The general solution of the homogeneous differential equation d² (23 (2) − 6 —y (2) +9y (z) = 0 "h = Aema + Brema is given by where m = 3 and A and B are arbitrary constants. Let us now find a particular solution to the non-homogeneous differential equation d² 23 (2) - 6 = y(x) + 9 y(x) = 34 cos(5 z). da2 a) What form would you take as your guess for a particular solution? a sin 5x ar sin 5x + bæ cos5a ar sin 52 up: a sin 5x + b cos5x b) Find a particular solution up and enter it (of the above form, evaluating a and/or b) in the box below. bz cos5a c) Let ug be the general solution to the non-homogeneous differential equation d² d da2y (z)-6- (2) +9y (2) = 34 cos(5 z). b cos 5x
(2 marks) Consider the Maclaurin series for sin and cos z2k+1 (2k + 1)! sinn = Σ(1)", k=0 valid for all real . Using the power series above and the identity where sin (3x) = 3 sin z - 4 sin³ z, it follows that the Maclaurin series for sin³ is given by T sin³ x = Pr + Qx³+ '+. P = 0 and more generally and 1 dk= cos z = (-1) k k=0 k=0 (-1) dk7 Hol 22k (2k)! z2k+1 (2k + 1)! B.Q=

Answer:

4.6

Step-by-step explanation:

Step 1:

AR + RB = AB     Equation

Step 2:

5x - 6 + 8 = 25     Substitute

Step 3:

5x + 2 = 25    Add

Step 4:

5x = 23       Subtract 2 on both sides

Step 5:

23 ÷ 5   Divide

Answer:

x = 4.6

Hope This Helps :)

Answer:4.6

Step-by-step explanation:

Alisha needs to use a fraction of 3/8 of each of the ingredients on the recipe.

We know that a pancake recipe calls for 8 eggs and some other ingredients.

But Alisha only has 3 eggs, so she needs to adjust the recipe.

The fraction of each one of the other ingredients that she needs to use is equal to the fraction between the number of eggs that she has and the number of eggs that the recipe calls, it is:

N = 3/8

So she needs to use 3/8 of each of the ingredients that the recipe calls.

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Answer:

y=-2/3x+2/3 i think... :)

Step-by-step explanation:

y=mx+b

-4=-2/3(-7)+b

-4=14/3+b

b=2/3

y=-2/3x+2/3

The given complex number is \(2+2√√/31\). Let us find the polar form of the given complex number with argument 0 between 0 and 2π.

Let us consider the rectangular form of the given complex number \(z = 2+2√√/31.\)

Here, the real part is 2 and the imaginary part is \(2√√/31.\)

Let us find the magnitude of the complex number, which is given by \(|z| = √(2^2+ (2√√/31)^2)\)

On simplifying, we get\(|z| = √(4 + 8/√31) |z| = √((4*√31+8)/√31) |z| = √(4(√31+2)/√31) |z| = 2√(√31+2)/√31\)

Let us find the argument of the given complex number.

Here, the real part is positive and the imaginary part is positive.

Hence, the argument lies in the first quadrant.

Using the formula for argument, we have \(θ = tan⁻¹ (2√√/31/2) θ = tan⁻¹ (√√/31)\)

Therefore, the polar form of the given complex number is \(2√(√31+2)/√31 cis (tan⁻¹ (√√/31)),\)

where cis represents cos + i sin.

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Answer:a)6,7,8

d)8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30

Step-by-step explanation:

The given problem involves sets M, R, and N, where M = {m⁻¹⁰, 2, 3, 6}, R = {4, 6, 7, 9}, and N = {x | x is a natural number less than 9}. We need to determine the universal set and evaluate the expression [Mᶜ∪(N - R)]× N.

a. The universal set is the set that contains all the elements under consideration. In this case, since the problem does not explicitly define a universal set, we can assume it to be the set of natural numbers. Therefore, the universal set can be represented as U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...}.

b. Now let's evaluate the expression [Mᶜ ∪ (N - R)] × N step by step. First, we find the complement of set M, denoted as Mᶜ. The complement of M will include all the elements that are not present in M but are in the universal set U. Therefore, Mᶜ = {1, 4, 5, 7, 8, 9, 10, 11, ...}.

Next, we calculate the set difference (N - R), which represents the elements that are in set N but not in set R. N = {1, 2, 3, 4, 5, 6, 7, 8}, and R = {4, 6, 7, 9}. Thus, (N - R) = {1, 2, 3, 5, 8}.

Now, we take the union of Mᶜ and (N - R), denoted as [Mᶜ ∪ (N - R)]. The union of two sets includes all the elements that are in either set. Therefore, [Mᶜ ∪ (N - R)] = {1, 4, 5, 7, 8, 9, 10, 11, ...}.

Finally, we multiply the resulting set [Mᶜ ∪ (N - R)] with set N. The multiplication of two sets involves pairing each element of one set with every element of the other set. Thus, [Mᶜ ∪ (N - R)] × N = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (5, 7), (5, 8), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8)}.

In summary, the universal set

is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...}. The expression [Mᶜ ∪ (N - R)] × N results in {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (5, 7), (5, 8), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8)}.

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Answer:

the slope would be (2,1) because thats how far from 0 those 2 numbers are

Step-by-step explanation:

Answer:

y = 2 x - 5

Step-by-step explanation:

Step-by-step explanation:

Cube ...so each side is 5 cm

Diagonal = sqrt ( 5^2 + 5^2 + 5^2 )    <====like Pythagorean theorem in 3-D

        = sqrt (75) = 5 sqrt 3  = 8.66 cm

Answer:

7.071

Step-by-step explanation:

this is sqrt(25+25)

which is 7.071

Brainliest?

The arrangement (D) HA + € has the greatest equivalent capacitance.

In order to determine the arrangement with the greatest equivalent capacitance, we need to analyze the different connections and their impact on the total capacitance.

In arrangement (A) EL HHH HA, the capacitors are connected in series and parallel combinations. However, the presence of the series connection reduces the overall capacitance of the arrangement.

In arrangement (D) HA + €, the capacitors are connected in parallel, which allows the total capacitance to increase. When capacitors are connected in parallel, their individual capacitances add up, resulting in a larger equivalent capacitance.

Therefore, arrangement (D) HA + € has the greatest equivalent capacitance among the two options.

It's important to note that the symbols used in the question (EL, HHH, HA, €) represent the configurations of the capacitors. Without further context or visual representation, it is difficult to provide a detailed analysis of the arrangement.

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The numerical or verbal descriptions that usually result from measurements are called data or observations.

When measurements are conducted, whether in scientific experiments, surveys, or other data collection processes, the outcome is typically a set of data or observations.

These measurements can be represented numerically, such as numerical values or quantities, or verbally, using descriptive terms or categories.

Numerical descriptions provide precise quantitative information, such as measurements of length, weight, temperature, time, or any other measurable attribute. These measurements are often expressed using numbers or units of measurement.

Verbal descriptions, on the other hand, use words or qualitative descriptions to convey information about the observations.

For example, when conducting a survey, respondents might provide verbal responses that describe their opinions, preferences, or experiences.

Both numerical and verbal descriptions play important roles in data analysis and interpretation.

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Answer:

slope = \(\frac{2}{3}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (15, 18 ) and (x₂, y₂ ) = (6, 12 )

m = \(\frac{12-18}{6-15}\) = \(\frac{-6}{-9}\) = \(\frac{2}{3}\)

Remember, when finding the slope, use this formula: \(\frac{y_{2}-y_{1}}{x_{2}-x_{1} }\)

We can start by labeling (15, 18) as \(x_{1}\) and \(y_{1}\) and (6, 12) as \(x_{2}\) and \(y_{2}\). Now, we can plug these number into the formula: \(\frac{y_{2}-y_{1}}{x_{2}-x_{1} }=\frac{12-18}{6-15}=\frac{-6}{-9} =\frac{2}{3}\)

Thus, the slope of the line is \(\frac{2}{3}\). Hope this helps! Let me know if you have any questions related to this problem.

This is not a function, we know this because the input x = 1 is mapped into two different outputs.

A relation maps elements from one set, the domain, into elements from another set, the range. A relation is only a function if each element of the domain is mapped into only one element of the range.

In this case, we have the relation:

x: 1, -2, 1, -3

y: 2, 1, 3, -2

The input x = 1 is mapped into two different values, y =2 and y = 3.

Thus, the relation is not a function.

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If f(x)=2x²-5x-3 g(x)=2x²+5x+2 then (f/g)(x) = (x - 3) / (x + 2).

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find (f/g)(x), we need to divide f(x) by g(x) as follows:

f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2

f(x) / g(x) = (2x² - 5x - 3) / (2x² + 5x + 2)

To simplify this expression, we can factor the numerator and denominator:

f(x) / g(x) = [(2x + 1)(x - 3)] / [(2x + 1)(x + 2)]

Now, we can cancel out the common factor of (2x + 1) from both the numerator and denominator:

f(x) / g(x) = (x - 3) / (x + 2)

Therefore, (f/g)(x) = (x - 3) / (x + 2).

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Answer:

Step-by-step explanation:

Covert 21 out of 175 into percentage:

We need percentage

\(\\ \bull\sf\dashrightarrow \dfrac{21}{175}\times 100\)

\(\\ \bull\sf\dashrightarrow \dfrac{21}{7}\times 4\)

\(\\ \bull\sf\dashrightarrow 3(4)\)

\(\\ \bull\sf\dashrightarrow 12\%\)

Answer:

Step-by-step explanation:

Corresponding sides of similar triangles have same ratio.

Correct option is D

To combine the given expressions into a single logarithm, we can simplify each term step by step and then combine them.

Let's simplify each term one by one:

3 ln(A):

This term can be simplified as ln(A^3).

[In(B) + 2 In(C²)]:

Using the property of logarithms, we can write this as ln(B) + ln(C²)², which simplifies to ln(B) + 2ln(C²).

m(H) ○ In(AC):

The ○ symbol is unclear, so I'll assume it represents multiplication. We can simplify this term as ln((AC)^m(H)), applying the power rule of logarithms.

On(4³):

The meaning of the On notation is unclear, so I'll assume it represents an exponentiation operation. This term simplifies to 4^(3n).

In(C² √/B):

The expression "√/B" is unclear, so I'll assume it represents the square root of B. We can simplify this term as ln((C²)^(1/2) / B), which further simplifies to ln(C / B).

○ In(4¹0²):

The ○ symbol is unclear, so I'll assume it represents multiplication. We can simplify this term as ln((4¹0²)^○), which becomes ln(4¹0²).

In(√/B):

Again, the expression "√/B" is unclear, so I'll assume it represents the square root of B. This term simplifies to ln(√B).

Now, let's combine all the simplified terms into a single logarithm:

ln(A^3) - [ln(B) + 2ln(C²)] + ln((AC)^m(H)) + ln(C / B) + ln(4^(3n)) + ln(4¹0²) + ln(√B)

We can now combine the terms inside the logarithm using the properties of logarithms:

ln(A^3) - ln(B) - 2ln(C²) + ln((AC)^m(H)) + ln(C / B) + ln(4^(3n)) + ln(4¹0²) + ln(√B)

Using the properties of logarithms, we can simplify further:

ln(A^3 / B) - 2ln(C²) + ln((AC)^m(H)) + ln(C / B) + ln(4^(3n)) + ln(4¹0²) + ln(√B)

This expression represents the combined logarithm of the given terms.

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Correct question:

Combine the following expressions into a single logarithm. 3 ln(A)-[In(B) + 2 In (C²)] m(H) ○ In (AC) On (4³) In (C² √/B) ○ In (4¹0²) In(√/B)

To find the graph that represents an absolute value function with a coefficient of least value, we need to understand the following:

An absolute value function with a coefficient of 1 takes the form:

The graph of this function is shown below:

If the function is reflected across the x-axis, it becomes :

Its graph is shown below:

For any absolute value function:

If a > 1 , the function is stretched,

if a < 1 and a >0, the function is dilated

Using the information provided above:

The coefficient with the least value is D

The coefficient closest to zero is C

To find the probability of accepting a lot with a defect rate of 4% using an acceptance sampling plan with n = 27 and c = 0, we need to calculate the binomial probability of having zero defects in a sample of 27 items.

The probability of accepting a lot is equal to the probability of having zero defects, which can be calculated using the binomial probability formula. The formula is P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where P(X = k) is the probability of getting k successes, n is the sample size, p is the probability of success (defect rate), and C(n, k) is the binomial coefficient.

In this case, we want to find P(X = 0) where n = 27 and p = 0.04 (4% defect rate). Substituting these values into the binomial probability formula and calculating it will give us the desired probability of accepting the lot with zero defects.

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Answer:

433345344 Answer

Step-by-step explanation:

cos(20°) is the correct answer.

Congratulations! This is the unit circle. Literally everyone hates this. Everyone takes this in Trigonometry though, and it's required. I literally failed Trigonometry because of this and had to retake it when getting my degree in Mathematics.

So, what is the x-coordinate of this? Well, for any angle or (angle in triangle) \(\alpha\), the coordinates are always (\(cos(\alpha), sin(\alpha)\)).

In this case, angle \(\alpha\) is 20°, and so the x-coordinate will be cos(20°) while the y-coordinate will be sin(20°).

Hope this helped!

Answer: cos 20

Step-by-step explanation:

The three friends spent:Jan spent $30.5, Danetta spent $18.5, and Elaine spent $37.

Let's denote the amount Jan spent as J. Danetta spent $12 less than Jan, so her expenditure is J - $12. Elaine spent twice as much as Danetta, so her expenditure is 2(J - $12). The total expenditure of the three friends is $86. By setting up an equation using these values, we can find the individual expenditures of each friend.

Let's denote the amount Jan spent as J. According to the given information, Danetta spent $12 less than Jan, so her expenditure can be expressed as J - $12. Similarly, Elaine spent twice as much as Danetta, so her expenditure can be expressed as 2(J - $12).

The total expenditure of the three friends is stated as $86. We can set up the equation J + (J - $12) + 2(J - $12) = $86 to represent the sum of their expenditures. Simplifying this equation, we have 4J - $36 = $86.

By rearranging the equation, we find 4J = $122, which implies J = $30.5. Therefore, Jan spent $30.5.

Using this value, we can calculate the expenditures of the other two friends. Danetta spent J - $12, which is $30.5 - $12 = $18.5. Elaine spent twice as much as Danetta, so she spent 2($18.5) = $37.

In summary, Jan spent $30.5, Danetta spent $18.5, and Elaine spent $37.

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Answer:

4/3

Step-by-step explanation:

Answer:

The answer is 4/3.

Answer:£1500

7500 divided by 10=750. £750 is 10% so 750x2 which is 1500, is 20%. Therefore, it is reduced by £1500

Answer:

£1500

Step-by-step explanation:

20% = 20/100 = 0.2

7500 - (7500*0.2)

= 7500 - 1500

= 6000

The reduction in price is:

£ 1500

The slope represents the predicted change in sales price for each additional square foot of a home. Using this slope, you can then create the regression line equation, which will help you predict the sales price based on square footage for homes in the subdivision.

To predict the sales price based on square footage for homes in this subdivision using the least squares regression line, you would need to follow these steps:

1. Collect data: Gather data on the sales prices and square footages of homes in the subdivision. This data will be used to calculate the regression line.

2. Calculate the mean: Find the average (mean) sales price and average square footage for the homes in your data set.

3. Calculate deviations: For each home, calculate the deviation of its sales price from the mean sales price and the deviation of its square footage from the mean square footage.

4. Calculate products: Multiply the deviations of sales price and square footage for each home, and then sum the products.

5. Calculate squared deviations: Square the deviations of square footage for each home, and then sum the squared deviations.

6. Calculate the slope: Divide the sum of products by the sum of squared deviations. This will give you the slope of the least squares regression line.

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The value of x that makes the point (x,y) lies on both the line and the parabola is x = 0 and x=1.

The values of x for which the point (x,y) lies on both the line and the parabola, we set the equation of the line y = 4x equal to the equation of the parabola y^2 = 16x.

By substituting y = 4x into the equation of the parabola we get (4x)^2 = 16x and further simplifying it results in 16x^2 = 16x.

so x=1 and x=0

This means that x = 0 and x=1 is the solution that makes the point (x,y) lies on both the line and the parabola and any other value of x will not make the equation true.

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Complete question:

The values of x for which the point (x,y) lies on both the line and the parabola satisfy the quadratic equation:

The equation of line is y = 4x

equation of parabola is \(y^2\) = 16x

Consider the given discrete-time dynamical system:

xₙ = xₙ₋₁ + A - xₙ₋₁²

where A is the parameter. This system has two steady states given as x = ± A.

To find out the parameter range for which these steady states are (a) stable (b) unstable, we need to find out the values of the first derivative of the given equation.

Let's find the first derivative of the given function:

xₙ = xₙ₋₁ + A - xₙ₋₁²xₙ' = 1 - 2xₙ₋₁

On the steady state, i.e., x = ± A,

we have:

x = A: 0 = 1 - 2A → 2A = 1 → A = 0.5x = -A: 0 = 1 + 2A → 2A = -1 → A = -0.5

a) For the stable steady states:

For A = 0.5, the steady state x = A is stable. For x = -A, the steady state is unstable.

b) For the unstable steady states:

For A = -0.5, the steady state x = -A is stable. For x = A, the steady state is unstable.Let's plot the last 50 iterations on time course diagram for A = 0.1.

This can be done by using the MATLAB code as given below:

```x(1) = 0; A = 0.1; for n = 2:51 x(n) = x(n-1) + A - x(n-1)^2; end plot(x,'-o')```

This plot will show how the system behaves for A = 0.1. Now, let's increase the value of A to show how the system moves from stable to unstable for A = 0.5, 1.0, 1.1, 1.5, and 1.6.

The MATLAB code to obtain these plots is as follows:

```A_values = [0.5 1.0 1.1 1.5 1.6];

for i = 1:length(A_values) A = A_values(i);

x(1) = 0; for n = 2:51 x(n) = x(n-1) + A - x(n-1)^2; end subplot(3,2,i) plot(x,'-o') title(sprintf('A = %0.1f',A)) end```

The resulting plot will be as follows:

Time course diagram:

Since we have plotted the last 50 iterations of the system, we can observe that for the stable steady state, the values of x become constant after a certain number of iterations.

Whereas, for the unstable steady state, the values of x oscillate and move away from the steady state as the number of iterations increase.

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According to the question The coefficient of variation for the given data set is 40%.

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation (SD) by the mean (μ) and expressing the result as a percentage.

The formula for the coefficient of variation is:

\(\[ CV = \left(\frac{SD}{\mu}\right) \times 100 \]\)

In this case, the standard deviation is 4 units and the mean is 10 units. Plugging these values into the formula, we get:

\(\[ CV = \left(\frac{4}{10}\right) \times 100 \]\)

\(\[ CV = 0.4 \times 100 \]\)

\(\[ CV = 40 \]\)

Therefore, the coefficient of variation for the given data set is 40%.

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Answer:

1, 2, 5 and 6 are functions

Step-by-step explanation:

u cant have a repeating x in a function