1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dafna11 [192]
3 years ago
15

(with steps please) Find the inverse Laplace transform, f(t), of the function: 16/(s-4)^3

Mathematics
1 answer:
Stells [14]3 years ago
6 0

Answer:  The required inverse transform of the given function is

f(t)=8t^2e^{4t}.

Step-by-step explanation:  We are given to find the inverse Laplace transform, f(t), of the following function :

F(s)=\dfrac{16}{(s-4)^3}.

We have the following Laplace formula :

L\{t^ne^{at}\}=\dfrac{n!}{(s-a)^{n+1}}\\\\\\\Rightarrow L^{-1}\{\dfrac{1}{(s-a)^{n+1}}\}=\dfrac{t^ne^{at}}{n!}.

Therefore, we get

f(t)\\\\=L^{-1}\{\dfrac{16}{(s-4)^3}\}\\\\\\=16\times\dfrac{t^{3-1e^{4t}}}{(3-1)!}\\\\\\=\dfrac{16}{2}t^2e^{4t}\\\\\\=8t^2e^{4t}.

Thus, the required inverse transform of the given function is

f(t)=8t^2e^{4t}.

You might be interested in
Step-by-step explanation please<br> (Worth 3 marks)
atroni [7]

Answer:

62°

Step-by-step explanation:

180-118=62

62+62=124

180-124=56

118-56=62

5 0
3 years ago
Read 2 more answers
A box of 24 greeting cards is sold at a gift shop for $3.00. The cost to the store is $2.40. What is the markup as a percentage
Murljashka [212]

Answer:

25%

Step-by-step explanation:

formula for percent markup/discount= absulute value of original-new/original

plug the numbers is

(2.40-3.00/2.40) absolute value=0.25

0.25 as a percent is 25%

8 0
3 years ago
Write an absolute value equation that satisfies the following condition.
lawyer [7]

Answer:

x=-17.......................

Step-by-step explanation:

x+17=0

3 0
3 years ago
Please help? <br> Find measure of angle C
Lelu [443]

Answer:

82

Step-by-step explanation:

Im pretty sure the answer is 82 as it's a striaght line and all you have to do is subtract 180-98

4 0
3 years ago
Geometry - The steps to rotating a shape on a graph.
irinina [24]
(x,y)

Quartile 1/original coordinates (x,y)
Quartile 2 (-x,y)
Quartile 3 (-x,-y)
Quartile 4 (x,-y)

use this to move a shape on the graph

the degree of rotation of a shape on a graph depends on where the shape starts and ends
6 0
3 years ago
Other questions:
  • A local drama production sold tickets for a play. Adult tickets sold for $10 each and child tickets sold for $5
    10·1 answer
  • Solve fot z show all your work. 7z - 18 =2z+ 18​
    7·1 answer
  • What does she need to score on the fifth teat to get exactly a mean of 90?
    9·1 answer
  • If (x)=3x-1 and s(x)=2x+1, which expression is equivalent to r over s (6) ?
    5·1 answer
  • write a rule that could be used to find the distance from any positive number to any negative number.
    10·1 answer
  • You buy 8 pencils for $8 at the bookstore. Standard pencils cost $0.85 and specialty pencils cost $1.25. How many specialty penc
    9·1 answer
  • The lines graphed below are parallel.The slope of the red line is-4/3. What is the slope of the green line?​
    6·2 answers
  • Plz this is due today help me explain the answer
    6·1 answer
  • Question 1 (1 point)
    5·1 answer
  • Find the area of the shaded region. Round your answer to the nearest tenth if needed.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!