Answers
Answer:
26
Step-by-step explanation:
Related Questions
Solve the following Differential Equations using the Frobenius Method.
1. 2xy''+5y'+xy=0
2. 4xy''+1/2y'+y=0
Answers
1. The general solution of the differential equation is:
y(x) = c₁x^(-3) + c₂x^(-2).
2.The general solution of the differential equation is:
y(x) = c₀x^(-1)ln(x) + c₁x^(-1),
To solve the given differential equations using the Frobenius method, we assume a power series solution of the form:
y(x) = ∑(n=0)^(∞) aₙx^(r+n),
where aₙ is the nth coefficient of the series, r is a constant, and x is the independent variable.
1. For the equation 2xy'' + 5y' + xy = 0:
Substituting the power series solution into the equation and simplifying, we obtain:
x²∑(n=0)^(∞) aₙ(r+n)(r+n-1)x^(r+n-2) + 5∑(n=0)^(∞) aₙ(r+n)x^(r+n-1) + x∑(n=0)^(∞) aₙx^(r+n) = 0.
Now, equating the coefficient of each power of x to zero, we get:
∑(n=0)^(∞) (aₙ(r+n)(r+n-1)x^(r+n-2) + 5aₙ(r+n)x^(r+n-1) + aₙx^(r+n)) = 0.
This gives us a recurrence relation:
aₙ(r+n)(r+n-1) + 5aₙ(r+n) + aₙ = 0.
Simplifying, we find:
aₙ[(r+n)² + 5(r+n) + 1] = 0.
Setting the coefficient to zero, we have:
(r+n)² + 5(r+n) + 1 = 0.
Solving this quadratic equation, we obtain the values of r:
r₁ = -3, r₂ = -2.
Therefore, the general solution of the differential equation is:
y(x) = c₁x^(-3) + c₂x^(-2),
where c₁ and c₂ are constants.
2. For the equation 4xy'' + (1/2)y' + y = 0:
Following the same steps as above, we obtain the recurrence relation:
aₙ[(r+n)(r+n-1) + (1/2)(r+n) + 1] = 0.
Simplifying, we find:
aₙ[(r+n)² + (3/2)(r+n) + 1] = 0.
Setting the coefficient to zero, we have:
(r+n)² + (3/2)(r+n) + 1 = 0.
Solving this quadratic equation, we find the value of r:
r = -1.
Therefore, the general solution of the differential equation is:
y(x) = c₀x^(-1)ln(x) + c₁x^(-1),
where c₀ and c₁ are constants.
These are the solutions obtained using the Frobenius method for the given differential equations.
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Let : R² R2 given by (r,0) = (r cos(0), r sin(0)), 0≤ r ≤ R, 0≤0 ≤ 2m (this is a disk of radius R centered at (0,0)). Compute ∫ fdx .
Answers
To compute the integral ∫ fdx over the disk D of radius R centered at (0,0), we need to express the function f in terms of the given coordinate transformation.
In polar coordinates, a point (r, θ) in the disk D can be represented as (r cos(θ), r sin(θ)).
Now, let's substitute these polar coordinates into the integral. The differential element dx becomes r cos(θ)dr, and the integral becomes:
∫ fdx = ∫ f(r cos(θ), r sin(θ)) r cos(θ)dr dθ
We can now evaluate this integral by integrating over the range of r and θ. The range for r is from 0 to R, and the range for θ is from 0 to 2π (since we are integrating over the entire disk).
Thus, the integral becomes:
∫ fdx = ∫[0 to R] ∫[0 to 2π] f(r cos(θ), r sin(θ)) r cos(θ)dr dθ
By evaluating this double integral, we can find the value of ∫ fdx over the given disk D.
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brand of water-softener salt comes in bags marked "net weight 18kg". The
company that packages the salt claims that the bags contain an average of 18kg of
salt and that the standard deviation of the weight of the bag is 0.68kg. Assume that
the weight of the bags is normally distributed and unless otherwise indicated use ? =
.05.
It is given that:
μ=18
0.68
n = 10
In general, what mean weights of 10 randomly select bags would you
consider evidence against the company’s claim?
Answers
Any mean weight falling outside the interval of (17.06, 18.94) would be considered evidence against the company's claim.
μ = 18 and σ = 0.68. n = 10. The formula for the z-test is given by:
z = (x - μ) / (σ/√n)
Where:
z = z-test score
x = sample mean
μ = population mean
σ = standard deviation
n = sample size
Let's calculate the upper and lower limits by using the above formula:
Lower limit = μ - z_(α/2) * (σ / √n)
Upper limit = μ + z_(α/2) * (σ / √n)
Where z_(α/2) is the standard normal variate which can be found from the standard normal table (at 5% significance level) to be 1.96.
Therefore,
Lower limit = 18 - 1.96 * (0.68/√10) = 17.06
Upper limit = 18 + 1.96 * (0.68/√10) = 18.94
Thus, any mean weight of 10 randomly selected bags that falls outside the interval of (17.06, 18.94) would be considered evidence against the company's claim.
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Find the measure of the missing angle
Help please
Answers
Answer:
≈ 56°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{34}{41}[/tex] , then
? = [tex]sin^{-1}[/tex] ( [tex]\frac{34}{41}[/tex] ) ≈ 56° ( to the nearest degree )
Which value of x makes the equation -2(1-4x)=3x+8 true?
Answers
Answer:
x = 2
Step-by-step explanation:
distribute -2 first
-2 + 8x = 3x + 8
-2 + 5x = 8
5x = 10
x = 2
How do I write [tex]\sqrt[4]{5}[/tex] using rational exponets?
Answers
Hope this help
Answer:
y=45u
Step-by-step explanation:
4 with a 5 try adding / bc its supposed to be like a check sin
A figure has a perimeter of 40 units and an area of 100 units2 . Which of the following describes the new perimeter and area after the figure is dilated by a scale factor of
A)Perimeter: 20 units; Area: 50 units2
B)Perimeter: 20 units; Area: 25 units2
C)Perimeter: 10 units; Area: 25 units2
D)Perimeter: 80 units; Area: 200 units2
PLEASE HELP MEEE < ILL GIVE 25 POINTS
Answers
Answer:
B
Step-by-step explanation:
You didn't write the full question but B is the only one that make since.
Can someone please help!!!
Ill give brainliest!!
Answers
Answer:
please what is the exact question
Answer:
161.56 ft^2
Step-by-step explanation:
base area = (leg 1 x leg 2)/2 = (5 x 5)/2 = 25/2 = 12.5 ft^2
base perimeter = 5 + 5 + 7.07 = 17.07 ft
lateral surface = (perimeter x height) = 17.07 x 8 = 136.56 ft^2
surface area = base area x 2 + lateral surface = (12.5 x 2) + 136.56 = 161.56 ft^2
Can someone help me out please
Answers
Answer:
area = (14 x 16) - (0.5 x 16 x 6) = 176 ft²
Step-by-step explanation:
Answer:
A = 176 ft²
Step-by-step explanation:
2 shapes: one rectangle and 1 triangle:
Rectangle:
A = bh
A = 16(14)
A = 224
Triangle:
A = 1/2bh
A = 1/2(16)(6)
A = 48
Combined:
224 - 48
176
A square ceiling has a diagonal of 23 ft. Shelton wants to put
molding around the perimeter of the ceiling. The molding is sold
by the foot
What is the minimum amount of molding he needs?
66 ft
l65 ft
17 ft
16 ft
Answers
Answer:
66ft
Step-by-step explanation:
I took the quiz
Which of the following is a
representation of 11!
Answers
Jared gets 10 heads when flipping a weighted coin 12 times. Based on experimental probability, how many of the next six flip should Jared expect to come up heads?
Answers
Answer:
5
Step-by-step explanation:
Experimental probability = number of tunes an event occurred / total number of trials
Experimental probability of getting head :
10 /12 = 0.833333
Expected number of heads from next 6 flips :
Experimental probability = expected number of heads / number of trials
0.833333 = x / 6
0.83333 * 6 = 5
5 times
What is the mode of the set of numbers?
2, 2, 3, 4, 4, 5, 7, 7, 7, 10, 16, 17
Answers
Answer:
It is 7
Step-by-step explanation:
Help!! please. will mark brainstest
Answers
Answer:(1,0)
Step-by-step explanation:
y=4/2x+1
Or simplify
y=2x+1
A restaurant used 231 eggs last week. 46 of them are colored white, w. The remaining eggs are colored brown.Write an equation that represents the situation.
Answers
Answer:
46 + W = 231
Step-by-step explanation:
Answer:
231-W=amount of brown eggs (185)
Step-by-step explanation:
Sofia bought a clothes iron that was discounted 15% off of the original price of $35. What was the dollar amount of discount of the clothes iron?
Answers
Answer:
$5.25
Step-by-step explanation:
Given data
Original price= $35
Discount= 15%
let us find 15% of $35
=15/100*35
=0.15*35
=$5.25
Hence the amount of the discount is
$5.25
PLEASE HELP!!! I need the answer now
Answers
Answer:
(-2,3)
Step-by-step explanation:
Answer:
C. (-2,3)
Step-by-step explanation:
(-2,3)
Calculate , the number of all partitions of a set of 6 elements into 3 disjoint sets. Calculate S73, the number of all partitions of a set of 6 elements into 3 disjoint sets.
Answers
The number of all partitions of a set of 6 rudiments into 3 disjoint sets is 69( S( 6, 3) = 69).
To calculate the number of all partitions of a set of 6 rudiments into 3 disjoint sets, we've to apply knowledge of Stirling numbers of the alternate kind. The Stirling figures of the alternate kind, denoted by S( n, k), represent the number of ways to partition a set of n rudiments into k non-empty subsets.
Then, we want to calculate S( 6, 3), which defines the number of ways to partition a set of 6 rudiments into 3 disjoint sets.
Using the conception of Stirling figures of the alternate kind
S(n, k) = k * S(n-1, k) + S(n-1, k-1)
we can calculate S(6, 3) as given below-
S(6, 3) = 3 * S(5, 3) + S(5, 2)
S(5, 3) = 3 * S(4, 3) + S(4, 2)
S(4, 3) = 3 * S(3, 3) + S(3, 2)
S(3, 3) = 1
S(3, 2) = 3
S(4, 3) = 3 * 1 + 3 = 6
S(5, 3) = 3 * 6 + 3 = 21
S(6, 3) = 3 * 21 + 6 = 69
Therefore, the number of all partitions of a set of 6 elements into 3 disjoint sets is 69 (S(6, 3) = 69).
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The correct question is given below -
Calculate S(6,3) , the number of all partitions of a set of 6 elements into 3 disjoint sets.
16 is what percent of 25
Answers
Answer:
4
Step-by-step explanation:
Answer:
64 %
Step-by-step explanation:
( 16 / 25 ) x 100
= ( 16 x 100 ) / 25
= 16 x 4
= 64 %
Exercise 1.5.9 Let R be an n x n upper-triangular matrix with semiband width s. Show that the system Rx = y can be solved by back substitution in about 2ns flops. An analogous result holds for lower-triangular systems.
Answers
The total number of flops required to solve the system is approximately 2ns.
Let R be an n x n upper-triangular matrix with semiband width s. Show that the system Rx = y can be solved by back substitution in about 2ns flops. An analogous result holds for lower-triangular systems.Back substitution is an efficient technique for solving systems of linear equations in matrix form.
This is because back substitution only works on upper- or lower-triangular matrices, which have certain features that make solving systems of equations easier.The back substitution algorithm starts by solving the first equation of the system and obtaining a solution for the first variable. It then uses this value to solve the second equation and obtain a solution for the second variable.
This process is continued until all the variables are solved for.Let R be an n x n upper-triangular matrix with semiband width s. The semiband width of a matrix is the maximum number of nonzero entries in any row or column of the matrix. This means that all entries below the diagonal of R are zero. Let y be a vector of length n.
We want to solve the system Rx = y using back substitution.Since R is upper-triangular, we can solve for the last variable x_n first. This only requires one multiplication and one subtraction. We can then use the value of x_n to solve for the second-to-last variable x_{n-1}, which requires two multiplications and two subtractions.
Continuing in this way, we can solve for all the variables x_1, x_2, ..., x_n, each time requiring one more multiplication and subtraction than the previous step.In total, the number of flops required to solve the system Rx = y using back substitution is approximately 1 + 2 + 3 + ... + n, which is equal to n(n+1)/2.
Since R has semiband width s, this means that each row of R has at most s nonzero entries, so each variable requires at most s multiplications and s-1 subtractions.
Therefore, the total number of flops required to solve the system is approximately 2ns.
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Solve the following system of equations by substitution
Answers
Answer:
(-1, 1)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 2x + 3
y = x + 2
Step 2: Solve for x
Substitution
Substitute in y: 2x + 3 = x + 2[Subtraction Property of Equality] Subtract x on both sides: x + 3 = 2[Subtraction Property of Equality] Subtract 3 on both sides: x = -1Step 3: Solve for y
Substitute in x [Original Equation]: y = -1 + 2Add: y = 1Answer:
x = -3, y = -1
Step-by-step explanation:
In order to solve an equation using substitution you need to make one of the variables values opposite of one another. For example, 4's opposite would be -4. Moving on, we multiply the bottom equation by -2. That gives us y = -2x -4. We combine like values and the remaing equation is y = -1. Finally, we can insert our value;-1 = x +2. We do inverse operations and we are left with x = -3.
Directions: Evaluate the following equation. Show all of your work.
4) 4.2x = 33.6
5) a/3 = 45
6) -8x = 4
Answers
Answer:
4) 8
5) 135
6) -.5
Step-by-step explanation:
4) 33.6/4.2=8
5) 3*45=135
6)4/-8= -1/2 or -.5
An amusement park thrill ride swings its riders back and forth on a pendulum that spins. Suppose the swing arm of the ride is 62 feet in length, and the axis from which the arm swings is about 64 feet above the ground. What is the height of the riders above the ground at the peak of the arc? Round to the nearest foot if necessar
PLEASE HELP
Answers
Answer:
118ft
Step-by-step explanation:
dont ask how i got it i just got the answer from my teacher but they didnt show me the work. ur welcome
Find the Perimeter of the figure below, composed of a rectangle and two
semicircles. Round to the nearest tenths place.
10
HELP MEHHH....pls
Answers
Answer:
Step-by-step explanation:
Find the value of k and x2
x^2+ 13x + k = 0, x1=-9
Answers
Given:
The quadratic equation is:
[tex]x^2+13x+k=0[/tex]
[tex]x_1=-9[/tex]
To find:
The value of k and [tex]x_1[/tex].
Solution:
We have,
[tex]x^2+13x+k=0[/tex] ...(i)
Putting [tex]x=-9[/tex], we get
[tex](-9)^2+13(-9)+k=0[/tex]
[tex]81-117+k=0[/tex]
[tex]-36+k=0[/tex]
[tex]k=36[/tex]
Putting [tex]k=36[/tex] in (i), we get
[tex]x^2+13x+36=0[/tex]
Splitting the middle term, we get
[tex]x^2+9x+4x+36=0[/tex]
[tex]x(x+9)+4(x+9)=0[/tex]
[tex](x+9)(x+4)=0[/tex]
[tex]x=-9,-4[/tex]
Here, [tex]x_1=-9[/tex] and [tex]x_2=-4[/tex].
Therefore, the required values are [tex]k=36[/tex] and [tex]x_2=-4[/tex].
HELP!!!!! What is the geometric mean of 3 and 7?
Answers
Answer:
4.5826
Step-by-step explanation:
What is the yield to maturity of a(n) eight-year, $5000 bond with a 4.4% coupon rate and semiannual coupons if this bond is currently trading for a price of $4723.70? A) 6.31% B) 5.26% C) 7.36% D) 2.63%
Answers
The yield to maturity of a(n) eight-year, if this bond is currently trading for a price of $4723.70 is B) 5.26%
Time = 8 years
Coupon rate = 4.4%
Value of the bond = $5000
Yield to maturity is the overall return on investment that a bond will have earned once all required payments have been made and the principal has been repaid. Since the investor would receive the initial bond price plus the interest rate that was finalised at the time of the total bond purchase.
Calculating yield to maturity -
[tex]P = C * [1 - (1 + r/2)^(-2n)] / (r/2) + F / (1 + r/2)^(2n)[/tex]
Substituting the values -
$4723.70 =
[tex]($5000 * 0.044/2) * (1 - (1 + Y/2)^(-28)) / (Y/2) + $5000 / (1 + Y/2)^(28)[/tex]
= 0.0526, or 5.26%
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The chess club has 25% more males and females. If there were 20 males, how many females are there in the club.
How many less were the females?
Number of Females =
Thank You!!!!
Answers
Answer:
number of females =16
Step-by-step explanation:
100% + 25% =125%. 125%=number of males. 100\125 ×20=16. 20 - 16 =4
Find the value of x in the picture below. (round to nearest tenth if needed) THANK YOU FOR HELPING ME:)
Answers
Answer:
17 feet
Step-by-step explanation:
L² = 15² + 8² = 225 + 64 = 289
L = √289 = 17 feet
Answer:
do you need the area or the perimiter?
xpress the function as the sum of a power series by first using partial fractions. f(x) = 7 x2 − 3x − 10 f(x) = [infinity] n = 0 find the interval of convergence. (enter your answer using interval notation.)
Answers
The radius of convergence is 5/7. The interval of convergence is (-5/7, 5/7) in interval notation.
To express the function f(x) = 7x² - 3x - 10 as the sum of a power series, we can start by factoring the quadratic term in the numerator:
f(x) = (7x² - 3x - 10)
The quadratic expression can be factored as follows:
f(x) = (7x + 5)(x - 2)
Now we can write the function f(x) as a sum of partial fractions:
f(x) = A/(7x + 5) + B/(x - 2)
To find the values of A and B, we can multiply both sides of the equation by the denominators and equate the coefficients of corresponding powers of x:
(7x + 5)(x - 2) = A(x - 2) + B(7x + 5)
Expanding both sides of the equation:
7x² - 14x + 5x - 10 = Ax - 2A + 7Bx + 5B
Grouping the terms with the same power of x:
(7x² + (5 - 14)x - 10) = (A + 7B)x + (-2A + 5B)
Equating the coefficients of corresponding powers of x:
7x² + (5 - 14)x - 10 = (A + 7B)x + (-2A + 5B)
Comparing the coefficients:
7 = A + 7B
5 - 14 = -2A + 5B
-10 = -2A
From the first equation, we can solve for A:
A = 7 - 7B
Substituting this value of A into the second equation:
-10 = -2(7 - 7B)
Simplifying:
-10 = -14 + 14B
14B = -10 + 14
B = 4/14
B = 2/7
Now we have the values of A and B:
A = 7 - 7B = 7 - 7(2/7) = 7 - 2 = 5
Therefore, the function f(x) can be expressed as:
f(x) = 5/(7x + 5) + 2/(x - 2)
Now, to find the interval of convergence for the power series representation of f(x), we need to determine the radius of convergence. The power series representation will converge within the interval (-r, r), where r is the radius of convergence.
In this case, since we have a rational function, the interval of convergence will be determined by the denominator with the smallest radius of convergence.
The denominators in the partial fractions are (7x + 5) and (x - 2). The radius of convergence for a power series centered at a point c is the distance from c to the nearest singularity.
For (7x + 5), the singularity occurs when 7x + 5 = 0, which gives x = -5/7.
For (x - 2), the singularity occurs when x - 2 = 0, which gives x = 2.
The distance from the center (c = 0) to the nearest singularity is the minimum of the absolute values of the two singularities: min(|-5/7|, |2|) = 5/7.
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