Hi could you please help me with this and explain how you got it?

To find the general solutions of the given differential equations using D-operator methods, we will use the fact that D-operator (D) represents differentiation with respect to x.

3.1 For the differential equation (D² - 5D + 6)y = e^(-x) + sin(2x), we can factorize the characteristic equation as (D - 2)(D - 3)y = e^(-x) + sin(2x). Solving each factor separately, we have: (D - 2)y = e^(-x) => y₁ = Ae^(2x) + e^(-x) (where A is a constant). (D - 3)y = sin(2x) => y₂ = Bsin(2x) + Ccos(2x) (where B and C are constants). The general solution is y(x) = y₁ + y₂ = Ae^(2x) + e^(-x) + Bsin(2x) + Ccos(2x).

3.2 For the differential equation (D² + 2D + 4)y = e^(2x)sin(2x), the characteristic equation is (D + 2i)(D - 2i)y = e^(2x)sin(2x). Solving each factor separately, we have: (D + 2i)y = e^(2x)sin(2x) => y₁ = Ae^(-2ix)e^(2x)sin(2x) = Ae^(2x)sin(2x)

(D - 2i)y = e^(2x)sin(2x) => y₂ = Be^(2ix)e^(2x)sin(2x) = Be^(2x)sin(2x)

The general solution for the first differential equation is y(x) = Ae^(2x) + e^(-x) + Bsin(2x) + Ccos(2x), and the general solution for the second differential equation is y(x) = Ae^(2x)sin(2x) + Be^(2x)sin(2x), where A, B, and C are constants.

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When solving proportions, we set the cross products equal, and then we solve for the unknown variable.

When solving proportions, we set the cross products equal to each other and then proceed to solve for the unknown variable. A proportion is an equation that states that two ratios or fractions are equal. To solve a proportion, we first identify the two ratios involved and set their cross-products equal.

For example, consider the proportion: a/b = c/d

To solve for the unknown variable, we set the cross products (a * d) and (b * c) equal:

a * d = b * c

This equation allows us to find the value of the unknown variable by manipulating the equation through multiplication or division to isolate the variable on one side of the equation.

By setting the cross products equal, we essentially establish an equality between the two ratios, indicating that the fractions on either side of the proportion are equivalent. Solving for the unknown variable allows us to determine its value based on the relationship between the given ratios.

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The number of rows in the log stack is 2. To find the number of rows in this log stack, we need to find the number of times we can subtract 3 from 48 until we reach 24.

48 - 3 = 45

45 - 3 = 42

42 - 3 = 39

We keep subtracting 3 until we reach 24. When we reach 24, we have found the second row, so the number of rows in the stack is 2.

This problem is asking for the number of rows in a stack of logs, where the number of logs decreases by three for each row. To solve this problem, we can use a simple mathematical equation. We can start with the number of logs on the bottom row, which is 48, and subtract 3 logs for each subsequent row. To find the total number of rows, we need to determine when the number of logs in a row becomes zero. This can be done by dividing the number of logs on the bottom row by 3, and rounding up to the nearest whole number. In this case, 48 divided by 3 is 16, so we would round up to 17. This means there are 17 rows in total, with the first row having 48 logs, the second row having 45 logs, and so on, until the last row with 24 logs.

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Answer:

C

Step-by-step explanation:

I tried my best, The coin has 2 outcomes and the dice has 6 so 6 times 2 is 12

Answer:

26

Step-by-step explanation:

Problem: f(x) = 28 + x + 7

Plug in f(-9)

New equation: f(-9) = 28 + (-9) + 7

Simplify: f(-9) = 26

Answer: f(-9) = 26

Answer:

1/12 or 0.0833

Step-by-step explanation:

P(Coin) = 1/2

P(Dice) = 1/6

1/2 × 1/6 = 1/12

Answer:

\(\boxed {h = -10.071}\)

Step-by-step explanation:

Solve for the value of \(h\):

\(h - (-2.22) = -7.851\)

The opposite of \(-2.22\) would be \(2.22\):

\(h - (-2.22) = -7.851\)

\(h + 2.22 = -7.851\)

-Subtract both side by \(2.22\):

\(h + 2.22 - 2.22 = -7.851 - 2.22\)

\(\boxed {h = -10.071}\)

So, the value of \(h\) is \(-10.071\).

Answer:

A. x= -5

B. x= 8

Step-by-step explanation:

A. 25 - 3x = 40

-3x = 40 - 25

-3x = 15

x= 15/-3

x= -5

B. 2 (x-10) =  -4

x-10 = -4/2

x-10 = -2

x = 8

A. 25 - 3x = 40

         -3x = 40 - 25

               = 15

            -x = 15/3

             x = -5

   Checking

    25 - 3*-5 = 40

    25 + 15 = 40

            40 = 40

       LHS = RHS

B. 2(x-10) = -4

    2x - 20 = -4

            2x = -4 +20

             x = 16/2 = 8

Hope u understand

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Number 1 answer :

Cream cheese = 12    Sugar= 15    12 divided by 15 = 0.8

There are 0.8 ounces of cream cheese for every ounce of sugar.

Number 2 answer:

 Sugar= 15   Cream cheese = 12   15 divided by 12 = 1.25

There are 1.25 ounces of sugar for every ounce of cream cheese.

Answer:

Step-by-step explanation:

Perpendicular formula

m1 * m2 = - 1

Givens

m1 = - 7

m2 = ??

Solution

-7 * m2 = -1

m2 = 1/7

y = 1/7 x + b

x = 8

y = -3                     Substitute these values into y = 1/7 x + b

-3 = (1/7)*8 + b    

-3 = 8/7 + b          Subtract 8/7  from both sides

-3 - 8/7 = b

-4 1/7 = b

Answer (perpendicular line) y = (1/7) x - 4 1/7  or

Answer (perpendicular line) y = (1/7) x - 4.14

Parallel line

Nothing changes except you have a different y intercept.

y = -7x + b

x = 8

y = -3                           Substitute these values into y = -7x + b

-3 = -7*8 + b

-3 = - 56 + b

-3 + 56 = b

b = 53

Equation Parallel line: y = -7x + 53

The values of following in parallel lines are:

Angle 3 and Angle 6 are an example of corresponding angles. (Option D is the correct answer).

Angle 1 and Angle 5 are an example of corresponding angles. (Option D is the correct answer).

Angle 6 and Angle 7 are an example of alternate interior angles. (Option B is the correct answer).

Angle 28 would not be congruent to the measure of 27. (Option A is the correct answer).

Angle 41 and Angle 23 are an example of corresponding angles. (Option D is the correct answer).

Option B: 23 is not an example of supplementary angles.

Angle 22 is vertical to Angle 27. Therefore, m22 = m27 = 115°.

Angle 23 and Angle 25 are alternate interior angles, so they are congruent. Therefore, m23 = m25 = 63°.

Angle 1 and Angle 26 are corresponding angles, so they are congruent. Therefore, mz1 = mz6 = 57°.

Parallel lines are two or more lines in a plane that never intersect each other, no matter how far they are extended. In other words, they are always at the same distance from each other and never cross.

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The value of the integral given in the question ∫(0 to π) f(x) dx is 0.

A key theorem in calculus, the fundamental theorem establishes the connection between integration and differentiation. It claims that evaluating the function's antiderivative at the interval's endpoints will yield the integral of a function over that interval. In other words, the definite integral of f(x) over the interval [a,b] is equal to the difference between F(b) and F(a) if f(x) is a continuous function over the interval [a,b] and F(x) is an antiderivative of f(x). The theory has significant applications in physics, engineering, and economics, among other disciplines.

Given the piecewise function f(x) and the bounds, the integral can be expressed as:

\(\int\limitsf(x) dx = \int\limits^a_b {x} \,sin(x) dx + \int\limits\cos(x) dx\)

Now, let's evaluate each integral separately:

1. \(\int\limits^{} \, dx (\pi /2 to \pi ) sin(x) dx\)
To evaluate this integral, find the antiderivative of sin(x), which is -cos(x). Now apply the Fundamental Theorem of Calculus:

\(-(-cos(\pi /2)) - -(-cos(0)) = cos(0) - cos(\pi /2)\) = 1 - 0 = 1

2. \(\int\limits^{} \, dx (\pi /2 to \pi ) cos(x) dx\):
To evaluate this integral, find the antiderivative of cos(x), which is sin(x). Now apply the Fundamental Theorem of Calculus:

\(sin(\pi ) - sin(\pi /2)\)= 0 - 1 = -1

Now, add the results of both integrals:

1 + (-1) = 0

So, the integral \(\int\limits^ {} \,f(x) dx\) = 0.

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Answer:

-14 x -4

Step-by-step explanation:

i did the quiz lol

Answer:

A

Step-by-step explanation:

took the quiz, hope this helps.

Answer:divideing by the whole number

Step-by-step explanation:

The quadratic function is given by f(x) = 5x² - 10x - 40 and the other zero is at x = -2

An equation is an expression that shows the relationship between two or more numbers and variables.

The function f(x) has one zero at x = 4, and maximum point at (1, -45), Hence:

Using the maximum point:

f(x) = a(x - 1)² - 45

The zero is at (4, 0),

f(4) = 0 = a(4 - 1)² - 45

0 = a(4 - 1)² - 45

a = 45

f(x) = 5(x - 1)² - 45

f(x) = 5x² - 10x - 40

The second zero is at:

0 = 5x² - 10x - 40

x = 4; and x = -2

The quadratic function is given by f(x) = 5x² - 10x - 40 and the other zero is at x = -2

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Answer:

Gather information like your principal loan amount, interest rate and total number of months or years that you'll be paying the loan.

Calculate your total interest by using this formula: Principal Loan Amount x Interest Rate x Time (number of years in term) = Interest.

Answer:

The most common form of explicit proof in high school geometry is two column proof consists of various five parts they are; the given, the proposition, the statement column, the reason column, and the diagram ( if its given).

Answer:

Proofs contain given information and a statement to be proven. You use deductive reasoning to create an argument with justification of steps using theorems, postulates, and definitions. Then you arrive at a conclusion.

Step-by-step explanation:

Step b is wrong. The slope is the change in y over the change in x.

Step b should be (18- 8)/( 10-6)

= 10/4

= 5/2

The equation 5x = x + 3 has 1 solution.

The solution to the equation 5x = x + 3 is x = 3.

The correct option e. Statements (1) and (2) TOGETHER are NOT sufficient.

For the stated question-

1. R is less than 20: insufficient since s is unknown.

2. Because there is no date for r, statement 2 is insufficient because S is bigger than 65.

We now have two conditions when combined. s>0 and s>65, r 20 and r>0.

Using the maximum possible value of r as an example and the least possible value of s as an example, the value is greater than 1/3.

Therefore, every values for r would only decrease, while s will rise.

Therefore, simply stating that it won't be below 1/3 will do.

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The complete question is-

If r and s are positive integers, is r/s less than 1/3 ?

(1) r is less than 20.

(2) s is greater than 65.

a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

d. EACH statement ALONE is sufficient.

e. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: Suppose y varies directly with x. Write a direct variation equation that relates x and y.

Step-by-step explanation:

Answer is y = -5x

The equation for y varies directly with x is, y = - 5x.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, y varies directly with x.

Therefore,

y ∝ x.

y = kx, where k is the proportionality constant.

At y = - 10 when x = 2.

- 10 = 2k.

k = - 5.

So, y = - 5x.

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Answer:

tehe but i still answer and get points :)

Step-by-step explanation:

Hi there!

We know that:

m∠WXZ = 112°

Since m∠1 is 48° greater than m∠2, we can write an expression:

m∠2 = x°

m∠1 = (x + 48)°

Since both angles sum up to m∠WXZ, we can write this as:

112° = x° + (x + 48)°

Solve for x:

112 = 2x + 48

64 = 2x

x = 32°

The value of the test statistic is approximately 2.54.

To find the value of the test statistic, we can use the formula for calculating the test statistic for a single-sample hypothesis test for the population mean. The formula is:

t = (\(\bar x\) - μ) / (s / √n)

Where:

\(\bar x\) is the sample mean,

μ is the population mean,

s is the sample standard deviation,

n is the sample size.

Given information:

Sample mean (\(\bar x\)) = 5.8 ppm

Population mean (μ) = 5.5 ppm

Sample variance (σ^2) = 0.36 ppm^2

Sample size (n) = 26

To calculate the sample standard deviation (s), we take the square root of the sample variance:

s = √(σ^2)

s = √(0.36)

s = 0.6

Now we can calculate the test statistic (t):

t = (5.8 - 5.5) / (0.6 / √26)

t = 0.3 / (0.6 / √26)

t = 0.3 / (0.6 / 5.099)

t = 0.3 / 0.118

t ≈ 2.54 (rounded to two decimal places)

Therefore, the value of the test statistic is approximately 2.54.

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The pound of Red Delicious apples that he bought more is 31. pounds.

Amount of pounds of Fuji apples bought = 4.54

Amount of pounds of Red Delicious apples = 6.8

Amount of pounds of Golden Delicious apples = 3.7

The amount of pounds of Red Delicious apples than Golden Delicious apples that he buy will be the difference between the values. This will be:

= 6.8 - 3.7.

= 3.1 pounds.

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Answer: The answer to your question is $18.40!

Hope this helped! :)

Step-by-step explanation:     can i have brinlest plzz

Answer:

She paid 18.40 dollars

Step-by-step explanation:

15% percent of $16 is 2.40, so if you add 2.40 and 16, you get the answer. I hope this helps :)

Let hours = x

She can work a maximum of 30 hours so x can be any number from 30 or below.

The inequality would be: X <= 30

Answer:

Let the maximum time be x

She can work 30 hrs or below ( maximum of 30 hrs)

Therefore, the equation is

\( \huge \boxed{x \leqslant 30 \: hours}\)

Answer:

3.16 x 10^-3

Step-by-step explanation:

Answer:

There are three zeroes before the first non-zero decimal, so we write \(0.00316 = \boxed{3.16 \cdot 10^{-3}}.\)

Step-by-step explanation:

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.