Given the second-order linear homogeneous ordinary differential equa- tion with variable coefficients dạy d.x2 2.0 (1 – 2:2) d?y dy +m(m+1)y = 0, MER, 0, dc use y(x) = ananth to obtain n=0 8 P}(k)aoxk-2 + P3(k)a1.mk-1 + branth - 0, n=0 - where Pi} (k), P2 (k) are polynomials of degree 2 to be determined. Find the roots of the polynomial equation P) (k) = 0 and comment on the coefficients ao and a, in light of the smaller one of these two roots. Next, using the smaller root, establish an explicit expression for the general term bn, and thus derive a recurrence relation between an+2 and an Finally, using the recurrence relation you have found above, obtain the first three terms of two linearly independent series solutions in their simplest form, one with even and one with odd powers of x.

Answer:

I'm not confident on this but:

L = 2(W + 1)

Hopefully this might help somewhat :]

L: Length

W: Width

Answer:

Step-by-step explanation:

First find out how much Mary was charging per hour:

= 500 / 20

= $25 per hour

She charges $60 for plants.

In a linear equation of the form: y = mx + c, the m represents the variable cost which in this case is the $25 per hour and the c is the fixed cost which is the $60.

Her rate as a linear equation would be:

y = 25x + 60

Looking a the value of the m of other gardeners will tell you who is charging higher hourly rates with anything above $25 doing so.

The gardeners with higher values of m than Mary are:

B. Y = 32x + 35

E. Y = 35x + 30

F. Y = 40x + 40

Nate had $3000 at the beginning.

The percentage is defined as a ratio expressed as a fraction of 100.

Let the original amount of money is P

Nate spent 12 % of his paycheck on car repairs

⇒ 12% of P = 12P/100

And he spent 25 % of the remainder on food.

⇒  0.25(88/100)P

He gave $ 1,320 of the remaining money to his parents

⇒ 1320  

If the usual price of the computer was $ 825 and the discount was 20 %

⇒ 825 - 0.20(825) = 660

P = 12P/100 + 0.25(88/100)P + 1320 + 660

P - 34P/100 = 1980

100P - 66P = 198000

P = 3000

Hence, Nate had $3000 at the beginning.

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I think 7/2 im not definate

Answer:

The measure of each angle will be 7 degrees. It is because a bisector divides an angle in two equal halves. 14 / 2 = 7

Answer:

4/15 is your answer my friend

Step-by-step explanation:

Answer:

when the equation says of, all you need to do is multiply the two numbers, so the answer is 4/15

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Answer:

y = 2x + 4

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-2,0) (0,4)

We see the y increase by 4 and the x increase by 2, so the slope is

m = 4/2 = 2

Y-intercept is located at (0,4)

So, the equation is y = 2x + 4

Answer:

The cell phone charges is an illustration of a piecewise function represented as: y = 20; x <=300 and y =  0.25x- 50; x > 300

How to draw the graph?

When the number of minutes is not more  than 300 minutes, the charge is:

y = 20; x <=300

When it is above 300, the function is:

y = 20 + 5 + (x - 300) * 0.25

Open the bracket

y = 20 + 5 + 0.25x - 75

Evaluate the sum

y =  0.25x- 50

So, the piecewise function is:

y = 20; x <=300

y =  0.25x- 50; x > 300

Step-by-step explanation:

The graph that represents the monthly cost, y, in dollars for making x minutes of calls is:

In the graph,

The line starts at y = 20 for x = 0 and then becomes a straight line with a slope of 0.25 for x > 300.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

To graph the monthly cost, we need to consider two cases:

Case 1: If x ≤ 300, then the monthly cost is a constant $20.

Case 2: If x > 300, then the monthly cost is a linear function of x:

Now,

y = 20 + 5 + 0.25(x - 300) = 25 + 0.25x - 75

y = 0.25x - 50

Therefore,

We can graph the monthly cost as follows:

For x ≤ 300, the graph is a horizontal line at y = 20.

For x > 300, the graph is a line with a slope of 0.25 and y-intercept -50.

Thus,

In the graph,

The line starts at y = 20 for x = 0 and then becomes a straight line with a slope of 0.25 for x > 300.

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Answer:

A. 2/3 book/hour

Step-by-step explanation:

rewrite the fractions as a decimal if it can make it easier for you (0.5 book/0.75 hours) then divide which is 2/3 book/hour

y = x^2 + 16x + 71

y - 71 = x^2 + 16x

y - 71 + (8)^2 = x^2 + 16x + (8)^2

y - 71 + 64 = x^2 + 16x + 64

Factor and simplify

y - 7 = (x + 8)^2

Vertex = (-8, 7)

Answer:

n=10.3

3n-30.9=0

Step-by-step explanation:

Answer:

n= -10.3

Step-by-step explanation: I took the test

The correct number line that can be used to find the distance between the given points (4, -1) and (8, -1) is a number line going from negative 2 to positive 8 in increments of 1, with the points at 4 and 8.Option (A)

The reason for this is that the two points have the same y-coordinate, which means they lie on a horizontal line. To find the distance between them, we simply need to measure the difference between their x-coordinates, which is 8 - 4 = 4. On the given number line, the distance between points 4 and 8 is also 4 units, so we can directly read off the distance as 4 units.

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Answer:

-1/10

I'm sure this answer is right.

Use the formula M= rise/run.

Then you will get this answer.

Given that the Laplace's equation on the quarter disk is ∇u= 0, with the boundary conditions

=u(r, 0)

= u (r, \(\pi/2\))

= 0

The Laplace's equation in polar coordinates is given by:

\(\nabla u = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial u}{\partial r} \right) + \frac{1}{r^2} \frac{\partial^2 u}{\partial \theta^2} = 0\)

where r is the radial distance and θ is the angular coordinate of a point.

To solve the Laplace's equation on the quarter disk, we use separation of variables and assume that u(r, θ) can be written as a product of functions of r and θ as follows:

u(r, θ) = R(r)Θ(θ)

Substituting the above expression in the Laplace's equation, we get:

\(\frac{r}{R} \frac{d}{dr} \left( r \frac{dR}{dr} \right) + \frac{1}{\Theta} \frac{d^2 \Theta}{d\theta^2} = 0\)

Separating the variables and equating the terms to a constant λ, we get:

\(r \frac{d^2R}{dr^2} + \frac{dR}{dr} - \lambda R = 0\)

\(\frac{d^2\Theta}{d\theta^2} + \lambda \Theta = 0\)

The general solution to the second equation is given by:

\(\begin{equation}\Theta(\theta) = A \sin(\sqrt{\lambda \theta}) + B \cos(\sqrt{\lambda \theta})\) where A and B are constants.

The boundary conditions u(r, 0) = u (r, π/2) = 0 give us

\(\Theta(0) = A \sin(0) + B \cos(0) = 0\) and

\(\Theta\left(\frac{\pi}{2}\right) = A \sin\left(\sqrt{\lambda}\frac{\pi}{2}\right) + B \cos\left(\sqrt{\lambda}\frac{\pi}{2}\right)\)

= 0

Solving the above equations, we get:

A = 0 and \(\sqrt{\frac{\lambda\pi}{2}} = \frac{(2n - 1)\pi}{2}\) where n = 1, 2, 3, ...Therefore,

\(\lambda_n = (2n - 1)^2 \pi^{-2}\), n = 1, 2, 3, ...The general solution to the first equation is given by:

\(R(r) = C_1J_0(\sqrt{\lambda_n r}) + C_2Y_0(\sqrt{\lambda_n r})\) where J₀ and Y₀ are Bessel functions of the first and second kind of order zero, respectively, and C₁ and C₂ are constants.

The general solution to the Laplace's equation on the quarter disk is given by:

\(u(r, \theta) = \sum_{n=1}^{\infty} C_n \sin((2n - 1)\pi \theta/2\pi) J_0((2n - 1)r/2)\)

where Cₙ are constants and J₀ is the Bessel function of the first kind of order zero.

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Answer:

3x²+8x-35

Step-by-step explanation:

FOIL stands for:

First -> (3x-7)(x+5)

Outer -> (3x-7)(x+5)

Inner -> (3x-7)(x+5)

Last -> (3x-7)(x+5)

Following FOIL, we get:

(3x-7)(x+5)

(3x)(x)+(3x)(5)+(-7)(x)+(-7)(5)

3x²+15x-7x-35

3x²+8x-35

Therefore, the expanded form is 3x²+8x-35

Answer:

h = 5m

Step-by-step explanation:

A = 1/2bh

15 = 1/2(6)h

15 = 3h

h = 5

Zina has 17,500 points in the video game after one week.

To find the percentage increase in points, we can use the formula:

Final value = Initial points + Initial points X (Percentage increase/100)

Initial points earned by Zina = 14000

Percentage increase = 25%

Therefore putting the values mentioned above in the formula we get:

14000 + 14000 x (25/100)

=14000+ 3500

=17,500

Therefore, Zina has 17500 points in the video game after 1 week.

Her points increased by 3500 in one week

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Answer:

-1 and 21

Step-by-step explanation:

Let the numbers be x and y.

x + y = 20

xy = -21

Solve the first equation for x and substitute in the second equation.

x = 20 - y

(20 - y)y = -21

20y - y^2 = -21

y^2 - 20y - 21 = 0

(y - 21)(y + 1) = 0

y - 21 = 0 or y + 1 = 0

y = 21 or y = -1

For y = 21:

x = 20 - y

x = 20 - 21

x = -1

For y = -1:

x = 20 - y

x = 20 - (-1)

x = 21

Solutions: (-1, 21) and (21, -1)

Answer: the numbers are -1 and 21

Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. The value of the account on January 1, 2021, would be $2,331.57.

To calculate the value of the account on January 1, 2021, we need to consider the compounding interest for each year.

First, we calculate the value of the initial deposit after three years (12 quarters) using the formula for compound interest:

Principal = $1,000

Rate of interest per period = 8% / 4 = 2% per quarter

Number of periods = 12 quarters

Value after three years = Principal * (1 + Rate of interest per period)^(Number of periods)

                           = $1,000 * (1 + 0.02)^12

                           ≈ $1,166.41

Next, we calculate the value of the additional $1,000 deposit made on January 1, 2019, after two years (8 quarters):

Principal = $1,000

Rate of interest per period = 2% per quarter

Number of periods = 8 quarters

Value after two years = Principal * (1 + Rate of interest per period)^(Number of periods)

                         = $1,000 * (1 + 0.02)^8

                         ≈ $1,165.16

Finally, we add the two values to find the total value of the account on January 1, 2021:

Total value = Value after three years + Value after two years

                ≈ $1,166.41 + $1,165.16

                ≈ $2,331.57

Therefore, the value of the account on January 1, 2021, is approximately $2,331.57.

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Answer:

9r²(r - 8)

Step-by-step explanation:

Step 1: Write expression

9r³ - 72r²

Step 2: Factor out 9

9(r³ - 8r²)

Step 3: Factor out r²

9r²(r - 8)

Using the cross-multiplication method we know that the price of the soda yesterday was $420.

One might cross-multiply an equation between two fractions or rational expressions in mathematics, more specifically in elementary arithmetic and elementary algebra, to make the equation simpler or to find the value of a variable.

So, calculate as follows:

100 - 76 = 24

We know that 24% is $100.80.

We need to find the rest 76% and add it to the 24% price.

Then, cross multiply:

24/100.80 = 76/x

24x = 76*100.80

24x = 7,660.8

x = 7,660.8/24

x = $319.2

Then, add the two amounts:

24 = $100.80

76 = $319.2

Then.

319.2 + 100.80 = $420

Therefore, using the cross-multiplication method we know that the price of the soda yesterday was $420.

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The nurse would document the observed findings as a "0.75 cm elevated, palpable, solid mass with a circumscribed border."

When documenting the observed findings, the nurse provides a description of the characteristics of the mass. Here's an explanation of the terms used in the documentation:

Elevated: This means that the mass is raised above the surrounding tissue. It indicates that the mass is not flat or flush with the skin or underlying structures.

Palpable: This means that the nurse can feel the mass by touch. It suggests that the mass can be detected through physical examination or palpation.

Solid: This indicates that the mass has a firm consistency, as opposed to being fluid-filled or soft. It suggests that the mass is composed of dense tissue or cells.

Circumscribed border: This means that the mass has a well-defined or clearly demarcated edge or boundary. It indicates that the mass is distinguishable from the surrounding tissue, with a distinct border between the mass and normal tissue.

The measurement of 0.75 cm refers to the size or diameter of the mass. It provides information about the dimensions of the mass and is helpful for monitoring any changes in size over time.

By documenting these characteristics, the nurse provides important details about the appearance and features of the observed mass, which can aid in further assessment, diagnosis, and treatment planning.

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Given:

Fractions \(\dfrac{1}{9},\dfrac{2}{9},\dfrac{3}{9}\) etc.

To find:

What happens with the “ninth” fractions.

Solution:

We have, the values of \(\dfrac{1}{9},\dfrac{2}{9},\dfrac{3}{9}\) are

\(\dfrac{1}{9}=0.11111...\)

\(\dfrac{2}{9}=0.22222...\)

\(\dfrac{3}{9}=0.33333...\)

Clearly we can spot a pattern, because after decimal the numerator digit of fraction is repeating.

Similarly,

\(\dfrac{9}{9}=0.99999...\)

Therefore, the decimal value of \(\dfrac{9}{9}\) is 0.99999..., which is approximately 1.

The value of x and y in the equations are are -2 and -1, 1 and 6, 10/6 and -1/3

Simultaneous equations are two or more algebraic equations that share common variables and are solved at the same time.

y=x+1 and y=4x +7

x+1=4x +7

Collecting like terms

x-4x = 7-1

-3x=6

x=-2

For the value y

y=-2+1

y = -1

For equation 2

3x -y =-1

y=-x+5

3x-(-x+5)=-1

3x+x-5=-1

4x=-1+5

4x=4

Therefore; x=1

For the value y

y= 1+5

y=6

For equation 3

x+2x=3

-x+3y = 7

x=3-2y

-(3-2y) +3y =7

-3+2y+3y=7

6y = 7+3

6y==10

y=10/6

For the value of x

x = 3+20/6

Simplifying to have -2/6 -1/3

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Jade rides 1.275 miles before stopping for a water break.

To solve this problem, we need to multiply the length of the trail by the fraction representing the portion of the trail that Jade rides.

First, we need to convert the mixed number 5 1/10 into an improper fraction. We do this by multiplying the whole number (5) by the denominator of the fraction (10) and adding the numerator (1). This gives us 51/10.

Next, we multiply 51/10 by 1/4 to find the fraction of the trail that Jade rides before stopping for a water break:

(51/10) x (1/4) = 51/40

To convert this fraction into a decimal, we divide the numerator by the denominator:

51 ÷ 40 = 1.275

Therefore, Jade rides 1.275 miles before stopping for a water break.

In summary, to find how many miles Jade rides before stopping, we convert the mixed number representing the length of the trail into an improper fraction, multiply it by the fraction representing the portion of the trail that Jade rides, and then convert the resulting fraction into a decimal to get our answer.

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Answer:

0.84 is the answers for the question

Step-by-step explanation:

please give me brainlest

Answer:

0.84

Step-by-step explanation:

Pr(A') = 1 - Pr(A)

Pr(A') = 1 - 0.16

Pr(A') = 0.84

Answer:

for output: 4, 6, 8, 10

Input: (i think) 1,5,5,1

Step-by-step explanation: