Find at least one solution to the following equation:
sin(x
2 − 1)
1 − sin(x
2 − 1) = sin(x) + sin2
(x) + sin3
(x) + sin4
(x) + · · ·
Answers
For |x| < 1, we have
[tex]1+x+x^2+\cdots=\displaystyle\sum_{n\ge0}x^n=\frac1{1-x}[/tex]
We have |sin(x)| ≤ 1, with equality when x = ± π/2. For either of these, the right side of the equation does not converge, since it's either an infinite sum of 1s or an infinite alternating sum of 1 and -1.
So for |sin(x)| < 1, we have
[tex]\sin(x)+\sin^2(x)+\sin^3(x)+\cdots=\dfrac1{1-\sin(x)}-1=\dfrac{\sin(x)}{1-\sin(x)}[/tex]
so the equation is equivalent to
[tex]\dfrac{\sin(x^2-1)}{1-\sin(x^2-1)}=\dfrac{\sin(x)}{1-\sin(x)}[/tex]
One obvious set of solutions occurs when x = x² - 1 :
x² - x - 1 = 0 → x = (1 ± √(5))/2
i.e. the golden ratio φ ≈ 1.618 and 1 - φ ≈ 0.618.
Related Questions
GIVING BRAINLIST PLEASE HELP (see picture above) !!!!
Answers
Answer:
Im sure that the answer is c
Answer:
C) 1 and 2
Plzzzz give me Brainliest!!!!!
is x + 8 ≥ 18 a closed or a open circle
Answers
Answer:closed
Step-by-step explanation:
find a factor of 5x^2+ 27x - 56
Answers
whoever answers first with an answer & explanation gets brainliest! iz a really easy question but you just have to be the fastest! The question is 2+2=? (btw imma come back in half an hour to award the brainliest)
Answers
Answer:
4
Step-by-step explanation:
Because if you have 2 apples and add 2 apples to that, you'll have a total of 4.
Answer:
4
Step-by-step explanation: thank you
Find the direction of AB where A(3,0) and B(4,1).
Answers
Answer:
Required Answer:-A (3,0)B (4,1)[tex]{:}\longrightarrow[/tex][tex]\sf AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf \sqrt {(4-1)^2+(1-0)^2}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf \sqrt {(3)^2+(1)^2}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf \sqrt {9+1}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf AB=\sqrt {10}[/tex]
I NEED THIS ASWERED NOW
0.07 + v = 0.28
v =
?
Answers
Answer:
V = 0.21
Step-by-step explanation:
subtract 0.07 from the other side to get v alone.
Use the elimination method to solve the system of equations. Choose the correct ordered pair. 2y = x + 2 x - 3y= -5 O A. (2, 2) O B. (4,3) O C. (6,4) O D. (8,5)
Answers
Answer:
(4,3)
Step-by-step explanation:
2y = x + 2
x - 3y = -5
Rearrange the second equation to equal y.
x - 3y = -5
x + 5 = 3y
(x+5)/3 = y
Substitute into the first equation.
2y = x +2
2[(x+5)/3] = x + 2
(2x + 10)/3 = x + 2
2x + 10 = 3(x + 2)
2x + 10 = 3x + 6
10 - 6 = 3x - 2x
4 = x
Therefore, the correct ordered pair is (4,3) since x is equal to 4.
For the function F defined by F(x)=x2−2x+4, find F(−2).
Answers
Answer:
F(-2) = 12
Step-by-step explanation:
F(-2) = (-2)²- 2(-2) + 4
= 4 - (-4) + 4
= 4 + 4 + 4
= 12
The required value of function F(x) = x² − 2x + 4 at F( -2 ) is 12.
A quadratic function is given F(x) = x² − 2x + 4, value of the function is to be determined at x = -2.
What is a polynomial function?
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.
F(x) = x² − 2x + 4
Above given function is a quadratic function,
in order to find F(-2) , we have to put x = -2 in above given function.
F( -2 ) = ( -2 )² − 2( -2 ) + 4
F( -2 ) = 4 + 4 + 4
F( -2 ) = 16
Thus, the required value of function F(x) = x² − 2x + 4 at F( -2 ) is 12.
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Caroline and Sarah in some money and share it in the ratio 2:1. Caroline gets £45 more than
Sarah How much did Sarah get ?
Answers
Answer:
£22.5
Step-by-step explanation:
We would have to split the ratio to 45:45/2 as 2:1 is 2:2/2
Which would give us the answer 45:22.5
Sarah got £22.5
What’s the greatest common factor of 36 , 48, an 80?
Answers
Answer: 4
Step-by-step explanation:
36,48,80
80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
What is sin45°*sin30°*cos60°
Answers
Answer:
[tex]\frac{\sqrt{2} }{8}[/tex]
Step-by-step explanation:
Using the exact values of the given trig functions, then
sin45° × sin30° × cos60°
= [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{\sqrt{2} }{8}[/tex]
can you solve what is 31 x 1/8
Answers
Answer:
3 6/8
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.8 inches, and standard deviation of 7.5 inches. A) What is the probability that a randomly chosen child has a height of less than 62.95 inches? Answer= (Round your answer to 3 decimal places.) B) What is the probability that a randomly chosen child has a height of more than 44.4 inches? Answer= (Round your answer to 3 decimal places.) Calculator Submit Question Question 10
Answers
Answer:
A) 0.889
B) 0.895
Step-by-step explanation:
Mean of 53.8 inches, and Standard deviation of 7.5 inches.
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
A) What is the probability that a randomly chosen child has a height of less than 62.95 inches?
For x < 62.95
z = 62.95 - 53.8/7.5
z = 1.22
Probabilityvalue from Z-Table:
P(x<62.95) = 0.88877
Approximately = 0.889
B) What is the probability that a randomly chosen child has a height of more than 44.4 inches?
For x > 44.4 inches
z = 44.4 - 53.8/7.5
z = -1.25333
Probability value from Z-Table:
P(x<44.4) = 0.10504
P(x>44.4) = 1 - P(x<44.4) = 0.89496
Approximately = 0.895
You are given the following sequences: Sequence A: 5, 11, 17, 23... Sequence B: 4000, 1000, 250, 62.5... Part A: Determine whether each sequence is arithmetic, geometric (2 pts) Part B: Write an explicit formula for each sequence (6 pts) Part C: Find the 6th term of each sequence (2 pts)
Answers
Answer:
I believe the first is arithmetic because it has a difference Of 6 between each number. The second is geometric because each number is divided by 4 to get the next number
Step-by-step explanation:
5, 11, 17, 23, 29, 35. (Difference of 6)
4000, 1000, 250, 62.5, 15.62, 3.90 (divide by 4)
As for the formulas I’m not sure, but I I would guess something like
an=6n-1
an=n/4
I am not sure about the formulas though
What’s the answer to this? Pls and thank you!
Answers
Answer:
Answer choice D
Step-by-step explanation:
You can see that the triangles have dashes on them. side DE has two and side AB also has 2. If you rotate triangle ABC, you can also see that AB and DE are congruent.
which of the following is an important step in the formation of a fossil
a.) the organism must be a reptile
b.) the organism must be buried quickly
c.) the organism must die of natural cause
d.) the organism must not have any fur
Answers
Answer:
b
Step-by-step explanation:
After a bone, wood fragment, or shell is buried in sediment, it may be exposed to mineral-rich water that moves through the sediment. This water will deposit minerals into empty spaces, producing a fossil. Fossil dinosaur bones, petrified wood, and many marine fossils were formed by permineralization.
Answer: fossils can be formed only when a living thing is buried soon after it dies. If it is not buried soon enough, it decays. For this reason, most fossils are found in sedimentary rocks that were once under water.
Step-by-step explanation:
Which function will have the steepest graph? O y=-2x O y=-* Oy = 3 x 2 2 Oy=
Answers
Answer:
Step-by-step explanation:
Y = 5/2x on edge
The steepest graph is given by y= 5/2x.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
First, y= -2x
Here the slope is -2.
Second, y = -1/2 x
Here the slope is -1/2.
Third, y= 3/2x
Here the slope is 3/2 or 1.5
Fourth, y= 5/2x
Here the slope is 5/2 or 2.5
As, we know A steeper slope in a graph means that the rate of change is faster.
Then, y= 5/2x have steeper slopes.
Learn more about Slope here:
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what the slope of (15,9) (-10,3)
Answers
Answer: 0.24
Step-by-step explanation: m = -6 / -25 = 0.24
Answer:
0.24
Step-by-step explanation:
cuz m = -6 / -25 = 0.24
hope this helps am in 8th grade and plz pick me as brainless
i need help with my homework
Answers
Answer:
(A = 2,3)(B = -2,-5)(C = 4,4)(D = -6,8)(E = 8,-6)(F = -8,-6)(G = 3, 2.5)
Modeling With Systems of Equations Quick Check
1 of 5Items
Assessment started: Modeling With Systems of Equations Quick Check.
Item 1
Two of the top-grossing concert tours were by a jazz band and a rock band. Together the two tours visited 177 cities. The jazz band visited 91 cities more than the rock band. Taking into account the constraint that the rock band must visit no less than 50 cities, find how many cities each group visited and determine whether the solution is viable or nonviable.(1 point)
The jazz band visited 134 cities and the rock band visited 43 cities. The solution is nonviable.
The jazz band visited 124 cities and the rock band visited 53 cities. The solution is viable.
The jazz band visited 124 cities and the rock band visited 53 cities. The solution is nonviable.
The jazz band visited 134 cities and the rock band visited 43 cities. The solution is viable.
Answers
Answer:
The jazz band visited 124 cities and the rock band visited 53 cities. The solution is viable.
Step-by-step explanation:
Answer:
The jazz band visited 124 cities and the rock band visited 53 cities. The solution is nonviable.
Step-by-step explanation:
5x + 2y = 6
Finding slope
Answers
Answer:
−5 /2 x + 3
Step-by-step explanation:
If by ‘finding slope’ you mean the slope-intercept form of the equation, then the following should be what you need.
5x+2y=6
2y=6-5x
Divide both sides by 2
y=3-5/2x
And by reordering the terms you get...
y=-5/2x+3
Select all that apply.
Which of the following are true?
Fractions and ratlos cannot have zero in the denominator.
Fractions and ratios can be simplified the same way.
Fractions and ratlos are different names for the same thing.
Some fractions and ratlos can be written as mixed numbers.
Answers
Answer:
A and D are the correct answers
Answer:
First, second and fourth are correct;
The third might be correct since fractions and ratios can often represent the same information in different ways and in some cases even in the same way, but this may not always be true.
Which of the relations below is a function?
{(2, 3), ( 3, 4), (6, 2), (3, 3)}
{(2, 3), (3, 4), (5, 1), (2, 4)}
{(2, 3), (3, 4), (6,2), (7,3)}
Answers
Answer:
k
Step-by-step explanation:
dw
Answer:
K
Step-by-step explanation:
Dw. Please give me like
challenge: if you can answer these you are genius
(4 x 6) x 2 =
8 x (7 x 3) =
(10 x 5) x 8 =
(9 x 2) x 7 =
(6 x 1) x 8 =
(7 x 11) x 2 =
5 x (9 x 6) =
4 x (12 x 3) =
Answers
2) 168
3) 400
4) 126
5) 48
6) 154
7) 270
8) 144
Answer:
1. 48
2. 168
3. 400
4. 126
5. 48
6. 154
7. 270
In ΔNOP, \text{m}\angle N = (5x-8)^{\circ}m∠N=(5x−8) ∘ , \text{m}\angle O = (x-5)^{\circ}m∠O=(x−5) ∘ , and \text{m}\angle P = (6x+1)^{\circ}m∠P=(6x+1) ∘ . Find \text{m}\angle O.m∠O.
Answers
Answer: m<O = 11
Step-by-step explanation: you add angle N, O, and P to equal to 180° and when you solve that equation you get 11. Hopes this helps love u ❤️
The measure of angle O from the given triangle is 9°.
Given that, m∠N=(5x-8)°, m∠O=(x-5)° and m∠P=(6x+1)°.
We need to find the measure of angle O.
What is the angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Now, m∠N+m∠O+m∠P=180°
⇒ (5x-8)°+(x-5)°+(6x+1)°=180°
⇒ 5x+x+6x-8-5+1=180
⇒ 12x-12=180
⇒ 12x=192
⇒ x=192/12
⇒ x=16
So, m∠O = 16-5=9
Therefore, the measure of angle O from the given triangle is 9°.
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What is the image of (-4,-7)(−4,−7) after a reflection over the x-axis?
Answers
Answer:
(-4,7)
Step-by-step explanation:
(-4,-7) is in the bottom left corner on a graph. The x axis goes horizontal so if it reflects it would be at (-4,7)
in the given figure ab parallel cd find the value of x
Answers
Step-by-step explanation: x = 73°
Draw PQ through E and parallel to AB, CD
Have x = ∠QED + ∠QEB
because PQ // CD => ∠QED = 50°
AB // PQ => ∠QEB + 157° = 180°
=> ∠QEB = 180 - 157 = 23°
=> x = 23° + 50° = 73°
( PQ is in the same direction as AB and CD )
angle efd = 130
180-50=130
angle ahe =23
180-157= 23
draw a imaginary line from h to f
this will create a triangle
now angle hfc = 90
90-50=40
now angle hfe =
90 - 23 = 67
therefore ,
x =
67+40+x=180
107 + x = 180
x = 180-107
x=73
Ieep doing this one wrong can someone tell me what it is? Please
Answers
Answer:
1.64 inches or about 1.6 inch
Step-by-step explanation:
The big skittle is 5.5 by 3 and the smaller one is 3 by ? which can be written out like [tex]\frac{5.5}{3}[/tex]=[tex]\frac{3}{?}[/tex] since the skittles proportional then ? = [tex]\frac{3times3}{5.5}[/tex]= 1.636363636...
so it's about 1.64
Which pair of lines are perpendicular?
A. x - y = 7 and y = x + 3
B. y = -4x + 1 and 8x + 2y = -10
C. y = -8 and y = 2
D. x = 4 and y = -1
Answers
I’m sorry if I’m wrong <3
What is the ratio of 3:6
Answers
Answer:
1:2
Step-by-step explanation:
You didn't really specify, but I'm going to assume you meant as simplified as possible. If you write it as a fraction, it will be ½ or as a decimal it will be 0.5.
Answer:
1:2
Step-by-step explanation:
Simplifying a ratio is like simplifying a fraction.
Simply put the number to the left as the numerator, and the number to the right as the denominator.
In this case, 3/6 = 1/2.
Hence, plug the numbers right back in and you get 1:2.
Hope this helped!