Find all solutions to the equation in the interval [0,2pi]. Enter the solutions in increasing order. sin 2x = sin x
please explain how you got the answer
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Answers
Step-by-step explanation:
[tex]sin2x=sinx\\sin2x-sinx=0\\2*sinx*cosx-sinx=0\\sinx*(2*cosx-1)-0\\sinx=0 \\x=\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_1=0\ \ \ \ x_2=\pi .\\2*cosx-1=0\\2*cosx=1\ |:2\\cosx=\frac{1}{2} \\x=б\frac{\pi }{3} +2\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_3=\frac{\pi }{3} \ \ \ \ \ x_4=\frac{5\pi }{3}.\\[/tex]
[tex]Answer: x=0,\ \frac{\pi }{3} ,\ 1\pi ,\ \frac{5\pi }{3} .[/tex]
Related Questions
Raymond spent $125.00 on a limousine for the prom. About how much should he give the driver for a 20% tip? $18.75 $25.00 $20.00 $6.25
Answers
Answer:
$25.00
Step-by-step explanation:
20% of $125 = $25
Flo sets a goal of walking 12,000 total steps per day. flo's normal routine involves walking 6,000 steps per day. if flo walks 100 steps per minute, how many extra minutes should she walk per day beyond her normal routine?
Answers
Flo should walk 60 extra minutes of time per day to accomplish her goal of walking 12,000 total steps per day.
Calculating the Time for Which Flo Walks Each Day
Flo walks 6,000 steps per day.
She walks 100 steps per minute.
⇒ Time taken by Flo to cover 6,000 steps = [tex]\frac{6000}{100}[/tex] minutes
⇒ Time taken by Flo to cover 6,000 steps, m₁ = 60 minutes
Hence, Flo walks for 60 minutes or 1 hour per day.
Calculating the Extra Hours of Walking
Steps to be covered by Flo each day = 12,000
Time required to walk 12,000 steps per day, m₂ = [tex]\frac{12000}{100}[/tex] minutes
⇒ m₂ = 120 minutes
Extra hours of walk per day = (m₂-m₁) minutes
= (120 - 60) minutes
= 60 minutes
Thus, Flow should walk 1 hour extra to be able to accomplish a goal of walking 12,00 steps per day.
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hi, I need help I don't understand
Answers
Answer: [tex]60cm^2[/tex]
Step-by-step explanation:
Looking at the figure, you can see that the length is 5cm + 3cm = 8cm and the width is 2cm + 5cm + 2cm = 9cm.
The formula for area is length x width, therefore you do 8x9 which is 72.
Next, we solve for the two "dips" in the rectangle. We can do that by subtracting the area of the "mini-rectangles" from the whole figure:
72-2(2x3) = 60
Thus, 60cm^2 is your answer.
Compute: -1 2/3 * 2 1/7
Answers
Answer:
Fraction form: -3 4/7
Decimal form: -3.57142
Step-by-step explanation:
convert mixed number to improper fractions
apply the fraction rule a/b * c/d = a * c / b * d
Factor the number
cancel the common factor
multiply the numbers
Conver improper fraction to mixed numbers
To get your final answer:
= -3 4/7
Hope this helps! :)
What is the x-coordinate of the vertex of the parabola whose equation is y = 3x² + 9x?
o-3
o-1 1/12
o-2/3
Answers
Answer: x=-1,5.
Step-by-step explanation:
[tex]y=3x^2+9x\\\boxed {x=-\frac{b}{2a} }\\a=3,\ \ \ \ \ b=9.\\x=-\frac{9}{2*3}=-\frac{3}{2}=-1,5.[/tex]
anybody can help me?
Answers
Graph C depicts the relation between No. of sweaters ( Nombre de chandails vendus ) and the fund raised in the campaign (Campagne de financements )
What is a Graph ?Graph is the statistical representation of data , It helps to observe large data systematically.
It is given that
Sale of one sweater gives $3
The relation between the amount raised for funding , M and the number of shirts sold , n is given by
M = 3n
It has to be found that which graph exactly depicts the relation and the condition as given
Graph C depicts the relation given as , The graph is between No. of sweaters ( Nombre de chandails vendus ) and the fund raised in the campaign (Campagne de financements ) , and for every 100 sweater , $300 is earned .
Therefore Graph C is the answer.
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PLS HELP ASAP!!! im struggling
Answers
The correct options, in order, are:
[tex]f(n) = 3*(2)^{n-1}[/tex]
[tex]f(n) = 2*(6)^{n - 1}[/tex]
[tex]f(n) = 2*(4)^{n - 1}[/tex]
How to match the equations and the tables?The first table is:
n f(n)
1 3
2 6
3 12
Notice that when n = 1, all the exponents are 0, then the initial value is 3.
When n = 2, all the exponents are 1. Then we need to find the exponential equation with a base equal to 2.
So the exponential equation is:
[tex]f(n) = 3*(2)^{n-1}[/tex]
The second table is:
n f(n)
1 2
2 12
3 72
By looking at the first pair, we conclude that the initial value is 2, and by looking at the second pair, we conclude that:
2*b = 12
b = 12/2 = 6
The base is 6.
So the exponential equation now is:
[tex]f(n) = 2*(6)^{n - 1}[/tex]
The last table is:
n f(n)
1 2
2 8
3 32
Here we again have an initial value of 2, and the base is:
2*b = 8
b = 8/2 = 4
Then the correct option now is:
[tex]f(n) = 2*(4)^{n - 1}[/tex]
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Scores on IQ tests are normally distributed, with a mean of 100 and a standard deviation of 15. What is the score such that 10 percent of people taking the test achieve a higher score
Answers
Answer:
103.75 score
Step-by-step explanation:
10 % scored higher than the mean?
50% is the mean % so we need to look for the z score corresponding to 60 % from z-score table this is z-score of .25
.25 standard deviations (which is 15) above 100 =
.25 * 15 + 100 = 103.75 score
translate triangle P by the vector (2 -7)
Answers
The transformation rule for triangle P by translating using the vector [tex](^{\ 2}_{-7})[/tex] is (x, y) ⇒ (x + 2, y - 7)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.
The transformation rule for triangle P by translating using the vector [tex](^{\ 2}_{-7})[/tex] is (x, y) ⇒ (x + 2, y - 7)
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If f(x)=x²-1, and
g(x)=x+2, then
Answers
Answer:
f(g(x) = 1x² + 4x + 3
Explanation:
Question: f(g(x))
Given following:
f(x) = x² - 1g(x) = x + 2While solving such function questions, solve from right to left.
⇒ f(x + 2)
⇒ (x + 2)² - 1
⇒ x² + 4x + 4 - 1
⇒ x² + 4x + 3
I need help fast please
Answers
Therefore 20=2(6)+2w. Solve for w to get
w=3
Hope this helped ;)
Answer:
4
Step-by-step explanation:
The formula is P = 2(l +w)
w = P/2 - l = 20/2 - 6 = 4m
Which expression is equivalent to
-[tex](-\sqrt{8-2)[/tex] +[tex]\sqrt{36[/tex]
Select one:
a. 2i
b. −10i
c. −4+6i
d. −4−6i
Answers
-(-root(6) + 6),
(Root 6)- 6
fully simplify 7h² + 2h + 5 - h² + h
Answers
Answer:
6h² + 3h + 5
Step-by-step explanation:
7h² + 2h + 5 - h² + h
= 7h² - h² + 2h + h + 5
= 6h² + 3h + 5
Write a formula for g(x) in terms of x.
Answers
The formula of g(x) is g(x) = -0.8x - 1.6
How to determine the formula of g(x)?The equation is given as:
-4x - 6 = 5y + 2
Subtract 2 from both sides
5y = -4x - 8
Divide through by 5
y = -0.8x - 1.6
Express as a function
g(x) = -0.8x - 1.6
Hence, the formula of g(x) is g(x) = -0.8x - 1.6
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Area= cm2
Help me please thank you so much :)
Answers
Answer:
153
Step-by-step explanation:
The formula for a triangle is 1/2 x base x height
17 x 18 = 306
306 x 1/2 = 153
So therefore your answer would be 153.
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calculate f (x) = 3 - | 2 - 3x| when x = - 5
Answers
Answer: fx=−14
Step-by-step explanation:
please please help meee!!!
What trigonometric function should be used when the opposite and adjacent side of
a triangle are known?
a) CSC
b) tan
c) tan^-1
d) sin^-1
e) sin
f) cos^-1
g) COS
h) sec
Answers
Using relations in a right triangle, the trigonometric function that should be used is given by:
b) tan.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Hence, if the opposite and adjacent side are know, the tangent function should be used, and option b is correct.
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Which of the following are possible equations of a parabola that has no real solutions and opens downward?
Oy=(x-4)2+2
Oy=-(x+4)²-2
Oy=(x-4) 2-2
Oy=-x²-2
Oy=-(x+4)² +2
Answers
Answer:
Oy= -(x+4)^2 -2
potentially Oy= -x^2 -2
Which is bigger, a third of 45 or one-sixth c
138?
Answers
Applying the knowledge of fractions, the bigger one is: one-sixth of 138.
What are Fractions?Fractions can be defined as a part of a digit or number, and are not whole numbers. For example, a third is 1/3, one-sixth is 1/6, which are both fractions.
Therefore, let's evaluate each statement:
1/3 of 45 = 1/3 × 45 = 15
1/6 of 138 = 1/6 × 138 = 23
Therefore, the bigger of the two is: one-sixth of 138.
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The diagram shows the length and width of a cell phone, and the length of a larger version of the same brand cell phone.
The lengths and widths of the two cell phones are proportional. What is the width, in inches?
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
missing length = 2.99 in[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Both the figures are similar to each other, so ratio of their corresponding sides will be equal to one another.
[tex] \qquad❖ \: \sf \: \dfrac{2.6}{5.4} = \dfrac{x}{6.21} [/tex]
( taking missing width be x )
[tex] \qquad❖ \: \sf \: x = \dfrac{1.3}{2.7} \sdot6.21[/tex]
[tex] \qquad❖ \: \sf \: x = {(1.3)}{} \sdot(2.3)[/tex]
[tex] \qquad❖ \: \sf \:x = 2.99 \: \: in[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Missing side measures : 2.99 inches
Question 3(Multiple Choice Worth 3 points)
(07.06)||||||
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
Which of the following inequalities best represents the graph above?
Ox<9
Ox>9
<|OT||||
Ox≤9
Ox≥9
Answers
Answer:
Please see attachment.
Step-by-step explanation:
Since there are no answer choices, I will just show you the graphs for each one.
Remember the dashed lines means it is either greater than, or less than.
The solid lines are either greater than or equal to, or less than or equal to.
Hope this helps!
If not, I am sorry.
The solutions of the equation given as |2/3x + 2| − 8 = 0 are x = 9 and x = -15
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
to determine the solutions of the equation:
The equation is given as:
|2/3x + 2| − 8 = 0
Start by adding 8 to both sides of the equation.
So, we have
|2/3x + 2| = 8
Next, we remove the absolute value expression
So, we have;
2/3x + 2 = 8 and 2/3x + 2 = -8
Subtract 2 from both sides of the equation
2/3x = 6 and 2/3x = -10
Multiply the equation by 3/2
x = 9 and x = -15
Hence, the solutions of the equation given as |2/3x + 2| − 8 = 0 are x = 9 and x = -15
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Complete question:
Determine the solutions of the equation:
|2/3x+2−8=0
Ox= -9 and x = 9
Ox= -15 and x = 4
Ox= -15 and x = 9
Ox= -15 and x = 15
help me please i am struggling
Answers
Answer:
46 cm²
Step-by-step explanation:
Find the area of the rectangle and the triangle, then subtract. Take a look at the steps to know how.
The area of the rectangle:
10×7=70
Area of triangle:
1/2×6×8=24
Subtract the area of the triangle from the area of the rectangle.
70-24=46.
The area of the new shape is 46 cm².
It is cm² because it is a 2D object.
Hope this helps!
If √5+√2=a+b√10 find a and b
Answers
Answer:
Firstly, we'll apply the below identity.
[tex]{\boxed{\sf{(a+b)^{2} = a^{2} + b^{2} +2ab}}}[/tex]
Applying the above identity.
⇒ (√5 + √2)²
⇒ (√5)² + (√2)² + 2×(√5)×(√2)
⇒ 5 + 2 + 2√10
⇒ 7 + 2√10
Comparing the LHS and RHS
⇒ 7 + 2√10 = a + b√10
∴ a = 7 and b = 2.
What is the answer to this
Answers
Answer: H
Step-by-step explanation:
TY:XY: = 2:5, not 3:5.
Answer:
H H H H H H H
Step-by-step explanation:
TY:XY: =2:5, NOT 3:5.
add 3x to 4
a. 7x
b. 7
c. 34x
d. 4+3x
Answers
Please mark brainliest
0.285714 as a fraction
Answers
Answer:
See below
Step-by-step explanation:
285714 / 1000 000 which simplifies to 142,857 / 500,000
Find the 17th term of Arithmetic progression(A.D):-6,-1,-4
Answers
Answer:
58 is the 17th term of the given arithmetic progression.The 17th term of the given Arithmetic progression -6,-1,-4 will be 74.
What is Arithmetic progression?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
Natural number = 1,2,3,4,5,6,7,8...
As per the given Arithmetic progression,
-6, -1, -4.
First term a = -6
Common difference d = -1 - (-6) = 5
The nth term of AP is given as a + (n - 1)d.
This 17th term will be as, -6 + (17 - 1)5
⇒ -6 + 16 × 5 = 74
Hence "The 17th term of the given Arithmetic progression -6,-1,-4 will be 74".
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HELP
Marbles: You have a bag with 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of pulling out a red marble 3 times in a row, assuming you put each marble back into the bag before drawing another?
Answers
The probability of pulling out a red marble 3 times in a row will be 1/64.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Marbles: You have a bag with 3 red marbles, 4 blue marbles, and 5 green marbles.
Then the probability of pulling out a red marble 3 times in a row will be
The total number of events will be
Total events = 3 + 4 + 5 = 12
The favorable event will be
Favorable event = 3
Then the probability will be
P = (3/12)(3/12)(3/12)
P = (1/4)(1/4)(1/4)
P = 1/64
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A high school senior applies for admission to college A and to college B. He estimates that the probability of his being admitted to A is .7, that his application will be rejected at B with probability .5, and that the probability of at least one of his applications being rejected is .6. What is the probability that he will be rejected to at least one of the colleges
Answers
The probability that he will be rejected to at least one of the colleges is 0.51.
Given probability that he will admit in A is 0.7, probability that he will not be admit in B is 0.5, probability that atleast one of his applications got rejected is 0.6.
We have to find the probability that he will be rejected to at least one of the colleges.
Probability that he will admit in A =0.7
Probability that he will not admit in A=1-0.7=0.3
Probability that he will not admit in B =0.5
Probability that he will admit in B=1-0.5=0.5
Probability that he will be rejected to at least one of the colleges=probability that he will admit in A* probability that he will not admit in B+ probability that he will admit in B* probability that he will not admit in A+ probability that he will not admit in A* probability that he will not admit in B
=0.7*0.5+0.5*0.3+0.5*0.3
=0.35+0.15+0.15
=0.51
Hence the probability that he will be rejected to at least one of the colleges is 0.51.
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What kinds of ""failures"" occur when you experiment in order to learn under conditions of high uncertainty?.
Answers
Intelligent failure occur when you experiment in order to learn under conditions of high uncertainty
It's always possible to move forward from failure stronger and wiser. To do this, we must
a) descry and accept our failures snappily,
b)Dissect what happed and how it happed effectively to maximize what we can learn,
c)Apply our literacy to change our mindsets, behaviours, and the way we do our work, and
d)Continue to take smart pitfalls and introduce, icing we make better miscalculations on our coming bold attempt.
Unfortunately, our instinct tends to be to exit the circle at every step.
That’s why the skill of Intelligent Failure takes practice.
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