
[tex]\implies x=\dfrac{\pi}{6} \pm2 \pi n, \dfrac{5\pi}{6} \pm2 \pi n[/tex]
[tex]\implies x=\dfrac{\pi}{6},\dfrac{5\pi}{6}\:\sf(for\:the\:given\:interval)[/tex]
Final solution:
[tex]x=0, \dfrac{\pi}{6},\dfrac{5\pi}{6},\pi \:\sf(for\:the\:given\:interval)[/tex]
Related Questions
Pls help me
Pls show your answer pls and thank you
Answers
Answer:Pls help mePls show your answer pls and thank you
Pls help mePls show your answer pls and thank you
Step-by-step explanation:Pls help mePls show your answer pls and thank you
bot responded dont reply
Simplify: ( 3x + 4xy + 6y ) + ( 4y - 2x + 3xy )
Answers
Answer:
x + 7xy + 10y
Step-by-step explanation:
Remove parenthesis:
3x + 4xy + 6y + 4y - 2x + 3xy
Group like terms:
3x + 4xy + 6y + 4y - 2x + 3xy
x + 4xy + 6y + 4y + 3xy
x + 7xy + 6y + 4y
x + 7xy + 10y
hope this helps!
Tell whether the triangle with the given side lengths is a right triangle
14mm, 19mm, 23mm
Answers
Answer:
not a right triangle
Step-by-step explanation:
The side lengths of a right triangle will satisfy the relation given by the Pythagorean theorem:
c² = a² +b²
23² = 14² +19²
529 = 196 +361
529 = 557 . . . . . . . . not true; not a right triangle
__
The longest side (23 mm) is too short for a right triangle, so the angle opposite will be smaller than 90°. This is an acute triangle.
_____
If you're doing a bunch of these comparisons, use of a triangle solver app or spreadsheet can help.
If the spinner below is spun twice, find the probability that it lands on N, then a vowel.
Answers
Answer:
0.29 or 29%
Step-by-step explanation:
There are 7 options per spin. Of which 3 vowels.
For 2 spins, total spins is 14.
conditions:
First spin is 1/7
Second spin is 3/7
so,
4/14 = 0.29 or 29% I think
Drag the following sentences into the appropriate categories
She said it was a
well opportunity,
but I am not sure !
am ready.
I am not feeling
well today, but
hopefully tomorrow
I will feel more
better.
The beach was
more beautiful than
the park.
There is a good
chance I will not be
able to run faster
than last year.
The comparative adverb is correct.
The comparative adverb is incorrect.
Answers
She said it was a well opportunity, but I am not sure ! am ready has the comparative adverb to be incorrect.
What is a comparative adverb ?A comparative adverb is known to be an adverb that is often used when a person want to make a comparison between one action of a verb with another.
The other part of the question are:
I am not feeling well today, but hopefully tomorrow I will feel more better have the comparative adverb to be correct.The beach was more beautiful than the park. This have the comparative adverb to be correct.There is a good chance I will not be able to run faster than last year. This have the comparative adverb to be correct..Conclusively, An example is: John ran fast, but Miracle came first because he ran faster than John.
Learn more about comparative adverb from
https://brainly.com/question/363915
Answer:
She said it was a well opportunity, but I am not sure I am ready. Incorect
I am not feeling well today, but hopefully tomorrow I will feel more better. Incorect
The beach was more beautiful than the park. Correct
There is a good chance I will not be able to run faster than last year. Correct
Step-by-step explanation:
I took the test
Help With this question
Answers
Answer:
i think it is 523.6
Step-by-step explanation:
α=4/3πr3=4/3·π·53≈523.59878
Hope This Helps
6. In acertain school the following data was compiled from a survery a 80 students 40study physics 30study chemistry 25study neither physics nor chemistry .how many students study
physics and chemistry?
Answers
Answer:
40+30
70÷2
35
hope this helps
Marguerite can save 130 pictures on a DVD.How many pictures can be stored on 7 DVDS
Answers
Answer:
910 pictures can be stored on 7 DVDs.
Step-by-step explanation:
130 X 7 = 910.
In AABC, m ZA=36° and m ZB =92°. What is M
?
Answers
m∠C = 52°
The total interior angle of a triangle sum ups to 180°Solve:
m∠A + m∠B + m∠C = 180°
36° + 92° + m∠C = 180°
m∠C = 180° - 92° - 36°
m∠C = 52°
Answer:
m∠C = 52°Step-by-step explanation:
Angle Sum Property
∠A + ∠B + ∠C = 180°Here we have :
∠A = 36°∠B = 92°Solving :
36° + 92° + ∠C = 180°∠C + 128° = 180°∠C = 52°For what value(s) of b will cause 6x^2+bx-7=0 to have two real number solutions
Answers
Answer:
B can be All real values.
Step-by-step explanation:
The discriminant = b^2 - 4*6*-7 > 0
b^2 + 168 > 0
b^2 > -168
All values of b will be > 0.
f(x) = x + 2 g(x) = 3x^2 - 5. find ( f-g )(x)
Answers
Step-by-step explanation:
(f o g)(x)
= f(3x² - 5)
= (3x² - 5) + 2
= 3x² - 3.
[tex]\text{Given that,}\\\\f(x) =x+2\\\\g(x) = 3x^2 -5\\\\\\(f-g)(x) =f(x) -g(x)\\\\~~~~~~~~~~~~~~=x+2 - 3x^2 +5\\\\~~~~~~~~~~~~~~=-3x^2 +x +7[/tex]
I'm an even number.
I'm > 758 and <893.
I'm a multiple of 100.
What am I?
Answers
Answer:
800
Step-by-step explanation:
Multiples of 100 to 1000:
100, 200, 300, 400, 500, 600, 700, 800, 900, 1000.
|___________________________| |________|
These dont match the given criteria.
800 is greater than 758 and less than 893.
Hope that helps
Which ones are functions and which are not?
Answers
Answer:
relation 2 is not a function.
Step-by-step explanation:
objects in function can only have one image.
•** Pls Help Me **•
Pls show your work thank you
Answers
Answer: 34 cm^2.
Step-by-step explanation: To find the area of a trapezoid, you need to add base 1 and base 2, multiply the height, and divide it all by 1/2. The steps are done below:
Find base 1, base 2, and the height: To find base 1 and base 2, you find the top and bottom lengths of the trapezoid. 5 is the top and 12 is the bottom of the trapezoid. You can assign whichever base to whichever number, as long as base 1 and base 2 have a number. For this problem, we'll assign 5 for base 1 and 12 for base 2. To find the height, you need to find the height of the trapezoid, which is 4.Make an equation: The equation should look like the following... 5 (base 1) + 12 (base 2) x 4 (height) / 1/2.Solve: The first thing you should do when solving is to add the bases together, which is 17. Next multiply the height which is 4, by 17, which is 68. Lastly divide 68 by 2, which can be done in two ways. You can either simply divide 68 by 2 or multiply 68 by 1/2, which will both give you the same answer. 68 x 1/2 = 34.Therefore, your answer is 34 cm^2. There's an image below if you need additional information.
Hope this helps! :)
if i have a dog and she weighs 31.8 kilograms how many grams is equivalent to 31.8 kilograms
Answers
Answer:31800grams
Step-by-step explanation:
Prospect Creek, Alaska, holds the U.S. record for the coldest temperature, -62.1C. What is the temperature in Fahrenheit
Answers
Answer:
i don't understand the last one?
What is eleven plus h squared in expression form?
Answers
this would be the correct answer
Answer:
h²+11
Step-by-step explanation:
answer is h²+11
h squared= h²
h²+11
Look at the following solution of the equation x raised to the power of 6=64.
x raised to the power of 6=64
so, x raised to the power of 3=8
so, x=2
There is an error in this solution. Write a corrected version.
Answers
Answer:
Nothing wrong with the solution x = 2
Step-by-step explanation:
2^6 = 64
2^3= 8
Hence x = 2
Factor rs - 5s + 5r - 25 by grouping
Answers
Answer:
(s+5)(r-5)
Step-by-step explanation:
From the first 2 terms, we can factor s to get
rs - 5s = s(r-5).
Similarly, we can factor 5 form the last 2 terms to get
5r - 25 = 5(r-5).
The original expression then becomes
s(r-5) + 5(r-5).
From here, we can treat (r-5) as a single term and factor the rest to get
(s+5)(r-5),
and we are done.
The most common ages of children that use the library are
Answers
Answer:
12-17
Step-by-step explanation:
this is right. trust (:
Simplify the radical expression. [tex]\sqrt{400/5}[/tex]
Answers
Answer:
option c is correct answer
Step-by-step explanation:
since 4×4×5=80
While 400/5=80
A model house has a scale of
lin: 2ft. If the real house is 26 ft
wide, then how wide is the
model house?
Answers
Answer: Assuming that you mean 1in:2ft the model house would be 13 inches wide.
Step-by-step explanation: well 1 is half of 2 right? So if you want to get the numbers easier to use then just divide that 26 by 2 and then you get the scale 1in:1ft. From there it is easy, 13 feet of the real house= 13 inches in the model house
H
Write the decimal as a fraction.
0.5 = 11
[?]
Simplify your answer completely.
Answers
Step-by-step explanation:
The answer to Your Question in the image is 2/3
2/3=0.6_
NO LINKS!!!! Please help me with this problem
Answers
Answers:
a) x+y = 70b) The graph is shown below. The lines intersect at (20, 50) meaning that she has 20 quarters and 50 dimes.========================================================
Explanation:
a)
x = number of quarters
y = number of dimes
x+y = number of dimes and quarters
x+y = 70 coins total
-----------
b)
Use a graphing tool like Desmos or Geogebra to plot each linear equation on the same xy grid. I'm using Geogebra to get what is shown below.
The red line 25x+10y = 1000 goes through (0,100) and (40,0)
The blue line x+y = 70 goes through (0,70) and (70,0)
The two lines intersect at (x,y) = (20,50)
This means x = 20 and y = 50 pair up together.
Kateri has 20 quarters and 50 dimes
20 quarters = 20*25 = 500 cents = 500/100 = $550 dimes = 50*10 = 500 cents = 500/100 = $5Total value = $5 + $5 = $10
Also note that 20 quarters + 50 dimes = 70 coins total
Both conditions have been confirmed.
Dans une boîte, il y a des jetons de différentes formes (triangle, disque flèche) décorées avec trois sortes de motif.
Flèch
Formes Triangle
30
Disque
10
Total
48
Motif
Motif 1
Motif 2
Motif 3
9
AD
4
16
90
45
23
Total
Answers
Answer:
The anwer for the top row is 30, 10, 8, and 48. The next row is 9, 8, 9, and 26. The next row is 6, 4, 6, and 16. The last row is 45, 22, 23, and 90.
Step-by-step explanation:
HELP
BRAINLEIST
AND 15 points!!!
Answers
Answer:
the product is 20 hope its helps :)
Step-by-step explanation:
find the L.C.M of 4x3 - 9x, 10x2 - 15x
Answers
Answer:
20x³ -45x
Step-by-step explanation:
The least common multiple of two expressions is the product of their unique factors.
__
4x³ -9x = x(4x² -9) = x(2x -3)(2x +3) . . . . factors of 1st expression
10x² -15x = 5x(2x -3) . . . . . . . . . . . . . . . . factors of 2nd expression
The unique factors are 5, x, (2x -3), and (2x +3). Their product is ...
5(4x³ -9x) = 20x³ -45x . . . . least common multiple
Use the information to answer the question.
A rectangular prism has a volume of 768 cubic inches. The area of the base of the rectangular prism is 48 square inches.
What is the height of the rectangular prism? Enter the answer in the box.
Answers
Answer:
16 inches
Step-by-step explanation:
Took the test
Hope this helps <3
Please thank if i got it right <3
Need help with this asap please
Answers
So KL is similar to PN
JL is similar to PM
So,
You need to find how much bigger is the second triangle from first.
It is proportionally scaled up.
KL/JL = PN/ PM
You basically put in order of triangles. Left triangle on left side of equal sign and right triangle on right side of equal sign. You put in denominator the similar sides and numerator the similar sides (the side that is similar to the side of the other triangle)
5/6 = PN / 9
Cross-multiply
PN * 6 = 5*9
6PN = 45
PN =45/6
PN =7.5
The value of PN is 7.5 if the triangles KLJ and NPM are similar triangles.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
The triangles KLJ and NPM are similar triangles.
So the sides of triangle are proportional.
KL/JL = PN/PM
Substitute the values:
5/6 = PN/9
Apply cross multiplication:
45=6PN
Divide both sides by 6:
45/6= PN
7.5=PN
Hence, the value of PN is 7.5.
To learn more on similar triangles click:
https://brainly.com/question/29731302
#SPJ3
this is a k 12 question
Answers
Area in interest is 30-20 = 10
What percentage is 10 of 40?
10/40 = 0.25
0.25*100 = 25%
Brainiest