Please help me, I’m struggling

Answer:

The answer is 3/4

Step-by-step explanation:

The given initial value problem using the method of undetermined coefficients. The final solution to the initial value problem is y = cos(2x) + x - (1/9)*sin(3x).

To solve the given initial value problem, we begin by finding the general solution to the associated homogeneous equation. The homogeneous equation is given by y'' + 4y = 0. The characteristic equation is obtained by substituting y = e^(mx) into the equation, resulting in the quadratic equation m^2 + 4 = 0. Solving this equation yields two distinct roots: m_1 = 2i and m_2 = -2i. Thus, the general solution to the homogeneous equation is y_h = c_1cos(2x) + c_2sin(2x), where c_1 and c_2 are arbitrary constants.

Next, we assume a particular solution in the form of y_p = Ax + B + Csin(3x) + Dcos(3x), where A, B, C, and D are undetermined coefficients. We substitute this particular solution into the given differential equation and solve for the coefficients. Comparing the coefficients of like terms, we find A = 0, B = 1, C = -1/9, and D = 0.

The particular solution is y_p = x - (1/9)*sin(3x), and the complete solution is obtained by adding the particular solution to the homogeneous solution: y = y_h + y_p. Applying the initial condition y(0) = 1, we find that c_1 = 1 and c_2 = 0. Therefore, the final solution to the initial value problem is y = cos(2x) + x - (1/9)*sin(3x).

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Using Simpson's [tex]\frac{1}{3}[/tex] rule with 6 strips, the approximate value of the integral ∫[2.0, 2.8] f(x) dx is -3.8492.

To integrate the function [tex]\begin{equation}y = f(x) = \frac{ax^2}{b + x^2}[/tex] using Simpson's 1/3 rule, we need to divide the interval [2.0, 2.8] into an even number of strips (in this case, 6 strips). The formula for approximating the integral using Simpson's 1/3 rule is as follows:

[tex]\begin{equation}\int_a^b f(x) dx \approx \frac{h}{3} \left[ f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + ... + 2f(x_{n-2}) + 4f(x_{n-1}) + f(x_n) \right][/tex]

Where:

h is the width of each strip ([tex]\begin{equation}h = \frac{b - a}{n}[/tex], where n is the number of strips)

[tex]x_0[/tex] is the lower limit (2.0)

[tex]x_n[/tex] is the upper limit (2.8)

f(xi) represents the function evaluated at each strip's midpoint

Given the values of a = 1.2 and b = -0.587, we can proceed with the calculations.

Step 1: Calculate the width of each strip (h):

[tex]\begin{equation}h = \frac{b - a}{n} = \frac{-0.587 - 1.2}{6} = \frac{-1.787}{6} \approx -0.2978[/tex]

Step 2: Calculate the function values at each strip's midpoint:

x₀ = 2.0

x₁ = x₀ + h = 2.0 + (-0.2978) = 1.7022

x₂ = x₁ + h = 1.7022 + (-0.2978) = 1.4044

x₃ = x₂ + h = 1.4044 + (-0.2978) = 1.1066

x₄ = x₃ + h = 1.1066 + (-0.2978) = 0.8088

x₅ = x₄ + h = 0.8088 + (-0.2978) = 0.511

x₆ = x₅ + h = 0.511 + (-0.2978) = 0.2132

xₙ = 2.8

Step 3: Evaluate the function at each midpoint:

[tex]f(x_0) = \frac{1.2 \times 2^2}{-0.587 + 2^2} = \frac{4.8}{3.413} \approx 1.406 \\\\f(x_1) = \frac{1.2 \times 1.7022^2}{-0.587 + 1.7022^2} \approx 2.445 \\\\f(x_2) = \frac{1.2 \times 1.4044^2}{-0.587 + 1.4044^2} \approx 2.784 \\\\f(x_3) = \frac{1.2 \times 1.1066^2}{-0.587 + 1.1066^2} \approx 2.853 \\\\[/tex]

[tex]f(x_4) = \frac{1.2 \times 0.8088^2}{-0.587 + 0.8088^2} \approx 2.455 \\f(x_5) = \frac{1.2 \times 0.511^2}{-0.587 + 0.511^2} \approx 1.316 \\f(x_6) = \frac{1.2 \times 0.2132^2}{-0.587 + 0.2132^2} \approx 0.29[/tex]

Step 4: Apply Simpson's 1/3 rule formula:

[tex]\begin{equation}\int_{2.0}^{2.8} f(x) dx \approx \frac{h}{3} \left[ f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + 2f(x_4) + 4f(x_5) + f(x_6) \right][/tex]

[tex]\begin{equation}\approx \frac{-0.2978}{3} \left[ 1.406 + 4(2.445) + 2(2.784) + 4(2.853) + 2(2.455) + 4(1.316) + 0.29 \right][/tex]

[tex]\begin{equation}= \frac{-0.2978}{3} \left[ 1.406 + 9.78 + 5.568 + 11.412 + 4.91 + 5.264 + 0.29 \right][/tex]

≈ (-0.09926) * 38.63

≈ -3.8492

Therefore, the approximate value of the integral ∫[2.0, 2.8] f(x) dx using Simpson's 1/3 rule with 6 strips is approximately -3.8492.

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Answer:

circle: ( 1, 0.5 )

square: ( 4.5, 3.5 )

triangle: ( 0, 2.5 )

Step-by-step explanation:

The probability of selecting  a girl to read the poem out loud in her class is 46.4% .

To calculate the probability of selecting a girl to read a poem out loud in a class of 28 students, we can use the formula:

Probability = Number of Desirable Outcomes / Total Number of Outcomes

Here, the desirable outcome is selecting a girl to read the poem, and the total outcomes are all the students in the class.

Number of Desirable Outcomes:

Mrs. Avery has 13 girls in her class, so there are 13 desirable outcomes.

Total Number of Outcomes:

Mrs. Avery has 28 students in her class, so there are 28 total outcomes.

Probability = Number of Desirable Outcomes / Total Number of Outcomes

Probability = 13 / 28

Probability = 0.464 or 46.4%

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Note: The complete question is -Mrs. Avery is planning to have one student read a poem out loud in class. She has a class of 28 students, consisting of 15 boys and 13 girls. What is the probability that she will select a girl to read the poem out loud?

Answer:

-18+ 13

-6 + 1

-20 + 15

-7 + 2

Step-by-step explanation:

Answer:

A) 90°

Step-by-step explanation:

if lines b and c are perpendicular then all 8 angles measure 90 degrees

Answer:

option B should be correct

Answer:

45

Step-by-step explanation:

x = -30/2(-5)

x = -30/(-10)

x = 3 sec

.

Plug above into equation to find height:

h=-5t^2 + 30t

h=-5*3^2 + 30(3)

h=-5*9 + 30(3)

h=-45 + 90

h=45

Answer:

5670 yards

Step-by-step explanation:

Length of first race = 2 miles

Since, 1 mile = 1760 yards

Therefore, 2 miles = 1760 × 2

                               = 3520 yards

Length of second race = 1300 yards

Length of third race = 850 yards

Total distance to be run by the horse = 3520 + 1300 + 850

                                                              = 5670 yards

Answer:

3/4 is 0.75 and 1 is 1

Step-by-step explanation:

:\

Answer: The number of hens are 4 and number of sheeps are 6

Step-by-step explanation:

Given : Total animals = 10

Total number of legs = 32

Let number of hens = h  and number of sheep = s

Thus h+s = 10    (1)

Now each hen has two legs and each sheep has 4 legs :[tex]2\times h+4\times s=32[/tex]   (2)

Solving for h and s we get:

s = 6 , h =4

Thus number of hens are 4 and number of sheeps are 6

Answer:

A, The probability that it will rain is 0.09 and the probability that the flight will be delayed is 0.18.

Step-by-step explanation:

Answer: 0.154

Step-by-step explanation:

The sum of the binomial coefficients nCk, where n ranges from 0 to 10 and k varies from 0 to 10, is equal to [tex]2^10[/tex], which is 1024.

The expression ∑10k=010Ck represents the sum of the binomial coefficients for all possible values of k from 0 to 10. The binomial coefficient nCk, also known as "n choose k," represents the number of ways we can choose k objects from a set of n objects.

In this case, we are summing up the binomial coefficients for n ranging from 0 to 10. For each value of n, we calculate the binomial coefficient nCk for k values ranging from 0 to 10. The formula to calculate the binomial coefficient is n! / (k!(n-k)!), where "!" denotes the factorial operation.

When we substitute the values into the formula, we find that all the binomial coefficients are 1, except when k equals 0 or n. In these cases, the binomial coefficient is equal to 1, as there is only one way to choose 0 objects or all n objects from a set.

Since there are 11 values of n (0 to 10), and for each n there is one non-zero binomial coefficient, the sum of all the binomial coefficients from 0 to 10 is equal to 11. Therefore, the expression simplifies to ∑10k=010Ck = 11.

So, the sum of all the binomial coefficients ∑10k=010Ck is equal to 11, which means we have 11 ways to choose k objects from a set of 10 objects. Another way to interpret this is that the sum of the binomial coefficients represents the number of subsets of a set with 10 elements, which is 11. However, if we are considering the case of choosing 0 to 10 objects, the sum becomes 2^10, which is equal to 1024.

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a. The total amount owed for the $525 loan at 9.9% interest for 6 months is approximately $556.19 when rounded to the nearest cent.

b. The total amount owed for the $12,460 loan at 5.6% interest for 30 months is approximately $33,504.80 when rounded to the nearest cent.

a. To calculate the total amount owed for the $525 loan at 9.9% interest for 6 months, we can use the formula for simple interest:

Total amount owed = Principal + (Principal × Interest Rate × Time)

Given:

Principal (P) = $525

Interest Rate (R) = 9.9% = 0.099 (converted to decimal)

Time (T) = 6 months

Plugging these values into the formula, we get:

Total amount owed = $525 + ($525 × 0.099 × 6)

Simplifying the equation:

Total amount owed = $525 + ($31.185)

Total amount owed = $556.185

Therefore, the total amount owed for the $525 loan at 9.9% interest for 6 months is approximately $556.19 when rounded to the nearest cent.

b. To calculate the total amount owed for the $12,460 loan at 5.6% interest for 30 months, we'll follow the same formula for simple interest:

Total amount owed = Principal + (Principal * Interest Rate * Time)

Given:

Principal (P) = $12,460

Interest Rate (R) = 5.6% = 0.056 (converted to decimal)

Time (T) = 30 months

Plugging these values into the formula, we get:

Total amount owed = $12,460 + ($12,460 * 0.056 * 30)

Simplifying the equation:

Total amount owed = $12,460 + ($21,044.8)

Total amount owed = $33,504.8

Therefore, the total amount owed for the $12,460 loan at 5.6% interest for 30 months is approximately $33,504.80 when rounded to the nearest cent.

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Answer:

I don't see any equations.

Answer:

what should i answer?

Step-by-step explanation:

Answer:

First term = 12

Step-by-step explanation:

A4 = 24

A12 = 56

An = A1 + (n-1)d; this defines the formula of an arithmetic series

A4 = 24 = A1 + (4-1)d

A4 = 24 = A1 + 3d

A12 = 56 = A1 + (12-1)d

A12 = 56 = A1 + 11d

Subtract A4 from A12 to get d (distance)

(56 = A1 + 11d) - (24 = A1 +3d)

32 = 8d

d = 4

Substitute d = 4 into A4

A4 = 24 = A1 + 3(d)

24 = A1 + 3(4)

24 = A1 + 12

24 - 12 = A1

12 = A1

Multiply the discount percent to the marked price and subtract from the marked price.

As we know that the discount is always given on the marked price of the product.

We will take one example to understand it supposes the marked price of any object is MP= 100 and the discount =15% so to find the SP

First, find the discount amount

[tex]MP\times Discout \ percent =100\times \dfrac{15}{100} =15[/tex]

Now to find the SP subtract the discount from the MP

[tex]SP=MP-Discount[/tex]

[tex]SP=100-15=75[/tex]

So for finding SP multiply the discount percent to the marked price and subtract from the marked price.

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I'm on my school computer so the picture is blocked sorry :(

Answer:

the answer is in the photo hope it help

Answer:

Explanation:

320.29 × 7 = 2,242.03 m = 1.39313285413187 miles ≈ 1.393

The requried, there are 495 possible combination lineups with eight bands out of twelve for the benefit concert.

To determine the number of possible lineups with eight out of twelve bands performing, we need to calculate the combination.

The number of ways to choose eight bands out of twelve without considering the order is given by the combination formula:

[tex]C(n, r) = \dfrac{n!}{ (r! * (n-r)!)}[/tex]

where n is the total number of bands (12 in this case) and r is the number of bands to be chosen (8 in this case).

Let's calculate it:

[tex]C(12, 8) =\dfrac {12!}{(8! * (12-8)!)}[/tex]

            [tex]= \dfrac{12!} {(8! * 4!)}[/tex]

            = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)
            = 495

Thus, there are 495 possible combination lineups with eight bands out of twelve for the benefit concert.

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Answer: 5

Step-by-step explanation: 21 + 4 = 25

square root of 25  = 5

Answer and Step-by-step explanation:

T = 21

U = 4

[tex]\sqrt{ 21 + 4} \\\\\\\sqrt{25} \\\\\\5[/tex]

5 is the answer to the expression.

#teamtrees #PAW (Plant And Water)

The value of the F-statistic for the test of overall significance of this regression relationship is approximately 11.245.

Given:SST = 2326.9523 SSR = 1632.8843 Independent variables = 7

Observations = 66Formula used:F = (SSR/K) / (SSE / (n-K-1))

Where SSR = Regression sum of squares SSE = Error sum of squaresK = Number of independent variables n = Number of observations

To calculate the F-statistic, we first need to calculate SSE which is given by:SSE = SST - SSR = 2326.9523 - 1632.8843 = 693.068

The degrees of freedom for the regression are K and the degrees of freedom for the error term are n - K - 1 = 66 - 7 - 1 = 58

The value of the F-statistic is given by:F = (SSR/K) / (SSE / (n-K-1))= (1632.8843/7) / (693.068 / 58)= 11.245

Therefore, the value of the F-statistic for the test of overall significance of this regression relationship is approximately 11.245.

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As per the given values, the after-tax salvage value is $435,200.

Amount required = $3,200,000

Time = 6 years

Calculating the accumulated depreciation -

Amount/ Number of years

=  $3,200,000 / 6

= $533,333.3.

Calculating the accumulated depreciation at project end -

= 6 x $533,333.33

= $3,200,000.

Calculating the book value of the fixed assets -

Book value = Cost of fixed assets - Accumulated depreciation

= $3,200,000 - $3,200,000

= $0

Calculating the taxable gain or loss on the sale of the fixed assets -

Taxable gain/loss = Selling price - Book value

= $640,000 - $0

= $640,000

Calculating the tax liability -

Tax liability = Tax rate x Taxable gain

= 0.32 x $640,000

= $204,800

Calculating the after-tax salvage value -

After-tax salvage value = Selling price - Tax liability

= $640,000 - $204,800

= $435,200

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Step-by-step explanation:

36 is your answer

I hope.it helps mate

have a nice day

#Captainpower

Answer:

18 units to the right.

Step-by-step explanation:

Hope this helps!

Answer:

[tex]\sqrt{53}[/tex]

Step-by-step explanation:

Use the distance formula:

[tex]\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex]

plug in (-5,6) for (x1,y1) and (-3,-1) for (x2,y2)

[tex]\sqrt{(-5-(-3))^2+(6-(-1))^2}[/tex]

[tex]\sqrt{4+49}[/tex]

[tex]\sqrt{53}[/tex]

Hope that helps :)

Approximately 0.11 percent of all samples have mean heights of at least 64.76 inches.

Given: 50 years prior, the mean level of ladies in a specific country in their 20s was 62.9 inches. With a standard deviation of 2.87 inches, women in their 20s today have heights that are roughly typical. We must determine the proportion of all 21 samples that have mean heights of at least 64.76 inches among today's women in their 20s. Bit by bit clarification:

Let μ be the mean level of ladies in this day and age and allow n to be the example size. We can find the likelihood of an example mean being more prominent than or equivalent to 64.76 inches utilizing the z-score recipe, as follows: z = (x - μ)/(σ/√n) = (64.76 - 62.9)/(2.87/√21) = 3.06The likelihood that an example of 21 ladies will have a mean level more noteworthy than or equivalent to 64.76 inches is equivalent to the likelihood that a typical irregular variable Z is more noteworthy than or equivalent to 3.06.

This probability is approximately 0.0011, or 0.11 percent, according to a typical normal table or calculator. This means that approximately 0.11 percent of all samples have mean heights of at least 64.76 inches.

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