To find the coefficients A and B in the inverse Laplace transform of F(s), we need to use partial fraction decomposition and the properties of Laplace transforms. Here's how we do it:
First, we factor the denominator of F(s) as (s-1)(s+6). Then we write F(s) as a sum of two fractions with unknown coefficients A and B:
[tex]F(s) = \frac{7s}{(s-1)(s+6)} = \frac{A}{s-1} +\frac{B}{s+6}[/tex]
To find A, we multiply both sides by (s-1) and then take the inverse Laplace transform:
[tex]L^{-1} [F(s)] = L^{-1}[\frac{A}{s-1} ] +L^{-1}[\frac{B}{s+6} ][/tex]
[tex]f(t) = A e^t + B e^{-6t}[/tex]
Since we know that the inverse Laplace transform of F(s) has the form of f(t) = A e^t + B e^(-6t), we can use this expression to solve for A and B. We just need to evaluate f(t) at two different values of t and then solve the resulting system of equations.
Let's start with t=0:
[tex]f(0) = A e^0 + B e^{0} = A + B[/tex]
Now let's take the derivative of f(t) and evaluate it at t=0:
[tex]f'(t) = A e^{t} - 6B e^{-6t}[/tex]
f'(0) = A - 6B
We can now solve the system of equations:
A + B = f(0) = 0 (since F(s) is proper, i.e., has no DC component)
A - 6B = f'(0) = 7
Solving for A and B, we get:
A = 21/7 = 3
B = -21/7 = -3
Therefore, the coefficients in the inverse Laplace transform of F(s) are:
A = 3
B = -3
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Rule: multiply by 2 Pattern: 3,6,12,24,48 Observation: Observation = something similar about the numbers
Step-by-step explanation:
This numerical sequence corresponds to a geometric progression, which occurs when there is a multiplication of the sequence numbers for a common reason whose result will always be the successor number of the numerical sequence.
Like for example:
3,6,12,24,48
The common reason for the geometric progression is the number 2, so the first term of the sequence multiplied by 2 will be equal to the second term of the sequence and so on:
3x2 = 6
6x2 = 12
12x2 = 24
24x2 = 48
It is necessary to emphasize that the ratio of a geometric progression will always be constant and will always be a number other than zero.
Use the distributive property to find the equivalent expression.
3(2 + x) =__+__x
Answer:
6+3x
Step-by-step explanation:
multiply each term in the parentheses by the outer term.
Multiplying positive and negative fractions how do you do it
Answer:
I GOTCHU BAEE
Step-by-step explanation:
its just like regular negative numbers
but with fractions
see:
-7/12 x 1/2 = -7/24
negative negates the negative
negative negates the positive
positive keeps the positive positive
For a year, a chef from a restaurant collected data about the cost of strawberries and cherries in his local food market. this data is summarized in the table below. based on the data collected, select all of the statements that are correct.
Answer:
A Strawberries generally cost less.
D If the chef pays $6.00 for a pound of fruit, it is most likely cherries.
Step-by-step explanation:
A and D
Find The Area of the parallelogram...
Answer:
162 ft^2
Step-by-step explanation:
the formula for finding the area of a triangle is [tex]\frac{b*h}{2}[/tex]
the base is 27 and the height is 12
[tex]\frac{27*12}{2}=\frac{324}{2} = 162[/tex]
HELP ASAP HELPPP MARKING BRAINLIEST
Answer:
answer is 68 1/8
Step-by-step explanation:
A yellow ball, a red ball, a white ball and a
black ball are placed in a barrel. Two balls
are drawn out of the barrel at random. What is the probability
that the yellow ball is drawn first?
Answer:
1/4 chance (this is equal to 25% as a percentage or 0.25 as a decimal)
Step-by-step explanation:
There are 4 balls and only one can be first. As there is only 1 yellow ball, there is 1/4 chance that the yellow ball is picked first.
HELP HELP HELP PLSSS
Answer:
option. c. 720°
.....................
Answer:
720degrees
Step-by-step explanation:
Kunal told Ana he was going to drop 10 dimes on the table. He said he would give her all the dimes where the "head" side was showing.How many dimes would Ana most likely get?
Answer:
10
Step-by-step explanation:
6.) Resuelve: 6(X + 8) - 30 + 7 = 49
Answer:
x=4
Step-by-step explanation:
6(x+8)-30+7=49
6x+48-30+7=49
6x=49-48+30-7
6x=1+23
6x=24
x=[tex]\frac{24}{6}[/tex]
x=4
Step-by-step explanation:
Para resolver esto yo use una app llamada m a t h w a y
(sin los espacios) esta puede estar en varios idiomas, aunque esto se modifica segun el idioma en donde la uses.
6(x+8) -30+7 = 49 1. Simplifica 6(x+8) -30+7
6x+25 = 49 2. Mueve todos los términos que no
contengan x al lado derecho de la ecuación
6x = 24 (25 pasa restando por lo cual sería, 49-25
que es igual a 24.)
3. Divide cada término por 6 y simplifica.
x = 4
Espero esto haya ayudado!
Whoever answers this question first gets brainly 2
There were 24 people invited to a pizza party. One-fourth of the people wanted sausage and olives. Three-fourths
wanted plain cheese. How many plain pizzas should Sam order?
18,16,14?
Answer:
the number of plain pizza does sam order is 18
Step-by-step explanation:
The computation of the number of plain pizza does sam order is shown below:
= Total people invited to a pizza party × plain cheese
= 24 × 3 ÷ 4
= 18
Hence, the number of plain pizza does sam order is 18
Look at the photo below.
Answer:
complement, 70; supplement, 160*
Step-by-step explanation:
randy needs to save 2550$ for a vacation. he has 6 months to save the money. how much money must he save each month?
Answer:
425
Step-by-step explanation:
2550/6=425
Answer:
425
Step-by-step explanation:
find the distance between j and k
Answer:
theres no picture...or points...
Step-by-step explanation:
15 points, 8-9 grade work
Polynomials
P(x) = 2x^4 + 3x^2 - 5x + 7
q(x) = -2x^2 + 4x - 3
calculation:
A. p(x) + q (x)
B. 2 • p (x)
C. p (x) - q (x)
D. 3 • p (x) + 4 • q (x)
E. p (x) • q (x)
F. (P (x) ) ^2
Answer:
A. p(x) + q (x) =2x^4 + 3x^2 - 5x + 7-2x^2 + 4x - 3 =2x⁴+x²-x+4
B. 2 • p (x)=2(2x^4 + 3x^2 - 5x + 7)=4x⁴+6x²-10x+14
C. p (x) - q (x) =2x^4 + 3x^2 - 5x + 7-(-2x^2 + 4x - 3 )=2x^4 + 3x^2 - 5x + 7+2x²-4x+3=2x⁴+5x²-9x-2
D. 3 • p (x) + 4 • q (x) =3(2x^4 + 3x^2 - 5x +7)+4(-2x^2 + 4x - 3 )=6x⁴+9x²-15x+21-8x²+16x-12=6x⁴+x²+x+9
E. p (x) • q (x)=sorry it is quite long.
F. (P (x) ) ^2this too.
what is the value of the expression -3y/x
when x = 12 and y=-8
Step-by-step explanation:
here is your answerr.
Was it helpful?
comment down
If there is any kind of suspicious mistake
then sorry
-(7p+6)-2(-1-2p)
what is that simplified?
Answer:
-3p-40
Step-by-step explanation:
-(7p+6)-2(-1-2p)
-7p-42+2+4p
-3p-40
If corresponding angles are on parallel lines, then their measure is the same _____.
always
never
sometimes
Step-by-step explanation:
always .
plz mark my answer as brainlist.hope this will be helpful to you
Answer: Always
Step-by-step-sumsum:
help me plz plz i need my grades up
Answer:
Decimal: 2.1
Fraction: 21/10
-6=3x+3
Does anyone know this answer
Answer:
-1 :)
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
x = −1
heyy could you help me out with this question I have been stuck in this question??
Answer:
true, false, true that is the answer I belive
tysm for whoever helps !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
Answer:
21
Step-by-step explanation:
When you simply the fractions down, you will get this
[tex]16 + 5 = 21[/tex]
Hope this Helped
If g(x) = 2x – 9, determine g(4) – g(1)
Step-by-step explanation:
g(x) = 2x - 9
g(4) = 2* 4 - 9
= 8 - 9
= - 1
g(1) = 2 * 1 - 9
= 2 - 9
= - 7
Now
g(4) - g(1)
= - 1 - ( -7)
= - 1 + 7
= 6
Hope it will help :)
Solve and graph the inequality.
7n - 1 > 76
Answer:
n>11
Step-by-step explanation:
I don't know how to graph this answer, sorry!
The solution of the inequality 7n - 1 > 76 gives n < 11 along with the graph.
Given Inequality:
7n - 1 > 76
To solve the inequality add 1 on both side of inequality as
7n - 1 + 1 > 76 + 1
7n > 77
Now, divide the inequality by 7 as
7n/ 7 > 77/ 7
n > 11.
Therefore, the solution is n > 11.
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− 2/3m = −1/2 solve for m
Answer:
m=-18
Step-by-step explanation:
-12=2/3m
How many fluid ounces are in 1 quart? With work!
Answer: 32 fluid ounce = 1 quart
Hey I'm sorry. I don't know if there are any work to show for this but I will try.
1 quart=2pints
2pints=4cups
4cups=32 fl oz
This is all the work I could show for this problem, you really should memorize this though 32 fl oz in a quart, it is very useful real life information :)
I need help I am really struggling with math
Answer:
Okay what is it i might be able to help
Step-by-step explanation:
Can 4(x+2)=10 equal 0
Answer:
x = 0.5
Step-by-step explanation:
The given expression is :
4(x+2) = 10
Using commutative property at LHS.
4x+8 = 10
Subtract 8 from both sides.
4x+8-8 = 10-8
4x = 2
x = (1/2) = 0.5
So, the value of x is equal to 0.5 instead of 0. Hence, the given expression cannot be equal to 0.
geometry: help needed, it’s urgent!
angle 1 measures 75 degrees, is this table right?
Answer:
angle 1 and 3 are alternate INTERIOR angles cos they are on the inside of the lines but you were close