Simplify the following and leave your answer in smallest form
1 + 2 + 1
_ _ _
2 3 6​

Answer:

[tex]w = \frac{93}{40} [/tex]

The approximate values of the solution to the given initial value problem at the four time steps t = 0.1, 0.2, 0.3 and 0.4 using the modified Euler formula with step sizes h = 0.05 and h = 0.001 are as follows:

Approximate solution using h = 0.05y(0.1) = 1.12116266y(0.2) = 1.25755476y(0.3) = 1.41728420y(0.4) = 1.59967883

Approximate solution using h = 0.001y(0.1) = 1.00372378y(0.2) = 1.00745820y(0.3) = 1.01119282y(0.4) = 1.01492766

The non-autonomous ordinary differential equation is given as:

dy/dt = f(t,y)......(1)

where f is a continuous function and is defined for all values of t and y. The numerical methods for non-autonomous ODEs are described below:

This method is based on the same idea as Euler's method, but the derivative is evaluated at the midpoint of the interval instead of the initial point. Consider the initial value problem (IVP) dy/dt = f(t,y), y(to) = yo, and suppose that we want to approximate the solution at tn+1 = tn + h. Then, using the improved Euler's formula, we obtain the following approximation:

Yn+1 = yn + hF(tn + h/2, yn + hF(tn,yn)/2)......(2)

Using h = 0.05

Substituting h = 0.05 in equation (2), we get

Y1 = Y0 + 0.05(F(0.025,Y0+F(0,Y0)/2))

Y2 = Y1 + 0.05(F(0.075,Y1+F(0.05,Y1)/2))

Y3 = Y2 + 0.05(F(0.125,Y2+F(0.1,Y2)/2))

Y4 = Y3 + 0.05(F(0.175,Y3+F(0.15,Y3)/2))

Using h = 0.001

Substituting h = 0.001 in equation (2), we get

Y1 = Y0 + 0.001(F(0.0005,Y0+F(0,Y0)/2))

Y2 = Y1 + 0.001(F(0.0015,Y1+F(0.001,Y1)/2))

Y3 = Y2 + 0.001(F(0.0025,Y2+F(0.002,Y2)/2))

Y4 = Y3 + 0.001(F(0.0035,Y3+F(0.003,Y3)/2))

For the given IVP, f(t,y) = 2t + ety, y(0) = 1

So, substituting f(t,y) in equation (1), we get

dy/dt = 2t + ety.....(3)

Using the modified Euler formula (equation 2), we get

Using h = 0.05

Y1 = 1 + 0.05(2(0.025) + e(0.025)Y0) = 1.12116266

Y2 = 1.12116266 + 0.05(2(0.075) + e(0.075)Y1) = 1.25755476

Y3 = 1.25755476 + 0.05(2(0.125) + e(0.125)Y2) = 1.41728420

Y4 = 1.41728420 + 0.05(2(0.175) + e(0.175)Y3) = 1.59967883

Using h = 0.001

Y1 = 1 + 0.001(2(0.0005) + e(0.0005)Y0) = 1.00372378

Y2 = 1.00372378 + 0.001(2(0.0015) + e(0.0015)Y1) = 1.00745820

Y3 = 1.00745820 + 0.001(2(0.0025) + e(0.0025)Y2) = 1.01119282

Y4 = 1.01119282 + 0.001(2(0.0035) + e(0.0035)Y3) = 1.01492766

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Let the number of 47-cent stamps be x, and the number of 8-cent stamps be y. So, the cost of x 47-cent stamps will be $0.47x.The cost of y 8-cent stamps will be $0.08y.Therefore, $2.99 = $0.47x + $0.08y  Multiply the entire equation by 100 to eliminate decimals. $299 = 47x + 8yEquation 1.47x + 8y = 299There are a couple of ways to solve the system of equations.

One method is substitution. We can rearrange equation 1 to solve for x:47x = 299 - 8y x = (299 - 8y)/47Substitute this expression for x into the first equation: 0.47(299 - 8y)/47 + 0.08y = 2.99 Simplifying the equation, we get: 299 - 8y + 4.76y = 299y = 299/0.76y = 393.4Hence, we cannot have fractional values of y; it must be a whole number, so Caitlyn can use 32 47-cent stamps and 15 8-cent stamps to mail a gift card to a friend.

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Answer:

87.75

Step-by-step explanation:

You are correct

Answer:

It depends on the size of the fish tank, so this question cannot be properly answered.

Answer:It depends I can give a ratio

Step-by-step explanation:

If one tank needs 45 gallons of water and another needs 30 you will need 75 gallons of water. If your using pints or quarts you can find converter calculators

The most expensive trailer can be purchased for $39,505.41. To determine the most expensive trailer that can be purchased at an interest rate of 3.12% compounded quarterly, we calculate the future value of the savings.

The formula for compound interest is given by the equation:

A = [tex]P(1 + r/n)^(nt)[/tex]

Where:

A is the future value of the savings,

P is the quarterly deposit amount ($1,200),

r is the interest rate per compounding period (3.12%),

n is the number of compounding periods per year (quarterly, so n = 4),

and t is the number of years (15).

Plugging the values into the formula, we have:

A =[tex]1200(1 + 0.0312/4)^(4*15)[/tex]

Calculating this expression, we find the future value of the savings after 15 years to be approximately $39,505.41.

Therefore, the most expensive trailer that can be purchased is $39,505.41 or less, as that is the maximum amount that will be saved over the 15-year period.

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Answer:

7/24 i think i hope this helps and im right

Answer:

ok so i can have i insteaof f too

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Y= MX (The Slope which is Rise/Run) minus 2 (The Y-Intercept).

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

( 1 , 1 )

Equation Form:

x = 1 ,   y = 1

Answer:   It is 3.>9

Step-by-step explanation:

because i dont know

The surface area of the figure is 204 sq.unit.

The surface area of a three dimensional figure is the sum of area of all its faces.

Here a three dimensional figure is given and surface area has to be calculated.

The base is a cuboid

Surface Area of a cuboid = SA= 2lw+2lh+2hw

SA = 2 * 6 * 6 +2 * 6 * 3 + 2 * 6 * 3

SA = 144 sq.units

The Surface Area of the 4 triangle surface = 4 * (1/2) * base * height

SA = 2 * 6 * 5 = 60 sq.units

The total surface area = 144 +60 = 204 sq.units

Therefore the surface area of the figure is 204 sq.unit.

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Answer:

21.21

Step-by-step explanation:

Area of a circle is A = π r^2

Variables:

r = 18/2 = 9

θ = 30 deg

Find the area:

A = π r^2

A = π 9^2

A = 254.47

Find the area of the sector:

θ/360 * A

= 30/360 * 254.47

= 21.21

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4a^2+7ab-b^2

Step-by-step explanation:

Add the first two equations together:

 3a^2-ab-2b^2

+ 2a^2+5ab-3b^2

---------------------------

5a^2+4ab-5b^2

Subtract that answer from the remaining trinomial:

5a^2+4ab-5b^2

- a^2-3ab-4b^2

--------------------------

4a^2+7ab-b^2

Answer:

4a^2 + ab - 9b^2

Step-by-step explanation:

First, perform the indicated addition:

3a^2-ab-2b^2

2a^2+5ab-3b^2

------------------------

5a^2 + 4ab - 5b^2

From this sum we subtract a^2 - 3ab - 4b^2:

 5a^2 + 4ab - 5b^2

-(a^2 - 3ab - 4b^2

------------------------------

 4a^2 + ab - 9b^2

Respuesta:

11,80 €

Explicación paso a paso:

Dado:

Importe o coste = 16,80 €

El valor de descuento sobre la cantidad = 5 €

El precio o costo con descuento sobre el monto entregado será; la diferencia entre la cantidad dada y el valor de descuento

Importe - valor de descuento

16,80 € - 5 €

= 11,80 €

The 99% confidence interval for the population mean based on the given sample is (61.86, 69.94). This means that we are 99% confident that the true population mean falls within this interval.

To find the 99% confidence interval for a sample with a sample size of 68, a sample mean of 65.9, and a standard deviation of 16.5, we can use the formula for calculating the confidence interval for a population mean when the population standard deviation is known.

The formula is given by:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / sqrt(sample size))

First, we need to find the critical value corresponding to a 99% confidence level. Since the sample size is large (n = 68), we can use the Z-table or a Z-table calculator to find the critical value. For a 99% confidence level, the critical value is approximately 2.576.

Next, we can substitute the given values into the formula to calculate the confidence interval:

Confidence Interval = 65.9 ± 2.576 * (16.5 / sqrt(68))

Using a calculator or mathematical software, we can calculate the standard error of the mean:

Standard Error = standard deviation / sqrt(sample size) = 16.5 / sqrt(68) ≈ 1.997

Substituting the standard error into the formula, we have:

Confidence Interval = 65.9 ± 2.576 * 1.997

Calculating the values inside the interval, we get:

Confidence Interval = (65.9 - 2.576 * 1.997, 65.9 + 2.576 * 1.997)

Simplifying further, we have:

Confidence Interval = (61.86, 69.94)

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Answer:

15.3125

Step-by-step explanation:

i gotchu

Answer:

8

Step-by-step explanation:

24/3 = 8

Answer:

8.1

Step-by-step explanation:

Subtract 2.9 to get Y alone.

11 - 2.9 = 8.1

Answer:

132.5 degrees. Check to see if there is missing information in the question or any mistakes.

Step-by-step explanation:

Supplementary angles = 180 degrees

180 - 47.5 = 132.5

Answer:

Independent events

Step-by-step explanation:

Given

[tex]P(A) = 0.50[/tex]

[tex]P(B)= 0.70[/tex]

[tex]P(A\ u\ B) = 0.85[/tex]

Required

Determine the relationship between the events

To do this, we simply calculate P(A n B) using:

[tex]P(A\ n\ B) = P(A) * P(B)[/tex]

and

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

So, we have:

[tex]P(A\ n\ B) = P(A) * P(B)[/tex]

[tex]P(A\ n\ B) = 0.50 * 0.70[/tex]

[tex]P(A\ n\ B) = 0.35[/tex]

and

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

[tex]P(A\ n\ B) = 0.50 + 0.70 - 0.85[/tex]

[tex]P(A\ n\ B) = 0.35[/tex]

Since: [tex]P(A\ n\ B) = P(A) * P(B)[/tex] [tex]= 0.35[/tex]

Then: the events are independent

Step-by-step explanation:

Factor −6 out of −6x

-6(x)+12

Factor −6 out of 12.

−6(x)−6(−2)

Factor −6 out of −6 (x)−6(−2).

-6(x-2)

Upon solving the given system of equations:

[tex]x(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * cos(2t) + (1/2) * (c_1 + e^{-t}) * sin(2t),\\y(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * sin(2t) - (1/4) * (c_1 + e^{-t}) * cos(2t)[/tex]

To solve the system of equations:

x' = 2x - 3y + 2sin(2t)

y' = x - 2y - 2cos(2t)

We can use the method of undetermined coefficients to find the particular solution. Assuming the particular solution takes the form:

[tex]x_p(t) = A sin(2t) + B cos(2t)\\y_p(t) = C sin(2t) + D cos(2t)[/tex]

Substituting these expressions into the original equations, we get:

2(A sin(2t) + B cos(2t)) - 3(C sin(2t) + D cos(2t)) + 2sin(2t) = 2sin(2t)

(A sin(2t) + B cos(2t)) - 2(C sin(2t) + D cos(2t)) - 2cos(2t) = cos(2t)

(2A - 3C + 2)sin(2t) + (2B - 3D)cos(2t) = 2sin(2t)

(A - 2C)sin(2t) + (B - 2D - 2)cos(2t) = cos(2t)

By comparing the coefficients of sine and cosine on both sides, we can equate them separately:

2A - 3C + 2 = 2

2B - 3D = 0

A - 2C = 0

B - 2D - 2 = 1

Solving these equations, we find:

A = 1

B = 3/2

C = 1/2

D = -1/4

So the particular solution is:

[tex]x_p(t)[/tex] = sin(2t) + (3/2)cos(2t)

[tex]y_p(t)[/tex] = (1/2)sin(2t) - (1/4)cos(2t)

To find the complementary solution, we solve the homogeneous system:

x' = 2x - 3y

y' = x - 2y

We can rewrite this system as a matrix equation:

X' = AX

where [tex]X = [x, y]^T[/tex] and

[tex]A = \left[\begin{array}{ccc}2&-3\\1&-2\end{array}\right][/tex]

The characteristic equation is:

det(A - λI) = 0, where I is the identity matrix. Solving this equation, we find the eigenvalues:

[tex]\lambda_1 = -1\\\lambda_2 = -1[/tex]

For each eigenvalue, we solve the corresponding eigenvector equation:

(A - λI)V = 0

For [tex]\lambda_1 = -1[/tex], we have:

[tex]\left[\begin{array}{ccc}3&-3\\1&-1\end{array}\right] * V_1 = 0[/tex]

Solving this system, we find the eigenvector:

[tex]V_1 = [1\ \ 1][/tex]

For [tex]\lambda_2 = -1[/tex], we have:

[tex]\left[\begin{array}{ccc}3&-3\\1&-1\end{array}\right] * V_2= 0[/tex]

Solving this system, we find the eigenvector:

[tex]V_2 = [3\ \ 1][/tex]

So the complementary solution is:

[tex]x_c(t) = c_1 * e^{-t} * [1\ \ 1]^T + c_2 * e^{-t} * [3\ \ 1]^T\\y_c(t) = c_1 * e^{-t} * [1\ \1]^T + c_2 * e^{-t} * [3\ \ 1]^T[/tex]

where

[tex]c_1\ and\ c_2[/tex] are arbitrary constants.

The general solution is the sum of the particular and complementary solutions:

[tex]x(t) = x_p(t) + x_c(t)\\y(t) = y_p(t) + y_c(t)[/tex]

Simplifying and combining terms, we get:

[tex]x(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * cos(2t) + (1/2) * (c_1 + e^{-t}) * sin(2t)\\y(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * sin(2t) - (1/4) * (c_1 + e^{-t}) * cos(2t)[/tex]

where [tex]c_1\ and\ c_2[/tex] are arbitrary constants.

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Answer:

6c for the total

Answer:

-4m

Step-by-step explanation:

=11m-7m-(2m+6m)

=11m-7m-8m

=-4m

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Answer:

-4m

Step-by-step explanation:

Hey!

==================================================================

First, We should remove the Parentheses.

To remove them, we distribute the negative over (2m + 6m).

⇒ 11m - 7m - (2m + 6m)

⇒ 11m - 7m - 2m - 6m

Work the Problem from Left to Right.

⇒ 4m - 2m - 6m

⇒ 2m - 6m

⇒ -4m

==================================================================

Hope I Helped, Feel free to ask any questions to clarify :)

Have a great day!

More Love, More Peace, Less Hate.

       -Aadi x

The time series component that exhibits a repeating pattern over successive periods, often one-year intervals, is called the seasonal component. It represents the regular and predictable variations in the data that occur due to seasonal factors, such as weather patterns, holidays, or annual events.

The seasonal component typically follows a consistent pattern, where the values tend to rise and fall in a similar manner within each season. For example, retail sales may experience higher values during the holiday season each year and lower values during other times.

Identifying and analyzing the seasonal component is crucial in many fields, including economics, finance, marketing, and forecasting. By understanding and accounting for the seasonal patterns, analysts and decision-makers can make more accurate predictions, adjust for seasonality in data, and develop strategies to optimize operations or sales during specific periods.

Methods such as seasonal decomposition or seasonal adjustment techniques are used to separate the seasonal component from other components, such as trend and irregular fluctuations, in order to better understand the underlying patterns and make informed decisions based on the data.

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Answer:

The front-end ratio is calculated by dividing an individual's anticipated monthly mortgage payment by his/her monthly gross income. The mortgage payment generally consists of principal, interest, taxes, and mortgage insurance (PITI). Lenders use the front-end ratio in conjunction with the back-end ratio to determine how much to lend.

Step-by-step explanation:

Answer:

y=1/9x+104

Step-by-step explanation:

I REALLY hope this helps

Sorry if im wrong

Best of luck!