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
Write an equation of the line passing through the point (2,8) that is perpendicular to the line 2x-3y=7
Answers
Answer:
y = (-3/2x) + (35/4)
Step-by-step explanation:
So the perpendicular line will have a slope that is the opposite reciprocal of the other line's slope. Solve for the original line's slope first:
2x - 3y = 7 --> -3y = -2x + 7 --> y = (2x/3) - (7/3)
So, the slope of the perpendicular line will be (-3/2x)
Solve for the y-intercept of the perpendicular like by using the linear equation and substituting in (2,8):
8 = (-3/(2*2)) + b --> (32/4) = -(3/4) + b --> b = (35/4)
So, y = (-3/2x) + (35/4)
Hope that helps! :D
Constant of proportionality characteristics what are some?
Answers
Answer: The constant of proportionality is the ratio between two directly proportional quantities.
Two quantities are directly proportional when they increase and decrease at the same rate.
Step-by-step explanation:
a line passes through the points 1 , -6 and 4,3 what is the Y intercept of this line
Answers
Answer:
y-intercept = -13
Step-by-step explanation:
So you have to put it in slope-intercept form to solve.
slope is 4 so you plug in the one of the coordinate points in for x and y in the equation to find b.
Put it in order yes or no?and how do yk if it is or not
Answers
9514 1404 393
Answer:
yes, yes, no, no
Step-by-step explanation:
An equation is linear if no term has a variable with an exponent other than 0 or 1. There can be no products of variables.
The equations with terms x³ or x² will not be linear.
(a, b) linear (yes)
(c, d) not linear (no)
9 t-shirts and a hat costs £93.00
4 t-shirts and a hat costs £43.00.
How much does a t-shirt cost?
How much does a hat cost?
Answers
Answer:
A t-shirt costs 10.00 pounds and a hat costs 3.00 pounds.
Step-by-step explanation:
x is a t-shirt
y is a hat
9x + y = 93.00
4x + y = 43.00
(9x + y) - (4x + y) = 93.00 - 43.00
9x + y - 4x - y = 50.00
5x = 50.00
x = 50.00/5
x = 10.00 [a t-shirt costs 10.00]
4x + y = 43.00
4×10.00 + y = 43.00
40.00 + y = 43.00
y = 43.00 - 40.00
y = 3.00 [a hat costs 3.00]
A college student takes out a $7,500 loan from a bank. What will the balance of the loan be after one year (assuming the student has not made any payments yet):
if the bank charges 5.3% interest each year?
Answers
Answer:
the balance of the loan be after one year is $7897.5.
Step-by-step explanation:
Given that a=10, b=40, and A=30 degrees, how many triangles can possibly be formed?
Answers
Answer:
None
Step-by-step explanation:
The minimum requirement is 180.
Select the section(s) of the graph where the function is decreasing.
1. blue line
2. red line
3. curved blue line
4. green line
can be more than one
Answers
Hope this helps, and happy holidays:)
The graph where the function is decreasing is represented by, the blue line, red line and the green line.
What is decreasing function?"If the value of the function f(x) is decreasing on increasing the value of x, then the function is called as decreasing function."
For given situation,
we have been given a piecewise function and its graph.
From the graph of a function,
we can observe that the function f(x) is decreasing for x < -3 , -3 ≤ x ≤ 0, and x > 0
This is represented by, the blue line, red line and the green line
Therefore, the correct options are 1, 2, 4.
Learn more about decreasing function here:
https://brainly.com/question/13391696
#SPJ2
Help me please
Make x the subject of the formula
X – 7r = bc
Answers
Answer:
x = bc + 7r
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesStep-by-step explanation:
Step 1: Define equation
x - 7r = bc
Step 2: Solve for x
Add 7r to both sides: x = bc + 7rWhat is the formula of area of a quadrant?
Answers
Answer:
that is, pi (π) multiplied by the radius squared (r2). Now, to calculate the area of a quadrant, divide the area of a circle by 4 (as four quadrants make a circle). We get, Area of a quadrant, A= (πr2)/4 Square units.
Consider the line segment below.
А
M
B
(7x + 8) cm
(9x – 8) cm
Part A - If AB is 128 centimeters long, what is the value of a?
Part B - What is the length of AM?
AM
cm.
Part C - What is the length of BM?
BM
cm.
Part D - Is point M the midpoint of AB? Justify your answer.
Answers
Answer:
Part A
x = 8
Part B
AM = 64 cm
Part C
BM = 64 cm
Part D
AB = AM + BM
Step-by-step explanation:
Consider the line segment below.
АM = (7x + 8) cm
BM = (9x – 8) cm
Part A - If AB is 128 centimeters long, what is the value of x?
AB = AM + BM
128 = (7x + 8) + (9x - 8)
128 = 7x + 9x + 8 - 8
128 = 16x
x = 128/16
x = 8
Part B - What is the length of AM?
АM = (7x + 8) cm
AM = 7(8) + 8 cm
AM = 56 + 8 cm
AM = 64 cm.
Part C - What is the length of BM?
BM = (9x – 8) cm
BM = 9 × 8 - 8 cm
BM = 72 - 8 cm
BM = 64 cm.
Part D - Is point M the midpoint of AB? Justify your answer.
A.............. M............... B
Hence: From the Above illustration,
M is the Midpoint because it divided AB into 2 equal parts
= AM and BM
Hence:
AB = AM + BM
Mickey simplified the expression below. He then checked his work by substituting 4 for x. He noticed his two values were not equal. What was Mickey's error when simplifying? Expression Simplified Expression 2 x squared minus 4 x minus 9 minus x squared + 2 x + 3 x squared minus 6 x minus 6 Mickey should have added –4 and 2 when combining the coefficients of the x terms. Mickey should have added 2 and 1 when combining the x squared terms. Mickey should have added 9 and 3 when combining the constant terms. Mickey should have added –4 and –1 when combining the x terms. Mark this and return
Answers
Full question attached:
Mickey simplified the expression below. He then checked his work by substituting 4 for x. He noticed his two values were not equal. What was Mickey’s error when simplifying?
Expression: 2x^2 - 4x - 9 - x^2 + 2x + 3
Simplified expression: x^2 - 6x - 6
ANSWER CHOICES:
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Mickey should have added 2 and 1 when combining the x^2 terms.
Mickey should have added 9 and 3 when combining the constant terms.
Mickey should have added –4 and –1 when combining the x terms.
Answer
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Explanation:
To simplify an expression means to group and organize the expression in a such a way that it becomes more understandable, and can now easily be solved
Given the expression 2x² - 4x - 9 - x² + 2x + 3 to simplify
We first group and find like terms and then add and cancel out
2x²-x²- 4x+2x - 9+ 3
=x²-2x-6
Mickey did not add the coefficients -4 and +2 for x terms in the expression, instead it looked like he added 4+2 as the coefficients
Therefore the correct option is
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Answer:
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Step-by-step explanation:
Please help:) Due soon!:)
Is it:
A: y-4= -2/3(x+3)
B: y-2= -2/3(x-6)
C: y+4= 2/3(x-3)
D: y+6= 2/3(x-2)
Answers
Describe the transformation of each function compared to its parent function.
I need help please!
Answers
Step-by-step explanation:
In general, for all problems like this, remember the acronym VOHI:
vertical outside, horizontal inside.
1. The parent function here would be [tex]f(x)=x^{2}[/tex]. 4 has been subtracted from the inside, so it is a horizontal change. You might think that it is moving left 4, but it's actually moving right 4. There is a reason for this, but it's not necessary for you to know right now. All you need to remember is that when inside the parentheses, minus means moving right, and plus means moving left. You also have a 9 added to the outside. Vertical outside. This is a vertical change, meaning up and down. This function has been moved right 4 and up 9.
2. First, the parent function is again [tex]f(x)=x^{2}[/tex]. This time, we have [tex]\frac{1}{4}[/tex] on the outside of our function. This means it is a vertical transformation. When the value on the outside is > 1, it is a vertical stretch. When the value is between 0 and 1 (0<a<1), it is a vertical shrink. [tex]\frac{1}{4}[/tex] is between 0 and 1. So, this is a vertical shrink by a factor of [tex]\frac{1}{4}[/tex]. Next, there is a 6 on the inside of the parentheses, meaning a horizontal translation. Remember from problem 1, though, minus=right and plus=left. So, this function has been vertically shrunk by [tex]\frac{1}{4}[/tex] and moved left 6.
3. Again, parent function: [tex]f(x)=x^{2}[/tex]. This one just has [tex]\frac{3}{2}[/tex] on the outside. We know that it's on the outside because otherwise there would be parentheses around both [tex]\frac{3}{2}[/tex] and x. There is not, so it is outside. Outside, vertical. This is a vertical change. Looking back at problem two, when a value is >1, which this is, it is a vertical stretch. So this function has a vertical stretch by [tex]\frac{3}{2}[/tex].
I hope this helps!
Transformation involves changing the position and/or size of a function.
The transformations are:
Translate f(x), 4 units right, and 9 units up.Translate f(x), 4 units left, then compress f(x) vertically by 1/4Vertically stretch f(x) by 3/2[tex]\mathbf{1.\ f(x) = (x - 4)^2 +9}[/tex]
The above function is a square function, and the parent function is:
[tex]\mathbf{f(x) = x^2}[/tex]
First, the function is translated right by 4 units (this is represented by subtracting 4 from x.
i.e.
[tex]\mathbf{f(x) = (x - 4)^2}[/tex]
Next, the function is translated up by 9 units (this is represented by adding 9 to the value of y.
i.e.
[tex]\mathbf{f(x) = (x - 4)^2 + 9}[/tex]
So, the transformation from the parent function is: Translate f(x), 4 units right, and 9 units up.
[tex]\mathbf{2.\ f(x) = \frac 14(x + 4)^2}[/tex]
The above function is a square function, and the parent function is:
[tex]\mathbf{f(x) = x^2}[/tex]
First, the function is translated left by 4 units (this is represented by adding 4 from x.
i.e.
[tex]\mathbf{f(x) = (x + 4)^2}[/tex]
Next, the function is vertically compressed a factor of 1/4 (this is represented by multiplying the function by 1/4
i.e.
[tex]\mathbf{f(x) = \frac 14(x + 4)^2}[/tex]
So, the transformation from the parent function is: Translate f(x), 4 units left, then compress f(x) vertically by 1/4
[tex]\mathbf{3.\ f(x) = \frac 32x^2}[/tex]
The above function is a square function, and the parent function is:
[tex]\mathbf{f(x) = x^2}[/tex]
The function is vertically stretched a factor of 3/2 (this is represented by multiplying the function by 3/2
i.e.
[tex]\mathbf{f(x) = \frac 34 \times x^2}\\[/tex]
[tex]\mathbf{f(x) = \frac 34 \timex x^2}[/tex]
So, the transformation from the parent function is: Vertically stretch f(x) by 3/2
Read more about transformations at:
https://brainly.com/question/13801312
Will give brainliest if correct.
Answers
The sencond one is D.
The first one is probable A hope i'm right on this on.
Jack works at a sporting goods store and makes a commission of 20 percent. His sales for each week are shown below. How much did Jack make in total in commission during all four weeks?
Week
Sales
1
$3,000
2
$2,500
3
$3,500
4
$4,000
$200.00
$260.00
$2,000.00
$2,600.00
Answers
Answer:
The answer is D
Step-by-step explanation:
Answer:
D.) $2,600.00
Step-by-step explanation:
Round each of these numbers to the degree of accuracy shown in the brackets
a) 4865
(Nearest ten)
Answers
Answer:
irst, 4865 rounded to the nearest ten is:
4870
Step-by-step explanation:
Here we will tell you what 4865 is rounded to the nearest ten and also show you what rules we used to get to the answer.
Remember, we did not necessarily round up or down, but to the ten that is nearest to 4865.
When rounding to the nearest ten, like we did with 4865 above, we use the following rules:
A) We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.
B) We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.
C) If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.
A picture 10 inches tall and 14 inches wide is to be scaled to 1.5 inches tall to be displayed on a webpage. How wide should the picture be on the webpage for the two pictures to be similar?
Answers
Answer:
1.8
Step-by-step explanation:
brain liest for who ever does all (NOTE: this is not a test!! ) thanks :D
Answers
I can't see what you posted it's blocked off but I could probably answer it if I knew what the questions were
500000 x 396 / sqrt of 72
Cheeseburger01, If you are there and you find this please repply or answer!
It says your account was deleted and i'm worried.....
Answers
Answer:
the answer of 500000x396 is 198,000,000
Answer:
hey, will you tell (at symbol)MichiChan i cant go on pixelart? i keep getting an error 400 on it and i cant do anything. i dont want her to think im ignoring her...thanks
Step-by-step explanation:
:P
Find one root of the following equation x2 + 8x - 9 = 0
Answers
Answer: was just for a challenge
Step-by-step explanation:
no
Step-by-step explanation:
[tex]x {}^{2} + 8x - 9 = 0 \\ {x}^{2} - x + 9x - 9 = 0 \\ x(x - 1) + 9(x - 1) = 0 \\ (x + 9)(x - 1) = 0 \\ x = 1 \: and \: \: \: \: - 9[/tex]
The senior classes at High School A and High School B planned separate trips to the local amusement park. The senior class at High School A rented and filled 13 vans and 5 buses with 370 students. High School B rented and filled 12 vans and 10 buses with 600 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
please show you work
Answers
Answer:
10 students/van
48 students/bus
Step-by-step explanation:
(a) 13v+5b = 370
(b) 12v+10b = 600
(a) - (b)
v -5b = -230
v = 5b-230
12(5b-230) + 10b = 600
60b+10b -2760=600
70b=3360
7b=336
b=48
v = 5(48) - 230 = 10
v = 10
Let's check
12(10) +10(48) = 600
is this correct? ILL MARK YOU BRAINIEST
Answers
Answer:
yes
Step-by-step explanation:
This is correct.
Since every operation in this is multiplication, you can remove the parentheses. This is the associative property of multiplication. Now you can group the exponents and the normal factors together.
[tex](1.5*2.0)*(10^{0} *10^{-5})[/tex]
[tex]3.0*10^{-5}[/tex]
So the answer you put is correct. But, if your test is online and has a dumb grading system (like edulastic) I suggest you put 3.0 instead of 3.
y = 3x – 21 is it proportional
Answers
Answer:
yes
Step-by-step explanation:
The diagram shows a triangle.
4s+9°
3s+1°
6s+1°
What is the value of s?
the number that s is has to equal to 180 once worked out
Answers
Answer:
s=13
Step-by-step explanation:
[tex]As\ we\ know\ that,\\"The \ sum\ of\ all\ angles\ of\ a\ triangle\ is\ 180"\\Hence,\\(4s+9)+(3s+1)+(6s+1)=180\\4s+3s+6s+9+1+1=180\\13s+11=180\\13s=180-11\\13s=169\\s=13[/tex]
please help. i would rly appreciate it. :/
Answers
What is the value of (–4) with an exponent of -3
Answers
Answer:
-64
Step-by-step explanation:
Because an exponent is basically a number repeated multiple times. So -4 x -4 x -4 would equal -64.
PLEASSSSSSSSSSSSSSSSSSSSSSSSSSeeee help 10+ points for you
Answers
Answer:
f < -2
Step-by-step explanation:
f+ 4 < 2
-4. -4
f < -2
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Answer:
the second
Step-by-step explanation:
US
Find the value of x.
es
les
2x - 4
10
Answers
Step-by-step explanation:
[tex]{:}\longrightarrow[/tex][tex]\sf 2x-4=10 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2x=10+4 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2x=14 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {14}{2}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=7 [/tex]
Kurt says that if he starts with the number n, multiplies it by the next whole number and then adds 3 he will get 45. N(n+1)+3=45 what number makes kurts equation true?
Answers
Answer:
6
Step-by-step explanation:
we start with:
n(n + 1) + 3 = 45
n² + 1n = 42
n² + 1n - 42 = 0
n can be either 6 or -7
(n - 6)(n + 7)
since we cannot have negative numbers, the answer should be 6, but we can verify which number fits our equation:
n = 7 ⇒ n(n + 1) + 3 = 45
7(7 + 1) + 3 = 59 WRONG
n = 6 ⇒ n(n + 1) + 3 = 45
6(6 + 1) + 3 = 45 ✓ CORRECT
Answer:
6
Step-by-step explanation: