To find a power series solution to the differential equation (x² - 1)y'' + xy' - y = 0, we will assume a power series solution in the form y(x) = Σ(a_n * xⁿ), where a_n are coefficients.
1. Calculate the first derivative y'(x) = Σ(n * a_n * xⁿ⁻¹) and the second derivative y''(x) = Σ((n * (n-1)) * a_n * xⁿ⁻²).
2. Substitute y(x), y'(x), and y''(x) into the given differential equation.
3. Rearrange the equation and group the terms by the powers of x.
4. Set the coefficients of each power of x to zero, forming a recurrence relation for a_n.
5. Solve the recurrence relation to determine the coefficients a_n.
6. Substitute a_n back into the power series to obtain the solution y(x) = Σ(a_n * xⁿ).
By following these steps, we can find a power series solution to the given differential equation.
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Can someone please help me with this? Right answer gets brainliest!!
Answer:
Part 1: y= 49
Part 2: y=12
Step-by-step explanation:
Part 1: The y is going up by 7, so if you add 7 to 42, you get 49
Part 2: The y is going up by 4, so if you add 4 to 8, you get 12
A number cube is rolled. What is the probability that a number greater than 4 will be rolled?
5/6
1/3
2/3
1/6
Answer:
1/3
Step-by-step explanation:
Anything under 4 has a 4/6 chance, so whats left is 2/6, which is equal to 1/3.
Answer:
1/3
Step-by-step explanation:
im assuming its a 6 sided dice
so each side is numbered 1-6
u want the probabilty if it being greater than 4
4 of the 6 numbers aren't greater than 4 so 4/6of the time it will be less than 4
which and be simplified to 2/3
so 1/1-2/3=1/3
so there is a 1/3 propbability that it will be greater than 4
A wire is attached to the top of a tower and to a point on the ground that is 35 m from the base of the tower. If the wire makes a 65 degree angle with the ground, how long is the wire? Round your answer to the nearest tenth.
Answer:
83
Step-by-step explanation:
The length of the wire is 83meter.
Given that,
A wire is attached to the top of a tower and to a point on the ground that is 35 m from the base of the tower.
If the wire makes a 65-degree angle with the ground.
We have to determine,
How long is the wire?
According to the question,
The computation of the length of the wire is shown below:
Let, the length of the wire be x,
There is 35m from the base of the tower,
And, the angle with the ground is 65 degree
Therefore,
The length of the wire is given by,
[tex]cos65 = \dfrac{35}{x}\\\\[/tex]
Substitute the value of cos65 in the equation,
[tex]cos65 = \dfrac{35}{x}\\\\x = \dfrac{35}{cos65}\\\\x = \dfrac{35}{0.42}\\\\x = 83.33 \ meter[/tex]
Hence, The length of the wire is 83meter.
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Q) Mr. John went to a restaurant. The cost of a meal was $40.00. If the
sales tax is 9%, what is the total amount he paid for the meal?
A principal simulated a student raffle using 500 trials and recorded the grade level of the winner each time. The results are shown in the table.
Based on the data from the simulation, what is the probability that the winner will be in Grade 11?
Answer:
0.16
Step-by-step explanation:
Given the data:
Students __ `Gr_9 __Gr_10 __ G_11 __G_12
Frequency : 152 ___130 ______ 80 ___98
The probability is :
Frequency of grade 11 / number of trials
80 / 500
What is the complete factorization of the polynomial below?
x^3- 2x²+x-2
A. (x-2)(x + 1)(x - 1)
B. (x + 2)(x + 1)(x - 1)
C. (x + 2)(x - 1)(x - 1)
D. (x-2)(x - 1)(x - 1)
Answer:
Let's start by rearranging this polynomial.
x^3 - 2x^2 + x - 2
x^3 + x - 2x^2 - 2
Now, factor out the common terms in the first two terms, and the second t wo terms. So we have: x(x^2 + 1) - 2(x^2 +1)
Apply the distributive property, and you have: (x-2)(x^2+1), which can't be factored further.
There's definitely something wrong with the answer choices here, or the problem itself.
Hopefully this helps!
The complete factorization of the polynomial is,
⇒ (x + i) (x - i) (x - 2)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The polynomial is,
⇒ x³ - 2x² + x - 2
Now, We can factor the polynomials as;
The polynomial is,
⇒ x³ - 2x² + x - 2
⇒ x² (x - 2) + 1 (x - 2)
⇒ (x² + 1) (x - 2)
⇒ (x + i) (x - i) (x - 2)
Therefore, The complete factorization of the polynomial is,
⇒ (x + i) (x - i) (x - 2)
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What is the slope of a line perpendicular to the line whose equation is 4x−y=9. Fully reduce your answer.
Answer:
slope of given line is 4.
so slope of line perpendicular to it will be -1/4
*find the area thats all *
Answer:
The area is 155 square feet
Step-by-step explanation:
[tex]\frac{(13+18)} {2}[/tex] × 10
[tex]\frac{31}{2}[/tex] × 10
15.5×10=155
Hope this helps! :)
1/2 as a decimal <3 thank you
Answer:
0.5 is the decimal form of 1/2
Answer:
0.5 I hope this helps!
Step-by-step explanation:
A costume designer is using exactly 264 yards of green fabric to make 36 frog costumes. If each costume requres the same amount of fabric, how many yards will be used for each one?
Answer:
Each costume will take 7 1/3 yards of green fabric
Step-by-step explanation:
They would each take this much because 264/36 is 7 1/3 which shows the total amount of fabric divided into each of the 36 costumes evenly.
4) -4(2a + 3) ????????????????????
Answer:
-4(2a + 3)
= -4a(2) -4(3)
= - 8a - 12
Hope it helps!
Step-by-step explanation:
-4(2a + 3)
= -4 × 2a + 3 × (-4) [-4 gets multiplied with both 2a and 3]
= -8a -12 (Ans)
I need help
I need u to answer this question. what's 2+2????
Answer:
2+2=4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
it's 4 lol, open 2 fingers and open another 2 fingers then count them
Construct a parallelogram whose diagonals
are 5.4 cm and 6.2 cm and an angle between
them is 70°.
Answer:
15.73 cm²
Step-by-step explanation:
Construct a parallelogram whose diagonals are 5.4 cm and 6.2 cm and an angle between them is 70°.
To construct the parallelogram, we find the Area of the parallelogram.
Area of a parallelogram = ½ × d1 × d2 × sin (y)
Where
d1 = Diagonal 1 = 5.4 cm
d2 = Diagonal 2 = 6.2 cm
y = Angle between them = 70°
Area of the parallelogram =
1/2 × 5.4 × 6.2 × sin 70
= 15.730454472 cm²
Approximately = 15.73 cm²
Simplify
(c+d)-(c-d)
Answer:
2d
Step-by-step explanation:
(c+d)-(c-d)
Distribute the minus sign
c+d-c+d
Combine like terms
c-c +d+d
2d
Rewrite as a log: y=7^x
Answer:
log7(y)=x
Step-by-step explanation:
Can someone help me with this answer thank you
Answer: bro cmon this is simple m8 but i will still help :D
Step-by-step explanation:35x3=105 and 28x5=140 the outfit couldve been 245 dollars in total!
write the coordinates of the image of P(-2,5) reflected in the line of y=2
Answer:
Q(-2, -1)
Step-by-step explanation:
P(-2, 5) is 3 units ABOVE the line y = 2. If we reflect this point in the line y = 2, we end up with a point Q(-2, -1), where the '-1' comes from subtracting 3 from 2.
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points. The new coordinate of the point P is (-2,-1).
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
If the point and the line are plotted on the graph as shown below. It can be observed that point P is 3 units away from the line.
Now, since the point is reflected along the horizontal line, therefore, the x-coordinate of the point will not change, while the y-coordinate will be 3 units below the line.
Thus, the new coordinate of the point can be written as,
New-coordinate = (-2, 2 - 3) = (-2, -1)
Hence, the new coordinate of the point P is (-2,-1).
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Select all the numbers that round to 387.4 when rounded to the nearest tenth
The numbers that round to 387.4 when rounded to the nearest tenth are in the following interval.
387.35 <= x < 387.4
How to round the numbers?To round a number to the nearest tenth, we must observe the second decimal digit of the number:
If the second decimal digit is less than five, the first digit remains constant and the other decimal digits are removed, example, 387.34 = 387.3.If the second decimal digit is at least five, one is added to the first digit and the other decimal digits are removed, example, 387.35 = 387.4.More can be learned about rounding at https://brainly.com/question/28128444
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What is UT?
U
8
17
UT equals
Answer:
8 is the correct answer of this question
Answer:
8
Step-by-step explanation:
Helpppp?? I need help on this cause I just don’t wanna solve it
Answer:
3 and 3/5
Step-by-step explanation:
I dont understand the work my teacher gave me and I Have 45 pages to do
Answer:
just send them here , I will answer the ones I know .
I REALLY NEED HELP!!! THIS IS DUE AT 12!!!
Jeremiah scored 32 points in yesterday’s basketball game. He made a total of 19 baskets.Some of the baskets were field goals (worth two points) and the rest were free throws (worth one point). Write and solve a system of equations to find the number of field goals and the number of free throws that Jeremiah made. Let x represent Field Goals and y represent Free Throws.
Answer:
x=16
y=3
Step-by-step explanation:
32÷2=16
19-16=3
x=16
y=3
Quadrilateral JKLM has vertices at J(0,0), K(0,6), L(9,12), and M(12,0). Find the vertices of the quadrilateral after a dilation with scale factor 2/3.
Answer choices
J'(0, 0), K'(0, 9), L'(27/2, 18), and M'(18, 0)
J'(0, 0), K'(0, 4), L'(6, 8), and M'(8, 0)
J'(0, 0), K'(0, −4), L'(−6, −4), and M'(−8, 0)
J'(2/3, 2/3), K'(2/3, 20/3), L'(9/3, 38/3), and M'(38/3, 2/3)
Answer:
The vertices of the quadrilateral after a dilation with scale factor [tex]\frac{2}{3}[/tex] are [tex]J'(x,y) = (0,0)[/tex], [tex]K'(x,y) = (0,4)[/tex], [tex]L'(x,y) = (6, 8)[/tex] and [tex]M'(x,y) = (8,0)[/tex].
Step-by-step explanation:
Let suppose that center of dilation is located at origin, that is [tex]O(x,y) = (0,0)[/tex]. Vectorially speaking, dilation is described by following expression:
[tex]D'(x,y) = O(x,y) + r\cdot [D(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Center of dilation.
[tex]D(x,y)[/tex] - Original point.
[tex]D'(x,y)[/tex] - Dilated point.
[tex]r[/tex] - Dilation factor.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]r = \frac{2}{3}[/tex], [tex]J(x,y) = (0,0)[/tex], [tex]K(x,y) = (0,6)[/tex], [tex]L(x,y) = (9,12)[/tex] and [tex]M(x,y) = (12,0)[/tex], then the dilated points are, respectively:
[tex]J'(x,y) = O(x,y) + r\cdot [J(x,y)-O(x,y)][/tex]
[tex]J'(x,y) = (0,0) +\frac{2}{3}\cdot [(0,0)-(0,0)][/tex]
[tex]J'(x,y) = (0,0)[/tex]
[tex]K'(x,y) = O(x,y) + r\cdot [K(x,y)-O(x,y)][/tex]
[tex]K'(x,y) = (0,0)+\frac{2}{3}\cdot [(0,6)-(0,0)][/tex]
[tex]K'(x,y) = (0,4)[/tex]
[tex]L'(x,y) = O(x,y) +r\cdot [L(x,y)-O(x,y)][/tex]
[tex]L'(x,y) = (0,0) + \frac{2}{3}\cdot [(9,12)-(0,0)][/tex]
[tex]L'(x,y) = (6, 8)[/tex]
[tex]M'(x,y) = O(x,y) +r\cdot [M(x,y)-O(x,y)][/tex]
[tex]M'(x,y) = (0,0) +\frac{2}{3}\cdot [(12,0)-(0,0)][/tex]
[tex]M'(x,y) = (8,0)[/tex]
The vertices of the quadrilateral after a dilation with scale factor [tex]\frac{2}{3}[/tex] are [tex]J'(x,y) = (0,0)[/tex], [tex]K'(x,y) = (0,4)[/tex], [tex]L'(x,y) = (6, 8)[/tex] and [tex]M'(x,y) = (8,0)[/tex].
Option B will be the correct option.
Dilation of a point about the origin by a scale factor 'k',If a point (a, b) is dilated by a scale factor 'k' about the origin, coordinates of the image point will be,
(a, b) → (ka, kb)
Following the rule for dilation,
If a quadrilateral J(0, 0), K(0, 6), L(9, 12) and M(12, 0) is dilated by a scale factor [tex]\frac{2}{3}[/tex], coordinates of the image points will be,
[tex]J(0,0)\rightarrow J'(0, 0)[/tex]
[tex]K(0,4)\rightarrow K'(0, 4)[/tex]
[tex]L(9,12)\rightarrow L'(6,8)[/tex]
[tex]M(12,0)\rightarrow M'(8,0)[/tex]
Therefore, Option B will be the correct option.
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can someone help me, file attached
Answer:
C. log 10m is the correct answer.
Step-by-step explanation:
The laws of logarithm states that if you have:
[tex] log(a) + log(b ) = log(a \times b) = log(ab) [/tex]
So, comparing that to your question,
[tex] log(m) + log(10) = log(10m) .[/tex]
please helppppppppppppppppp??????/
Answer:
Its C trust me cuh
Step-by-step explanation:
Please give me Brainlist bro I just need 2 more
I hope u have a good day
Which of the following is the graph of y = negative StartRoot x EndRoot + 1? On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = negative 1. On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = 1. On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at y = 1. On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at y = negative 1.
Answer:
B. On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = 1.Step-by-step explanation:
Graph of the function:
y = -√x + 1The domain is x ≥ 0, the range y ≤ 1
Correct answer choice is B
On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = 1.The graph is attached
Answer: it’s B
Step-by-step explanation: got it right on edge 2021
HELP I NEED HELP ASAP
Answer:
A. The number of people infected increases expontially by approximately 80/ per month
Step-by-step explanation:
I'll just remind
The bakers at Healthy Bakery can make 340 bagels in 10 hours . How many bagels can they bake in 24 hours ? What was that rate per hour ?
PLEASE HELP ME
Answer: 816
Step-by-step explanation:340+340=680 in 20 hours and 340 divided by 10=34/hour so 34x4=136
So.., 680+136=816
Frank the earth, llc signed a three-year lease for office space. This lease is considered an what?
Answer: Long-term Liability
Step-by-step explanation:
This question relates to the classification of the lease above in accounting.
A long term liability is a payment that is owed by a company for a period lasting more than a year.
When a lease is for more than a year as is the case here, you take the present value of the lease and consider that amount to be a long term liability because it would represent an amount that the company is to pay for more than a single period.,
A local natural market employs 80 people. It expands this year and needs to hire 10% more people. How many people will work at the market after they hire the new people?
Answers:
A. 98
B. 90
C. 81
D. 88