Mathematics College

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

An equilateral triangle has a side length of 10 units. What is its area?

Answers

Answer:

Hope my ans help you plz if u can mark me brainlist

Step-by-step explanation:

A = 43.3

The area of an equilateral triangle has a side length of 10 units is 43.3 square units.

What is an equilateral triangle?

An equilateral triangle is one with equally long sides on both sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle.

Given the side of an equilateral triangle  = 10 units

the area is given by,

A = √3/4 × a²

where a is the length of the side,

A = √3/4 × 10²

A = 1.732 x 100/4

A = 43.3 square units.

Therefore, the area of a triangle is 43.3 square units.

Learn more about equilateral triangle;

https://brainly.com/question/3461022

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Paul has some money in his wallet, all in $1 bills. He buys a hat and has $6 left, as shown in
the model below.
How much did Paul pay for the hat?
Enter your answer in the box.

Answers

Answer:

we need to see the model

Step-by-step explanation:

model please

Which of the lines below has a negative slope?
A
B
6
-5
15
6
10
5
D
5
5

Answers

Well, negative slope has the word negative in it right? So, it will be the negative number. Answer: -5 (negative 5)

are 4x and 15 + x equivalent expressions? Explain your reasoning

Answers

Answer:

no.

Step-by-step explanation:

4x means 4 times any given number

15 + x means take any number and add 15.

if x = 2, 4x = 8

if x = 2, 15 + x = 17

HELP PLEASE PLEASE I WILL GIVE BRAINLIEST

Answers

In the top the "f(x)" equals 9, now they are asking you to add onto the 9 by 1 causing it to be 10. If you did the first few you would have noticed that it takes 9 in order to get to 5 from -4.

here are the answers btw:

Please please help me I have to finish and on question 2

Answers

The answer is D


I’m pretty sure I hope it helped

.A town fair charges $6 for general
admission and $1.50 for each ride. Use
the pattern in the table to find the cost of 7
rides and 10 rides. Then write an equation
for the pattern.

Answers

Answer: $1.50r + $6

Step-by-step explanation:

1.50 times 7 is $10.5 without admission

1.50 times 10 is $15 without admission

(R for rides)

so $1.50r + $6 is the equation

Find the slope of the line that passes through the two points. (-3, -4), (6, 8)

Answers

Answer:

Step-by-step explanation:

let (x1 , y1) = ( - 3, - 4) and (x2 , y2) = ( 6 , 8)

Slope (m)

= y2 - y1 / x2 - x1

= 8 + 4 / 6 + 3

= 12 / 9

= 4/3

Olivia has 1/2 pound of raisins. She plans to eat them for snacks over the next 6 days. If she eats the same amount each day, What fraction of a pound of raisins will she eat each day

Answers

Answer :

1/12

Step by step :

Pounds of raisins : 1/2 = 0.5

Number of days : 6

Pounds of raisins she will eat every day :

0.5 ÷ 6 = 0.83333... = 1/12

Find n(E), given that n(C×E)=18 and C={4,5,6}

​

Answers

Answer:

ncx(2.718282)=18;c=456

ncx(2.718282)=18;c=456

Plz help with this one I have ten minutes to turn it in! Will give u points! And mark u BRAINLY

Answers

i think it’s -3,0,0 but i’m not 100% sure

Step-by-step explanation:

[tex]f(\pi) = - 3 \\ f( \frac{\pi}{2} ) = 0 \\ f( - \frac{3\pi}{2} ) = 0[/tex]

ANYONE PLEASE JUST HELP ME I HAVE ASKED THE SAME QUESTION 3 TIME BUT NO ONE ANSWERS IT. I WILL GIVE BRAINLEST PLEASE JUST HELP ME.

Answers

Answer:

Umm the pic is blocked

Its the blocked picture or meh

Step-by-step explanation:

2/5 g = 3/5 help I don't know what the answer is

Answers

Answer:

Step-by-step explanation:

2/5 g = 3/5

g = 3/5 - 2/5 = 1/5

please help!
Which transformation could NOT be used to prove that two circles are congruent to one another?

a dilation with a scale factor of 2

a dilation with a scale factor of 1

a reflection

a rotation

Answers

A transformation which can not be used to prove that two circles are congruent to one another is: A. a dilation with a scale factor of 2.

The types of transformation.

In Mathematics, there are different types of transformation and these include the following:

ReflectionRotationTranslationDilation

What is dilation?

Dilation can be defined as a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

In this context, we can reasonably infer and logically deduce that a dilation with a scale factor of 2 would change the size of the two circle and as such making them incongruent.

In conclusion, a dilation with a scale factor of 1, reflection and rotation can be used to congruency in two circles.

Read more on dilation here: brainly.com/question/20482938

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Find the value that makes the proportion true.

Answers

Answer:

can not see page

Step-by-step explanation:

Which ratio is equivalent to 17:1?
Ο Α.
A. 17
17
0 B. 34 to 2
O C. 1 through 17
D. 1 to 1

Answers

34:2 or 34 to 2
Hope this helps!❣️

Pls help me plssss plsssss

Answers

Answer:

B

Step-by-step explanation:

how many 1/2's in 4? thats how many bows so 4 ÷ 1/2

Answer:

it's b.

debbie can make 8 bowls

FIRST TWO PLEASE, HELP ASAP! THANK YOU SO MUCH I WILL MARK AS BRAINLIEST!!!

Answers

Answer:

Th answer to the first question is 18+6=24 the answer to the second question is 9 weeks

Please mark me brainliest!

blank divided 2/3 = 9/10

Answers

Answer:3/5

Hope this help :)

Aaron rolls a die 40 times. On 25 of those rolls, he has a 3. Michelle rolls a die 80 times. On 40 of those rolls, she has a 6. Which
statement is TRUE about the experimental and theoretical probabilities?
A)The theoretical probability for rolling a 3 is the same as for rolling a 6.
B)The theoretical probability for rolling a 3 is greater than for rolling a 6.
C)The experimental probability for Aaron's tries is the same as Michelle's
tries.
D)The experimental probability for Aaron's tries is less than the experimental
probability for Michelle's tries.

Answers

Answer:

Pretty sure its D lemme know if I'm right

Solve: 0=-x2+2x+8

[tex]0=-x2+2x+8[/tex]

Answers

Answer:

x = 4

x = -2

Step-by-step explanation:

please help 7m - 10 - 4m + 3

Answers

Step-by-step explanation:

7m - 10 - 4m + 3

3m-7

Hope it helps

7m-10-4m+3
=7m-4m-10+3
=3m-7

Simplify the expression:
2n + 10(9 + 4n)

Answers

Answer:

42n+90

Step-by-step explanation:

Answer: 42n+90
Explaination:

2
n
+
10
(
9
+
4
n
)
Distribute:
=
2
n
+
(
10
)
(
9
)
+
(
10
)
(
4
n
)
=
2
n
+
90
+
40
n
Combine Like Terms:
=
2
n
+
90
+
40
n
=
(
2
n
+
40
n
)
+
(
90
)
=
42
n
+
90

John multiplies 85 by 1.35. Which number might John be trying to find?
A. 135% of 85
B. 35% of 85
C. 13.5% of 85
D. 1.35% of 85

Answers

Answer:

A. 135% of 85

Step-by-step explanation:

When you find the percent of something, you multiply it by 100, so 1.35 ÷ 100 is 135

Factorise
1) 9a^2 - 6a​

Answers

Answer:

9a^2 - 6a

taking common

3a(3a-2)

When a certain kind of bacterium takes a step, it moves 3 x 10^-7 meters. When
Joe takes a step, he moves 0.75 meters. How many times larger is Joe's step
than the bacterium's step?
Joe's step is[ ] x 10^[ ]
times larger than the bacterium's step

Answers

Answer:

Step-by-step explanation:

0.75/(3*10^(-7)) = 0.25*10^7 = 2.5*10^6

WILL MARK BRAINLELIST HELPPPP ME

Answers

Answer:

17

Step-by-step explanation:

180 - 5 - 5 = 170 : 2 = 85 : 5 = 17

How many minutes is 65% of 3 hours? ____ just write the number part of the answer.

Answers

Answer:

117

Step-by-step explanation:

There are 60 minutes in each hour, and to find how many minutes there are in 3 hours you would have to multiply 3 x 60.

3 x 60 = 180

To find 65% of 180 you can use the equation

65 x 180/100

65 x 180 divided by 100 is 117.

i need help with this pls.

Answers

Answer:

The answer is D

Step-by-step explanation:

Plug all of the numbers in and they all work with the problem.

PLEASE HELP‼️‼️
A
B
C
D

Answers

Answer:

C i think

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

use the side splitter theorem

6/12 = x/18 (replacing AQ with x)

12x = 108 (cross multiply)

x = 9

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