Brainlest for correct awnser :D

Inverse Laplace transform of f(s) = s³ / (s² + 6s + 13) is

[tex]f(t) = [(-3 + 2i)^{13} / (2i)] e^{(-3 + 2i)t} + [(-3 - 2i)^{13} / (-2i)] e^{(-3 - 2i)t[/tex]

The inverse Laplace transform of f(s) = s¹³ / (s² + 6s + 13) needs to be found.

To find the inverse Laplace transform, we first need to factor the denominator of f(s) using the quadratic formula:

s² + 6s + 13 = 0

s = [-6 ± √(6² - 4(1)(13))] / 2(1)

s = -3 ± 2i

Now we can rewrite f(s) as:

f(s) = s¹³ / [(s + 3 - 2i)(s + 3 + 2i)]

Using partial fraction decomposition, we can write:

f(s) = A / (s + 3 - 2i) + B / (s + 3 + 2i)

where A and B are constants to be determined. Multiplying both sides by the denominator, we get:

s¹³ = A(s + 3 + 2i) + B(s + 3 - 2i)

Substituting s = -3 + 2i, we get:

(-3 + 2i)¹³ = A(2i)

Solving for A, we get:

A = (-3 + 2i)¹³ / (2i)

Similarly, substituting s = -3 - 2i, we can solve for B:

B = (-3 - 2i)¹³ / (-2i)

Now we can write f(s) as:

f(s) = [(-3 + 2i)¹³ / (2i)] / (s + 3 - 2i) + [(-3 - 2i)¹³ / (-2i)] / (s + 3 + 2i)

Taking the inverse Laplace transform of each term separately using the table of Laplace transforms, we get the final answer:

[tex]f(t) = [(-3 + 2i)^{13} / (2i)] e^{(-3 + 2i)t} + [(-3 - 2i)^{13} / (-2i)] e^{(-3 - 2i)t[/tex]

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The given question is incomplete, the complete question is below

Find the inverse Laplace transform. f(s) = s¹³ / (s² + 6s + 13)

Newton has just gone grocery shopping. The mean cost for each item in his bag was $3.38. The price of the 6th item in his bag is $1.64

To determine the price of the 6th item in Newton's bag, we can use the concept of the mean (average). We know that the mean cost for each item in his bag is $3.38, and he bought a total of 6 items.

To find the sum of all 6 item prices, we can multiply the mean cost by the total number of items:

Sum of all item prices = Mean cost * Total number of items

                                    = $3.38 * 6

                                    = $20.28

We also know the prices of 5 of the items, which are $4.09, $4.03, $4.19, $2.24, and $4.09.

To determine the price of the 6th item, we subtract the sum of the known prices from the sum of all item prices:

Price of the 6th item = Sum of all item prices - Sum of known prices

= $20.28 - ($4.09 + $4.03 + $4.19 + $2.24 + $4.09)

= $20.28 - $18.64

= $1.64

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Answer:

Circumference ~ 233.7

Step-by-step explanation:

Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is about 37.2. Plug 37.2 into the formula 2(pi)r to find the Circumference. The answer is 233.7 rounded to the nearest tenth.

The graph of this function begins at 5 and moves down to 2 and back to 5 again in a repeated pattern over one period of 1.

A cosine function is a periodic function that fluctuates about its midline and follows a predictable pattern. The formula for a cosine function with a midline of y = c, amplitude of a, and period of b is:y = a cos(bx) + cTo shift the graph of a cosine function,

you can add or subtract a value inside the parentheses of the formula, which results in a horizontal shift.

The shift is to the right if you add, and to the left if you subtract.In this instance,

the cosine function has the following characteristics:Midline = y = 5Amplitude = 3Period = 1Horizontal shift to the right = 1/4We'll have to adjust the formula to include all of these parameters.

First and foremost, let's figure out the function's frequency, which is determined by dividing 2π by the period of the cosine function. In this example, the frequency is 2π/1, which equals 2π.

y = a cos(bx) + c is the formula we'll use. We'll substitute the values given into the formula. The resulting formula is:y = 3cos(2π(x - 1/4)) + 5This is the cosine function with a midline of y = 5, an amplitude of 3, a period of 1, and a horizontal shift of 1/4 to the right.

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Answer:

The measure of the inscribed angle is [tex]40^{\circ}[/tex]

Step-by-step explanation:

Recall that the measure of the inscribed angle is one-half the measure of the central angle subtended by the same arc.

So, if the measure of the central angle is [tex]80^{\circ}[/tex], so the measure of the corresponding inscribed angle is:

[tex]\frac{1}{2}\times 80^{\circ}=40^{\circ}[/tex]

A differential equation is an equation involving a differentiable function, which is a critical tool in modeling physical phenomena like population growth, radioactive decay, and fluid flow.

A differential equation is an equation that involves a differentiable function. It is an equation in which the variables' derivatives appear. Differential equations are used to model physical phenomena like population growth, radioactive decay, and fluid flow. The order of a differential equation is the highest order of the derivative of the function. A first-order differential equation has the highest order of 1, and a second-order differential equation has the highest order of 2.A differential equation can be classified into three types: Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), and Differential Algebraic Equations (DAEs). Ordinary differential equations have a single independent variable and one or more dependent variables that depend on it. Partial differential equations have more than one independent variable and multiple dependent variables that depend on each other. Differential algebraic equations have both derivatives and algebraic equations in them.A differential equation is essential in physics, engineering, and mathematics. It is used to model many natural phenomena and helps in predicting the future. Most differential equations can not be solved analytically, so numerical methods are used to find approximate solutions. In conclusion, A differential equation is an equation involving a differentiable function, which is a critical tool in modeling physical phenomena like population growth, radioactive decay, and fluid flow.

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Answer:

Acute angles are less than 90

obtuse is more than 90

right angles are exactly 90

Step-by-step explanation:

Answer:

First option: 90 degrees

Step-by-step explanation:

Obtuse is greater than 90.

Acute is less than 90.

Right is 90.

Answer:

57.33

Step-by-step explanation:

50+28+3x=180

78+3x=180-78

3x=172/3

x = 57.33

240÷30=8

8×30=240

30 height 8 with

Answer:

5/12

Step-by-step explanation:

add 3/12 and 2/12 to get 5/12 (decimal form is .416)

Answer:5/12 pounds

Step-by-step explanation: You take the 3 and add it with the 2 and you get 5/12

[tex]\frac{3}{12}[/tex] + [tex]\frac{3}{12}[/tex] = [tex]\frac{5}{12}[/tex]

Answer:

rectangular prisim

Step-by-step explanation:

Answer:

rectangular prism

Step-by-step explanation:

rectangle shaped box

1) Play

2)Dribble

3)Paint

4)Center

5)Assists

6)Perimeter

7)Benchwarmer

8)Aboard

9)Technical

10)Rebound

11)Penalty

12)screen

13)Overtime

14)guard

15)? Host

16)Quarter

17) Bounce

18)Swish

19)Halftime

20)Backcourt

Answer:

126+111+43+8=288

360-288=72

72÷12=6

x=6

Answer:  

x=6

Step-by-step explanation:

Step by step explaination attached below.

An object located at the point (4, 55) on a distance time graph is later located at the point (9, 45). If distance is in metres and time is in seconds, the average speed is -2 m/s.

To calculate the average speed of an object, we need to find the total distance traveled divided by the total time taken.

Given that the object is located at the point (4, 55) initially and later located at the point (9, 45), we can determine the total distance traveled and the total time taken.

Total distance traveled = Difference in distance = 45 - 55 = -10 meters (negative because the object moved from a higher distance to a lower distance)

Total time taken = Difference in time = 9 - 4 = 5 seconds

Average speed = Total distance traveled / Total time taken = -10 meters / 5 seconds = -2 meters/second

Therefore, the average speed of the object is -2 m/s.

Option (a) -2 m/s is the correct answer.

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Answer:

i guess you multiply 3and 30good lu8ck

Step-by-step explanation:

Answer:

3x+30=90 complementary

3x=90-30

x=60/3=20

x=20° is your answer

Answer:

I think the volume of the figure is 60 but I'm not 100 % sure

Step-by-step explanation:

I belive the formula for this figure was (a+b)xh/(2)

So 40x 3 = 120

120/2 = 60

Answer:

1.The two major types of metal electrical cable are:

A.wire and fibre

2. What are the most common forms of wireless connection?

C.Radio news

3. Wi-fi connections have limited range of :

D.300 metres

Answer:

exponential growth or exponential decay , and what ... The value of a car purchased for $20,000 decreases ... population, P, increases by 20%each year,

Answer:

Other dude is correct

Step-by-step explanation:

Answer:

32x

Step-by-step explanation: 4(8x)=32x

Answer: 11 units

Step-by-step explanation:

-3 and 3 are 6 units apart, so that would be 6 units, and when you add the -5 into the problem, the 6 units become 11 units. Hope this helped :)

Answer:

Exact Form:

√ 61

Decimal Form:

7.81024967 …

The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

To draw the state diagram of a PDA that accepts the language L = {w ∈ {a, b}^∗ | w has twice as many a's as b's}, we can design a simple PDA with two states.

State 1: Initial state

Transition: (a, ε, a) -> State 1

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

State 2: Secondary state

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

Accepting state: Final state to indicate that the input string is accepted.

Here is the state diagram representation of the PDA:

Note: Find the attached image for the state diagram representation of the PDA.

In this PDA, State 1 is the initial state, and State 2 is the secondary state. The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).

The PDA works as follows:

This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

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Answer:

yes,yes,yes,no :) hope it helps

Step-by-step explanation:

Answer:

1. Yes

2. No

Definition of a Polygon: a plane figure with at least three straight sides and angles, and typically five or more.

Answer:

Choice B - (1.02)

Step-by-step explanation:

With the teachers starting salary being $40,000, we can rightfully assume that it their salary would not increase with Choice A, $40,000 * 0.2 = $800.

2% otherwise known as 0.02, would make the teachers yearly salary $40,000 * 1 + 0.02, or $40,000 * 1.02. Making the correct answer, Choice B - (1.02). (This would also give the teacher an additional $800 per year!)

Answer:

5-8

Step-by-step explanation:

you just had to move the 8 over

The confidence interval using a 90% confidence level is (1.601, 1.819)

Confidence Interval = Sample Mean ± Margin of Error

Given the parameters:

Sample Mean (x) = 1.71

Population Standard Deviation (σ) = 0.86

Sample Size (n) = 170

Confidence Level = 90%

The standard Error(SE) is given by:

SE = σ / √n

SE = 0.86 / √170 ≈ 0.0663

The margin of Error is related to standard error by the relation:

ME = Z × SE

ME = 1.645 × 0.0663 ≈ 0.109

Confidence Interval = Sample Mean ± Margin of Error

Confidence Interval = 1.71 ± 0.109

Confidence Interval= (1.601, 1.819)

A decrease in sample size from 170 to 120 would lead to increase in error margin , since decrease in sample size will increase the standard error.

If confidence interval were raised from 90% to 95% , the error margin would be larger since increase in confidence interval would increase the critical value

Based on the confidence interval , it is very likely that the mean number of personal computers is greater than 1.

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The sequence continues as follows:2, 5, 11, 21, 36, 67, ...

Given sequence2 5 11 21 36...

First differences 3 6 10 15...

Second differences 3 4 5...

Third differences 1 1...

The third differences are constant, which means that we can use a cubic polynomial for the fitting.

The formula for a cubic polynomial is

an³ + b

n² + c

n + d

Let us denote the nth term of the sequence by fn. Then, we have

f1 = 2, f2 = 5, f3 = 11, f4 = 21, f5 = 36...

We can write a system of equations using the first four terms of the sequence.

2 = a + b + c + d

5 = 8a + 4b + 2c + d

11 = 27a + 9b + 3c + d

21 = 64a + 16b + 4c + d

Solving this system, we get a = 1/3, b = 1, c = 11/3, and d = 0.

Thus, the closed-form expression for the nth term of the sequence isf(n) = (1/3)n³ + n² + (11/3)n

The next term in the sequence is f(6) = (1/3)(6)³ + (6)² + (11/3)(6) = 67.

Therefore, the sequence continues as follows:2, 5, 11, 21, 36, 67, ...

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