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
kirill115 [55]
3 years ago
12

Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [inf

inity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. Find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = −1, 0 ≤ t < 1 1, t ≥ 1 ℒ{f(t)} = (s > 0)
Mathematics
1 answer:
Alla [95]3 years ago
3 0

f(t)=\begin{cases}-1&\text{for }0\le t

Write f(t) in terms of the unit step function u(t):

f(t)=-1(u(t)-u(t-1))+1u(t-1)=2u(t-1)-u(t)

where

u(t)=\begin{cases}1&\text{for }t\ge0\\0&\text{for }t

Then the Laplace transform of f(t), denoted F(s), is

F(s)=\displaystyle\int_0^\infty f(t)e^{-st}\,\mathrm dt

F(s)=\displaystyle2\int_1^\infty e^{-st}\,\mathrm dt-\int_0^\infty e^{-st}\,\mathrm dt

\implies F(s)=\dfrac{2e^{-s}}s-\dfrac1s=\dfrac{2e^{-s}-1}s

You might be interested in
which is the equation of a line that has a slope of 1 and passes through the point (5,3)? y=x-2 , y=x+2 , y=x+2 , y=x-1
Margarita [4]

Answer:

y=x-2

Step-by-step explanation:

if x: 5, x-2=3

y=x-2

therefore:

y=3

x=5

4 0
2 years ago
Joan how to save 7 quarters from washing cars how many cents does Joan have?​
natka813 [3]

Answer: 175 Cents

Step-by-step explanation:

First, 1 quarter is 25 cents. 4 quarters would be 100 cents. If you add the remaining 3 quarters, it would be 175 cents.

6 0
3 years ago
Sam spent StartFraction 5 Over 6 EndFraction of an hour at the dentist’s office. He spent StartFraction 1 Over 10 EndFraction of
ioda

Answer:

Step-by-step explanation:

Dentist's Office = 5/6 of an hour. An hours is 60 minutes

therefore he spent 5/6 x 60 = 50 minutes at the Dentist

1/10 of those 50 minutes were spent in the waiting room that is 1/10 x 50 = 5 minutes

Therefore Sam Spent 45 minutes at the Dentist office

I think the second part of your question is missing

6 0
2 years ago
Read 2 more answers
Could someone help me with this question
Lelechka [254]

Answer:

try b=32

Step-by-step explanation:

6 0
3 years ago
PLEASE HELP Residents of Eastport are convinced about the number of drivers who speed when driving down Main street. A group of
ZanzabumX [31]

Answer:

The answer is B I think

Step-by-step explanation:

They are talking about how they are convinced about the people who speed

3 0
2 years ago
Read 2 more answers
Other questions:
  • Tom drank quarts of water and his sister Jane drank 1.75 quarts of water. Write the amount that Jane drank using a fraction. Who
    13·1 answer
  • Julie needs 3 lengths of string that are each 6 inches long. Marlene needs 7 lengths of string that are each 8 inches long.
    8·1 answer
  • (2/5 - 1/10) + 2^3 - 23/25<br> A) 1 12/25<br> B) 2 2/5<br> C) 3 8/25<br> D) 4 3/5
    14·2 answers
  • v squared minus 4v minus 21over 3v squared plus 6v times v squared plus 8v over v squared plus 11v plus24
    11·1 answer
  • Not sure how to solve. Julia uses the shadow of a flagpole to estimate its height. She stands so that the tip of her shadow coin
    12·1 answer
  • Find the slope of the line that passes through the pair of points.
    9·2 answers
  • Tính thể tích m³ hồ tròn: đường kính 1,2m; cao 1,2m?
    14·1 answer
  • Need help finding area
    6·1 answer
  • Solve the equation.<br> d-7 = -18
    6·2 answers
  • What is 4/5 plus 2/3 and in simplest terms
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!