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Find the inverse laplace transform of: (2 s + 4) / (s - 3)^3

Answers

Answer 1

Answer:

Answer:

$e^(3t)(2t+5t^(2))$

Step-by-step explanation:

$L^(-1)[(2s+4)/((s-3)^(3)) ]=$

Using the Translation theorem to transform the s-3 to s, that means multiplying by and change s to s+3

Translation theorem: $L^(1) [F(s-a)=L^(-1)[F(s)|_(s \to s-a)\n L^(1) [F(s-a)=e^(at) f(t)$

$L^(-1)[(2s+4)/((s-3)^(3)) ]=e^(3t) L^(-1)[(2(s+3)+4)/(s^(3)) ]$

Separate the fraction in a sum:

$e^(3t) L^(-1)[(2s+10)/(s^(3)) ]=e^(3t) L^(-1)[(2s)/(s^(3))+(10)/(s^(3)) ]=e^(3t) (L^(-1)[(2)/(s^(2))]+ L^(-1)[(10)/(s^(3))])$

The formula for this is:

$L^(-1)[(n!)/(s^(n+1)) ]=t^(n)$

Modify the expression to match the formula.

$e^(3t) (2L^(-1)[(1)/(s^(1+1))]+ (10)/(2) L^(-1)[(2)/(s^(2+1))])=e^(3t) (2L^(-1)[(1)/(s^(1+1))]+ 5 L^(-1)[(2)/(s^(2+1))])$

Solve

$e^(3t) (2L^(-1)[(1)/(s^(1+1))]+ 5 L^(-1)[(2)/(s^(2+1))])=e^(3t)(2t+5t^(2) )$

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Let f be the linear function (in blue) and let g be the parabolic function (in red) below. I have already tried 0,2,-1 and none of them work for the g o g(2) one and I'm soo confused. Please help!

Answers

Based on the graph of the linear function (in blue) and parabolic function (in red), the corresponding output values include the following;

(f∘g)(2) = -1.

(g∘f)(2) = 1.

(f∘f)(2) = 0.

(g∘g)(2)= 4.

(f + g)(4) = 7.

(f/g)(2) = DNE.

What is a function?

In Mathematics and Geometry, a function composition is an operation (∘) that combines two functions f(x) and g(x), in order to produce a composite function h(x) = (g∘f)(x), such that h(x) = g.

In this exercise, we would determine the corresponding output values for each of the composite functions by using the substitution method as follows;

(f∘g)(2) = f(g(2))

f(g(2)) = f(0)

f(0) = -1.

Part 2.

(g∘f)(2) = g(f(2))

g(f(2)) = g(1)

g(1) = 1.

Part 3.

(f∘f)(2) = f(f(2))

f(f(2)) = f(1)

f(1) = 0.

Part 4.

(g∘g)(2) = g(g(2))

g(g(2)) = g(0)

g(0) = 4.

Part 5.

(f + g)(4) = f(4) + g(4)

f(4) + g(4) = 3 + 4

f(4) + g(4) = 7.

Part 6.

(f/g)(2) = f(2)/g(2)

f(2)/g(2) = 1/0

f(2)/g(2) = DNE.

Read more on composite function here: brainly.com/question/30660139

#SPJ2

Step-by-step explanation:

g(g(2))

= g(0)

= 4

- Use the unit circle to evaluate
the six trigonometric functions
of theta= 4pi

Answers

The six trigonometric functions, $\sin (\pi)/(4) =(1)/(√(2))$ , $\cos (\pi)/(4) =(1)/(√(2))$ , $\tan (\pi)/(4) =1$ , $\cot (\pi)/(4) =1$ , $\sec (\pi)/(4) =√(2)$ and $\csc (\pi)/(4) =√(2)$ .

Step-by-step explanation:

We have,

$(\pi)/(4)$

To write the six trigonometric functions = ?

$\sin (\pi)/(4) =(1)/(√(2))$

$\cos (\pi)/(4) =(1)/(√(2))$

$\tan (\pi)/(4) =1$

$\cot (\pi)/(4) =1$

$\sec (\pi)/(4) =√(2)$

$\csc (\pi)/(4) =√(2)$

∴ The six trigonometric functions, $\sin (\pi)/(4) =(1)/(√(2))$ , $\cos (\pi)/(4) =(1)/(√(2))$ , $\tan (\pi)/(4) =1$ , $\cot (\pi)/(4) =1$ , $\sec (\pi)/(4) =√(2)$ and $\csc (\pi)/(4) =√(2)$ .

Someone help me simplify this 3t+12-9=

Answers

it's simple

3t+3

just this

You would subtract 9 from 12 which would give you 3 which would lead you to 3t+3

What is a root function of the polynomial function F(x)= x^3 + 3x^2 - 5x - 4

Answers

This is your answer
Xxxx

Step-by-step explanation:

Factor by grouping.

f(x) = x³ + 3x² − 5x − 4

f(x) = x³ + 3x² − 4x − x − 4

f(x) = x (x² + 3x − 4) − (x + 4)

f(x) = x (x − 1) (x + 4) − (x + 4)

f(x) = (x² − x) (x + 4) − (x + 4)

f(x) = (x² − x − 1) (x + 4)

A community is deciding whether to find a new gymnasium

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Whats the question ELAISSAROYER22

I NEED AN EXPLANATION PLEASE!! I need a fast answer

Answers

Answer:

B) 74 degrees

Step-by-step explanation:

three angles = 180

2x+32=180

2x=148

x=74

Hope this helps plz hit the crown :D

Answer:

i think B which is 74

Step-by-step explanation:

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Find the inverse laplace transform of: (2 s + 4) / (s - 3)^3

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What is a function?

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The six trigonometric functions, , ,, , and .

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The six trigonometric functions, $\sin (\pi)/(4) =(1)/(√(2))$ , $\cos (\pi)/(4) =(1)/(√(2))$ , $\tan (\pi)/(4) =1$ , $\cot (\pi)/(4) =1$ , $\sec (\pi)/(4) =√(2)$ and $\csc (\pi)/(4) =√(2)$ .