Use a table of Laplace transforms to find the Inverse Laplace transform of


F(s)= [tex]\frac{3s+9}{s^2+9}[/tex]


f(t)=_____

Answers

Answer 1

Answer:

The inverse Laplace transform of [tex]F(s) = \frac{3\cdot s + 9}{s^{2}+9}[/tex] is [tex]f(t) = 3\cdot \cos \omega t + 3\cdot \sin \omega t[/tex].

Step-by-step explanation:

In this case, we should use the following direct and inverse Laplace Transforms:

[tex]F(s) = G(s) + H(s)[/tex] (1)

[tex]\mathcal{L}^{-1} \{\frac{s}{s^{2}+\omega^{2}} \} = \cos \omega t[/tex] (2)

[tex]\mathcal{L}^{-1}\{\frac{\omega}{s^{2}+\omega^{2}} \} = \sin \omega t[/tex] (3)

[tex]\mathcal\{L\}^{-1}\{c\cdot F(s)\} = c\cdot \mathcal\{L\}^{-1}\{F(s)\}[/tex] (4)

Then, we apply all these trasforms:

[tex]F(s) = \frac{3\cdot s + 9}{s^{2}+9}[/tex]

[tex]F(s) = 3\cdot \left(\frac{s}{s^{2}+9} \right)+3\cdot \left(\frac{3}{s^{2}+9} \right)[/tex]

[tex]f(t) = 3\cdot \cos \omega t + 3\cdot \sin \omega t[/tex]

The inverse Laplace transform of [tex]F(s) = \frac{3\cdot s + 9}{s^{2}+9}[/tex] is [tex]f(t) = 3\cdot \cos \omega t + 3\cdot \sin \omega t[/tex].


Related Questions

Which number is not a factor of 42?
2 3. 4 7

Answers

Answer:

3

by using divisibility test

Answer: Its 3

Step-by-step explanation: This is because 42 can be divided by 2 4 and 7 and still be a whole number but when you divide 3 by 42 you get 10.5

Hope this helps and have a nice day

Helppppppppppppppppppppp

Answers

C hope that helps because if you look at your answers and compare your question to that there u go

please help me find the missing side !

Answers

Answer:

x=14 and y=7

Step-by-step explanation:

This is a 30-60-90 triangle

So in terms of x it would be [tex]x-x\sqrt{3} -2x[/tex]

If across the 60 is [tex]7\sqrt{3}[/tex] then y would be 7 which is across the 30 degrees

And x would be 14 because 2(7)=14

The Davis family is going to reseed the grass in the backyard. Their yard is irregularly shaped with a cement patio and rectangular garden as shown below. Given that the family will not need grass seed for the patio or the garden areas, what is the total area of the land will they be reseeding?

Answers

Answer:

1,482 square feet

Step-by-step explanation:

Find total area - 37 x 46 = 1,702

Find area of patio and garden - 16 x 10 = 160 for the patio, 12 x 5 = 60 for the garden

Subtract from total area - 1702 - 160 = 1542, 1542 - 60 = 1,482 sq ft

Which of the following is equivalent to log 25 125?

Answers

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Did you mean [tex]log_{25}[/tex] 125, so that your base is 25?  If so then all you do is ask  yourself "25 to what power is 125?" since [tex]25^{\frac{3}{2} }[/tex] = 125, then the  [tex]log_{25}[/tex] 125 = 3/2

Can someone please help me I’m desperate it due tomorrowwww

Answers

Answer:

Step-by-step explanation:

First box: m=1/2

Second box: m=2

Third box: m=1

Fourth box: m=2

Does the table represent an exponential function? Explain why or why not.
(3,-10 ), (4,-7 ), (5,-4), (6,-1), (7,2),(8,5)

Answers

Answer:

No, it does not.

Step-by-step explanation:

It's a linear function, with a slope of -3 (down 3 for every new X as you move right)

No, it does not........

Divide x2 by x - 1. What is the value of the remainder?
A) 1
B) -1
C) 2
D) o

Answers

Answer:

I think it's B.

Step-by-step explanation:

Divide using polynomial division.

x + 1 + 1/ x − 1.

Maybe not 100% sure.

In ΔJKL, j = 520 inches, k = 730 inches and l=640 inches. Find the measure of ∠K to the nearest degree.

Answers

Answer:

It’s 56.7

Step-by-step explanation:

Fudisks

Help please !!!! This is really hard

Answers

Answer:

Option -c  :5^ -12  .  2^ 40

Step-by-step explanation:

(  5^6 . 2^8    )( 5^-2  . 2^5 )

(  5^6 . 5^-2  )   ( 2^8  . 2^5 )

5^ -12  .  2^ 40

Option -c :  5^ -12  .  2^ 40

I hope im right!!  

3 (7/5x+4) -2 (3/2 - 5/4x)​

Answers

Answer:

I know the mixed number will be 1 because u subtracts that's all I know and just subtracts the fractions ok sorry

Answer:

[tex]6\frac{7}{10}x + 9[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]3(\frac{7}{5}x + 4)-2(\frac{3}{2}-\frac{5}{4}x)[/tex]

[tex](3*\frac{7}{5}x) + (3 * 4) + (-2 * \frac{3}{2}) + (-2 * -\frac{5}{4}x)[/tex]

[tex]\frac{21}{5}x + 12 + \frac{-6}{2} + \frac{10}{4}x[/tex]

Step 2:  Combine Like Terms

[tex]12 - 3 + \frac{21}{5}x + \frac{5}{2}x[/tex]

[tex]9 + (\frac{21*2}{5*2}x + \frac{5*5}{2*5})[/tex]

[tex]9+(\frac{42}{10}x + \frac{25}{10}x)[/tex]

[tex]9+\frac{67}{10}x[/tex]

[tex]6\frac{7}{10}x + 9[/tex]

Answer:  [tex]6\frac{7}{10}x + 9[/tex]

Please let me know if you need to make it more clear!  :)

Value of ratio 3/4 to 2

Answers

Answer:

3/8 or 0.375

Step-by-step explanation:

0.75/2 = 3/8

Whats the answer to these? (These are called Proper fractions.)

Jeremiah ran for 3/10 of a mile and then walked another 2/5 of a mile. How far did he travel in all?

Daniel read 4/5 books and Edgar read 1/2 books. How many more books did Daniel read than Edgar?

Jared drove 2/8 miles to the restaurant. He drove another 1/4 miles to the mall. How many miles did he drive in all?

Answers

Answer:

1: 7/10

2: 3/10

3: 4/8 (2/4 or 1/2 if you need to simplify it)

Step-by-step explanation:

1: Convert 2/5 to tenths by multiplying the denominator and numerator by two. 3/10 plus 4/10 is 7/10

2: Convert 4/5 and 1/2 to tenths.

4/5 is going to be 8/10, 1/2 is going to be 5/10.

Subtract 5/10 from 8/10 to get 3/10

3: Convert 1/4 to eighths to get 2/8. Then add 2/8 and 2/8 to get 4/8.

Jeremiah: convert the 5ths to 10ths
3/10 + 4/10 = 7/10

Daniel: convert both fractions to 10ths
8/10 - 5/10 = 3/10

Jared: reduce 8ths to 4ths
1/4 + 1/4 = 2/4 = 1/2

Write down the name of the solid.

Answers

Answer:

Cube

Step-by-step explanation:

Is 2 a solution of 4z + 12 = 4? Complete the statement.​

Answers

Answer:

No im pretty sure its not a solution.

Step-by-step explanation:

See if “z” is 2 than the answer to the solution would be 20

Answer:

The solution is -2

Step-by-step explanation:

4z + 12 = 4

Subtract 12 on each side (4z + 12 - 12 = 4 - 12)

4z = -8

Divide 4 on each side (4z / 4 = -8 / 4)

z = -2

Who can help me with this question problem

Answers

Answer:

use the formula and evaluate the givens

Step-by-step explanation:

336=(14/11)^2 * 22/7*h

336=196/121 * 22/7h

336= 4312/847h

336= 5.09h

h=66

Use the table to write a linear function that relates y to I.
X
-2
0
2
4
y
-7
- 7 - 7
- 7
=
10

Answers

Answer:

y = -7

Step-by-step explanation:

✔️Find the slope (m) using any two pairs of values, say (0, -7) and (2, -7):

Slope (m) = ∆y/∆x = (-7 -(-7))/(2 - 0) = 0/2 = 0

Slope (m) = 0

✔️Find y-intercept (b):

y-intercept is the value of y when x = 0. From the table, when x = 0, y = -7.

Therefore, y-intercept (b) = -7

✔️ Substitute m = 0 and b = -7 into y = mx + b (slope-intercept form):

y = 0(x) + (-7)

y = -7

Help and show work please

Answers

Answer:

11111111    111 1 1 1 11

Step-by-step explanation:

Answer:

ok 1+1= 25 and add 3000 and you get 1

Step-by-step explanation:

2|2x-6|=20

How the hell do you do this guys :(

Answers

Its 8
2x -6 =10
2x= 10+6
2x=16
X= 8

Answer:

x1 = -2, x2 = 8

Step-by-step explanation:

You can first divide both sides of the equation by 2 so now you have:

I 2x - 6 I = 10

Then use the absolute value definiton and rewrite it into two separate equations:

1.) 2x - 6 = -10

2.) 2x - 6 = 10

From here you can solve both equations:

1.) x = -2

2.) x = 8

i hoped this helps

Evaluate the expression 6h ÷ 2 when h = 3

Answers

Answer:

9

Step-by-step explanation:

18 / 2 = 9

Answer:

9

Step-by-step explanation:

6h/2

Since H is = to 3, u plug in 3 to H and 6 times H would be 3. 6*3 is 18 so then you wuold divide 18 by 2 which would equal 9

.nooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

Answers

Answer: What is this free?

Answer:

yes

Step-by-step explanation:

yes+yes(no-no)

=yes

i rlly need help. plssssss

Answers

I don’t understand

Answer:

10

Step-by-step explanation:

5 x 8 / 4

40/4=10

Given 10 shirts, 6 pants, and 4 pairs of shoes to choose from, how many different combinations containing 1 shirt, 1 pants, and 1 pair of shoes are there?​

Answers

9 shirts, 5 pants, 4 pairs.

4 Combinations since the lowest of them is 4.Answer:

Step-by-step explanation:

9 shirts, 5 pants, 4 pairs.

4 Combinations since the lowest of them is 4.

P = 2l + 2w, when P = 28 ft. and w = 5 ft.

Answers

Answer:

9

Step-by-step explanation:

5*2=10 28-10=18 18/2=9

I Question 7 (2 of 13)
Find area of shaded region. Round to the nearest tenth.
50 cm
radius: 20 cm
80 cm
Enter your answer by clicking the bubbles.

Answers

Method:
Area of trapezium - Area of a half circle

Trapezium = 40(50+80) divided by 2

= 2600

Half circle = 1/2 x pi x 20^2

= 628.3185....
~ 628.3

2600 - 628.3 = 1971.7 cm^2

Hope this helps!!




Martina is currently 18 years older than her cousin Joey. In 5 years she will be 3 times as old as Joey . Use this information to answer the following questions.
If you let x represent Joey's current age, what expression can you use to represent Martina's? PLEASE HELP
current age?

Answers

Answer:

The age of Joey is 4 years  and

The age of Martina is 22 years .

Step-by-step explanation:

Given as :

Martina is 18 years older than her Joey

In 5 years, Martina will be three times older than Joey

Let The age of Martina = M years

And The age of Joey = J years

Now, According to questions

M = J + 18          ........1

(M+5) = 3 × (J+5)

Or, M + 5 = 3 J + 15

Or, M - 3 J = 15 - 5

∴ M - 3 J = 10                ..........2

Solving eq 1 and 2

Put the value of M from eq 1 into eq 2

So, (J + 18) - 3 J = 10

Or, J - 3 J = 10 - 18

Or, - 2 J = - 8

∴ J =

i.e J = 4 years

So, The age of Joey = J = 4 years

Now, Put the value of J in eq 1

So, M = J + 18

Or, M = 4 + 18

∴ M = 22 years

So, The age of Martina = M = 22 years

Hence,The age of Joey is 4 years  and The age of Martina is 22 years . Answer


The equation y = 10x shows how the
cost relates to the number of hours.
How much does it cost to rent a canoe
for 8 hours?

Answers

$80.00 hope this helps!

Is 6 right?? Please help

Answers

Answer:

yes, it should be

Step-by-step explanation:

if you put y =Alan’s cards you can put
10+x= y
but if not then 10+x is the amount of cards Alan would have except i wouldn’t put the =10x because that says you are multiplying and that doesn’t happen in this problem

Can you help me please

Answers

270 miles. 10 x 3 is 30, x9 is 270

Answer:

270

Step-by-step explanation:

bc if he does 9 miles for 3 days every week thats already 27 miles. for 10 weeks that would be 270 bc 10*27 is 270.

The Property where if the order of addends changes, the sum stays the change

Answers

Property of addiction
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