Solve for z. -2 (52 - 4) +62 = -4​

The algebraic equation is given by:[tex]L[y(t)](s) = (s^2 + 1)Y(s) + 3s - 1 + e^{(-2s)}F(s)[/tex]

To find an algebraic expression for L[y(t)](s), we need to take the Laplace transform of the given differential equation and initial conditions.

Given:

Sy" + y + y = f(t - 2)

y(0) = 3

y'(0) = -1

Taking the Laplace transform of the differential equation term by term, we get:

[tex]L[Sy"](s) + L[y](s) + L[y](s) = L[f(t - 2)](s)[/tex]

Applying the derivative property of the Laplace transform, we have:

[tex]s^2Y(s) - sy(0) - y'(0) + Y(s) + Y(s) = e^{(-2s)}F(s)[/tex]

Substituting the initial conditions y(0) = 3 and y'(0) = -1, we have:

[tex]s^2Y(s) - 3s + Y(s) + Y(s) = e^{(-2s)}F(s) - 1[/tex]

Combining like terms, we get:

[tex](s^2 + 1)Y(s) + 3s - 1 = e^{(-2s)}F(s)[/tex]

Therefore, the algebraic expression for L[y(t)](s) is:

[tex]L[y(t)](s) = (s^2 + 1)Y(s) + 3s - 1 + e^{(-2s)}F(s)[/tex]

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Answer:

[tex](2x + 7) ( x + 7)[/tex]

Step-by-step explanation:

R = 1 / L = ∞. Thus, the radius of convergence of the given power series is ∞. The interval of convergence is (-1,1) is the answer.

a)The indefinite integral of x7ln(1 + x) can be obtained by using the formula for integration by parts. For the same, we need to select the parts as u and dv, such that on differentiating u and integrating dv, the obtained integrals get easier to solve.

Let us select x7 as u and ln(1 + x)dx as dv.u = x7 => du/dx = 7x6 => du = 7x6dx, and v = ∫ ln(1 + x)dx.

Using u and v, we can express the integral as,x7ln(1 + x)dx= ∫ u dv= uv - ∫ v du= x7 ln(1 + x) - ∫ 7x6/ (1 + x) dx = x7ln(1 + x) - 7 ∫ x6/ (1 + x) dxThe indefinite integral of the term ∫ x6/ (1 + x) dx can be obtained by the substitution method, let t = 1 + x, then x = t - 1, and dx = dt.∫ x6/ (1 + x) dx= ∫ (t - 1)6/t dt= ∫ (t6 - 6t5 + 15t4 - 20t3 + 15t2 - 6t + 1)/ t dt= ∫ t6/t dt - 6 ∫ t5/t dt + 15 ∫ t4/t dt - 20 ∫ t3/t dt + 15 ∫ t2/t dt - 6 ∫ t/t dt + ∫ 1/t dt= ∫ t5 dt - 6 ∫ t4 dt + 15 ∫ t3 dt - 20 ∫ t2 dt + 15 ∫ t dt - 6 ln|t| + ln|t| + C= t6/6 - 6t5/5 + 15t4/4 - 20t3/3 + 15t2/2 - 6 ln|t| + C.

Substituting the value of t, we get the indefinite integral of the original expression as,x7 ln(1 + x)dx= x7ln(1 + x) - 7 [x6/6 - 6x5/5 + 15x4/4 - 20x3/3 + 15x2/2 - 6 ln|1 + x|] + C= x7ln(1 + x) - x6 - 42x5/5 - 280x4/4 - 1125x3/3 - 1875x2/2 - 3150x - 735 ln|1 + x| + C.

Now, we need to obtain the power series for f(x) = x7ln(1 + x).

The formula to obtain the power series for f(x) = (1 / 1 - x)2 is as follows,f(x) = Σn=0 ∞ (n + 1)xn.

The integral x7ln(1 + x) can be written as Σn=1 ∞ (-1)n-1 xn / n.

Therefore, the power series for x7ln(1 + x) can be written as,f(x) = ∑n=1 ∞ (-1)n-1 xn / n= -x + x2/2 - x3/3 + x4/4 - x5/5 + x6/6 - x7/7 + ...= C + ∑n=1 ∞ (-1)n-1 xn / n, Where C is a constant, we can evaluate the value of C by substituting x = 0 in the power series. f(0) = 0, therefore, the constant C = 0.

Now, we need to obtain the radius of convergence of the obtained power series using the formula for the radius of convergence, R = 1 / lim supn→∞ |an|where an is the nth term in the power series.

In this case, |an| = |(-1)n-1 / n| = 1 / n.Let L = lim supn→∞ |an| = limn→∞ |an| = 0Therefore, R = 1 / L = ∞Therefore, the radius of convergence is ∞.

b)To obtain the power series for the given function f(x) = 13 / (x2 - 5x - 36), we need to first perform the partial fraction decomposition of the given function. The partial fraction decomposition of the given function is given as follows,f(x) = 13 / (x2 - 5x - 36)= 13 / [(x - 9)(x + 4)] = A / (x - 9) + B / (x + 4) where A and B are constants.

To obtain the values of A and B, we can equate the numerators on both sides and solve for A and B.13 = A(x + 4) + B(x - 9)At x = 9, we get 13 = 13B, B = 1.At x = -4, we get 13 = -4A, A = -13/4.

Therefore, the partial fraction decomposition of the given function is,f(x) = 13 / (x2 - 5x - 36)= -13/4 * 1 / (x + 4) + 1 / (x - 9)

Now, we can write the power series for the above partial fractions. The power series for 1 / (1 - x) is given by,f(x) = Σn=0 ∞ xn, |x| < 1

The power series for 1 / (x + 4) is given by,f(x) = -1/4 * Σn=0 ∞ (-x / 4)n, |x / 4| < 1

The power series for 1 / (x - 9) is given by,f(x) = Σn=0 ∞ (x / 9)n, |x / 9| < 1

Substituting the above power series in the original function, we get the power series for the given function as,f(x) = -1/4 * Σn=0 ∞ (-x / 4)n + Σn=0 ∞ (13 / 4) (x / 9)n= Σn=0 ∞ [-1/9 * (x / 4)n - 1/4 * (-x) n](x / 9)

Therefore, the power series for the given function is,f(x) = Σn=0 ∞ [-1/9 * (x / 4)n - 1/4 * (-x) n](x / 9)

The given function f(x) has the power series representation, f(x)= ∑n=0 ∞ [-1/9 * (x/4)n - 1/4 * (-x)n] * (x/9)n where c= 0.

Now, the radius of convergence of a power series is given by the formula,R = 1 / lim supn→∞ |an| where an is the nth term in the power series.

In this case, the nth term in the power series is given by |an| = |(-1)n-1 / 9 * 4n-1 | + |(-1)n / 4 * n|Let L = lim supn→∞ |an|. L = limn→∞ |(-1)n-1 / 9 * 4n-1 | + |(-1)n / 4 * n|L = 0 + 0 = 0.

Therefore, R = 1 / L = ∞Thus, the radius of convergence of the given power series is ∞.The interval of convergence is (-1,1)

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Step-by-step explanation:

[tex](2y - 3) = 45 \\ 2y = 48 \\ y = 24[/tex]

Answer:

$3200

Step-by-step explanation:

i had the answer but wanted to make sure

when added up everything equals 273,900

                                                                -700

                                                                --------

                                                           273,200

his networth is 270,000 that means when you subtract it from the 273,200 you are left with 3,200

Answer:

the answer is A

Step-by-step explanation:

-1+6=5

0+6=6

1+6=7

The equation that can be used to solve the problem is: 4x = 36. The solution is x = 9, indicating that 9 cupcakes were purchased. total cost of $36.00.

the equation that can be used is: 4x = 36. This equation represents the cost of each cupcake ($4.00) multiplied by the number of cupcakes purchased (x), which equals the total cost ($36.00).

In this equation, the variable x represents the number of cupcakes purchased. Multiplying the cost per cupcake ($4.00) by the number of cupcakes (x) should give the total cost of $36.00. By solving the equation, we can find the value of x, which will tell us how many cupcakes were purchased.

To solve the equation, divide both sides by 4: x = 36/4. Simplifying the division, x = 9. Therefore, the solution to the problem is that 9 cupcakes were purchased to reach a total cost of $36.00.

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Answer

i think the answer is c but i dont know good luck

Step-by-step explanation:

Answer:

£75

Step-by-step explanation:

Current value= 80

previous value= 100

current value 1

previous value = 100/80

current value-  £60

previous value 100x60/80

=6000/80

= £75

plz  mark me as brainliest.

The approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX.

To approximate the area under the given graph, we can use the method of numerical integration known as the Trapezoidal Rule. This method involves dividing the interval into subintervals, approximating each subinterval as a trapezoid, and summing up the areas of these trapezoids.

In this case, we are given 4 subintervals within the interval [5,13]. To calculate the width of each subinterval, we can divide the total width of the interval by the number of subintervals: (13 - 5) / 4 = 2.

Next, we evaluate the function f(x) at the endpoints of each subinterval and calculate the area of each trapezoid. Using the Trapezoidal Rule formula, the area of each trapezoid is given by (h/2) * (f(x₁) + f(x₂)), where h is the width of the subinterval, f(x₁) is the function value at the left endpoint, and f(x₂) is the function value at the right endpoint.

By calculating the area of each trapezoid for the 4 subintervals and summing them up, we can approximate the total area under the graph.

Performing the necessary calculations, the approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX (replace with the numerical result).

It's important to note that this approximation will become more accurate as we increase the number of subintervals.

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Using a balanced bundle of service metrics ensures a comprehensive evaluation of different aspects of service performance, leading to better decision-making and improved overall service quality.

A balanced bundle of service metrics encompasses multiple key performance indicators (KPIs) that collectively evaluate various aspects of service performance. Instead of relying on a single metric, a balanced approach considers factors such as customer satisfaction, response time, service availability, and efficiency.

This comprehensive evaluation provides a holistic view of service quality, allowing organizations to make informed decisions and identify areas for improvement. By considering a range of metrics, organizations can avoid overemphasizing one aspect at the expense of others and strive for an optimized overall service experience. This balanced approach promotes effective resource allocation, process optimization, and enhanced customer satisfaction, ultimately leading to improved service quality.

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Answer:

x = -2.

Step-by-step explanation:

2 ln(x + 3) = 0

ln(x + 3) = 0

Now ln 1 = 0 so

x + 3 = 1

x = -2.

(1) The given function f(x) = 12x³ - 13x² + 15x - 6 has a root in [0,1].

(ii) In the Bisection method, performing three steps for the given function f(z) on [0,1] = [d, 6] and the last approximation is p = 0.625. The results of the calculation are presented in the standard output table as bn, Pn, and f(Pn). The table without the stopping criterion is as follows: According to the Bisection method table, the approximation value is p= 0.625.

(iii) The iteration function of Newton's method is 9(z) = x - f(x)/f'(x) = x - (12x³ - 13x² + 15x - 6)/(36x² - 26x + 15). (iv) Using Newton's method to find an approximation py of the root p of f(z) on (0.1] satisfying RE(PNPN-1) < 10-7 by taking Po = 0.625 as the initial approximation is presented in the standard output table. Therefore, the root of the equation is approximately 0.6188.

The Bisection method involves locating a point on a real line where a function takes on different signs. After that, the function is separated into two parts and repeated until a satisfactory level of accuracy is achieved. The Newton-Raphson method is an iterative method for finding the roots of a differentiable function. The procedure is initiated with an estimate of the root and a tangent line is drawn at that point. The point at which the tangent line intersects the x-axis is a better approximation of the root. The procedure is repeated until the desired level of accuracy is achieved.

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Answer:

100 Nm

Step-by-step explanation:

Work is said to be done when a force moves a body through a distance. This may be expressed as

work done = Force * distance

where

work done is measured in joules or Newton-meter

Force is measured in newtons and distance in meters

Substituting the given values,

Workdone = 20 * 5

= 100 Nm

= 100J

y(1) equal to zero and x equal to 2, the differential equation dy/dx = x2 + y2 has an approximate solution of y(2) 0.0101005. y(2)_c = y(1) + (0.01/2)*[(12 + 02) + (22 + 0.012)]= 0.0101005.

In numerical analysis, the predictor-corrector method is an important tool for solving ordinary differential equations. It is a combination of two distinct strategies, the corrector and the indicator. The indicator technique uses a limited distinction conspire to predict the value of the dependent variable at the subsequent time step, whereas the corrector strategy uses this anticipated value to correct the indicator's error.

To deal with dy = x2 + y2 using the marker corrector method; When y(1) = 0 dx for y(2) and h = 0,01, we can begin by employing the Euler's technique as the indicator strategy and the adjusted Euler's technique as the corrector strategy. The following is the equation for Euler's method: Coming up next is the way we can decide the anticipated worth of y(2) utilizing this strategy: where f(x,y) = x2 + y2 and y(i+1) = y(i) + h*f(x(i),y(i)).

Utilizing the altered Euler's strategy, we can decide the adjusted worth of y(2) as follows: y(1) + h*f(x(1),y(1)) = 0 + 0.01*(12 + 02) = 0.01 y(i+1) = y(i) + (h/2)*(f(x(i),y(i)) + f(x(i+1,y(i+1)_p) The differential equation dy/dx = x2 + y2 has an approximate solution of y(2) 0.0101005 when y(1) is set to zero and x is set to 2. y(2)_c = y(1) + (0.01/2)*[(12 + 02) + (22 + 0.012)]= 0.0101005.

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The given data represents the ages of world leaders on their day of inauguration. The five-number summary consists of the minimum value, which is 44, the first quartile (Q1) at 53, the median at 61, the third quartile (Q3) at 67, and the maximum value at 69.

The five-number summary for the given data is as follows: Minimum: 44, First quartile (Q1): 53, Median (Q2): 61, Third quartile (Q3): 67, Maximum: 69.

To construct a boxplot, we can represent the five-number summary on a number line. The boxplot will have a box representing the interquartile range (from Q1 to Q3) with a line inside representing the median (Q2). Whiskers will extend from the box to the minimum and maximum values, and any outliers will be shown as individual data points.

The shape of the distribution can be inferred from the boxplot. If the box is symmetrically positioned and the whiskers are roughly equal in length, the distribution is likely to be approximately symmetric. If the box is skewed or the whiskers are unequal, the distribution may be skewed or have outliers.

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Two distinct lines are said to be parallel if they have no point of intersection. This statement is true.

A line is a straight figure that continues infinitely in both directions. It has no endpoints. The term "parallel lines" is used to describe two or more lines that do not intersect. When we draw parallel lines, they seem to be straight and never touch each other. Therefore, the two distinct lines are said to be parallel if they have no point of intersection and the statement is true.

A line is a boundlessly lengthy item with no width, profundity, or shape. Lines can be embedded in spaces of two, three, or higher dimensions, but they are one-dimensional objects. The word line may likewise allude to a line fragment in regular day to day existence, which has two focuses to mean its closures.

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Answer:

2x² - 5x - 3

= 2x² -6x + 1x -3

= 2x( x - 3) + 1 (x - 3)

= ( x - 3) (2x + 1)

1. Y-intercept b=5

That means it has a 5.00 starting fee.

2. Using the formula (Y2-Y1)/(X2-X1) we will find the slope between the two points.

Point one (X1 and Y1) will be the Y-intercept.

X1,Y1 = (0, 5.00)

Point 2 (X2 and Y2) will be the point on the trend line.

X2, Y2 = (200, 6.00)

Plug in:

(6.00 - 5.00)/(200 - 0) = 00.5 or 1/200.

3. When printing 200 pages each page will cost $.005.

4. .005x+5

5. .005x+5

.005(300)+5=6.5

good luck♡♡!!

Answer:

The median is 6.5 :)

Step-by-step explanation:

Brainliest please?

The median of the data in the bar chart given is 6.5 kilometers.

Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order.

Given is a bar chart which shows the distance that each family member run in a relay race.

The data is given as :

4, 11, 5, 8

In order to find the median, first arrange the data in an increasing order.

4, 5, 8, 11

Since there are even number (4) of data points, median is the average of the middle two elements.

Median = (5 + 8) / 2 = 6.5 km

Hence the median of the given data is 6.5 kilometers.

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Answer:

= $88.7429

Step-by-step explanation:

Regular price: $124.99

Total off: $124.99 x 20% + 15% = 43.7465%

Tax: $124.99 x 6% = 7.4994

So he should pay: 124.99 - 43.7465 +7.4994

The total cost of her meal would be amount of $88.74.

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

For example, If Misha obtained a score of 57% on her exam, that corresponds to 67 out of 100.

As per the given information, the required solution would be as

Regular price of dinner = $124.99

Total off =  $124.99 × 20% + 15% = 43.7465%

Total tax = $124.99 × 6% = 7.4994

The total cost of her meal = Regular price of dinner - Total off + Total tax

The total cost of her meal = 124.99 - 43.7465 +7.4994

Apply the arithmetic operation to get the cost

The total cost of her meal = 88.74

Therefore, the total cost of her meal would be amount of $88.74.

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Answer:

huhhhhh ?????// thanks for the points but what words did u mean to say /???//

Step-by-step explanation:

Answer:c

Step-by-step explanation:the y has to be greater than -1 and x is just a longer negative y

Answer:

See Below.

Step-by-step explanation:

Remember that:

Where c is the longest side, and a and b are the two remaining sides.

[tex]4^2\text{ is }\textbf{ less than (or $<$) } 3^2+3^2[/tex]

[tex]\text{Therefore, }\Delta JKL \text{ is }\textbf{an acute triangle.}[/tex]

(16 is less than 9 + 9 or 18.)

[tex]5^2\text{ is } \textbf{equal to (or $=$) } 3^2+4^2[/tex]

[tex]\text{Applying the same method, $\Delta ABC$ is }\textbf{ a right triangle.}[/tex]

(25 is equal to 9 + 16 = 25.)

Answer:

less then

acute

equal to

right

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, that is

∠ 1 = 60° + 25° = 85° →  C

Answer:

C 85

Step-by-step explanation:

Answer:

a4 = 5/9

Step-by-step explanation:

a1 = 15 , r = 1/3

, a4 =?

Explanation:

To find a4 we use formula

an = a1 · r

n−1

In this example we have a1 = 15 , r = 1/3

, n = 4. After substituting these values to above

formula, we obtain:

an = a1 · r

n−1

a4 = 15 ·

1

3

4−1

a4 = 15 ·

1

27

a4 =

5

9

Answer:

257.6

step by step explanation:

1472×2.5×7÷100