The inverse Laplace transform of f(s) is f(t) = 10t + 7t^2/2 + 7t^3/3 + 80.125 t^4.
The inverse Laplace transform of f(s) = (3s - 7s^2 - 4s)/s^5 can be found by partial fraction decomposition. First, we factor the denominator as s^5 = s^2 * s^3 and write:
f(s) = (3s - 7s^2 - 4s) / s^5
= (As + B) / s^2 + (Cs + D) / s^3 + E / s^4 + F / s^5
where A, B, C, D, E, and F are constants to be determined. We multiply both sides by s^5 and simplify the numerator to get:
3s - 7s^2 - 4s = (As + B) * s^3 + (Cs + D) * s^2 + E * s + F
Expanding the right-hand side and equating coefficients of like terms on both sides, we obtain the following system of equations:
-7 = B
3 = A + C
0 = D - 7B
0 = E - 4B
0 = F - BD
Solving for the constants, we find:
B = -7
A = 10
C = -7
D = 49
E = 28
F = 343
Therefore, we have:
f(s) = 10/s^2 - 7/s^3 + 28/s^4 - 7/s^5 + 343/s^5
Using the inverse Laplace transform formulas, we can find the inverse transform of each term. The inverse Laplace transform of 10/s^2 is 10t, the inverse Laplace transform of -7/s^3 is 7t^2/2, the inverse Laplace transform of 28/s^4 is 7t^3/3, and the inverse Laplace transform of -7/s^5 + 343/s^5 is (343/6 - 7/24) t^4. Therefore, the inverse Laplace transform of f(s) is:
f(t) = l^-1 {f(s)}
= 10t + 7t^2/2 + 7t^3/3 + (343/6 - 7/24) t^4
= 10t + 7t^2/2 + 7t^3/3 + 80.125 t^4
Hence, the inverse Laplace transform of f(s) is f(t) = 10t + 7t^2/2 + 7t^3/3 + 80.125 t^4.
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GIVING BRAINLIEST ‼️
order the following numbers from least to greatest. 3/4, -1/8, |1/4|, -3, -1/2, |-1|
the series : 6/8 , -1/8 , 2/8 , -24/8 , -4/8 , 8/8
the ascending arrangement : -24/8 , -4/8 , -1/8 , 2/8 , 6/8 , 8/8
=
-3 , -1/2 , -1/8 , |1/4| , 3/4 , |-1|
pls give me brainliest
1)y=4
2)y=4x
3)y=4x+4
4)x=4
Answer:
I think number letter shape 14
Answer:
I am pretty sure that the answer is y=4x
please help picture attached
Answer:
triangle B and D
What does y = 1/3x + 5 look like on a graph?
Please help, I beg of y'all
FIND BD -
9514 1404 393
Answer:
14 units
Step-by-step explanation:
The angle bisector divides the sides proportionally.
BD/BA = CD/CA
(x+4)/8 = (2x+1)/12
3(x +4) = 2(2x +1) . . . . . multiply by 24 (the least common denominator)
3x +12 = 4x +2 . . . . . . . eliminate parentheses using the distributive property
12 = x +2 . . . . . . . subtract 3x
10 = x . . . . . . . . . subtract 2
Then the length of BD is ...
BD = x +4
BD = 10 +4 . . . . substitute the value of x
BD = 14
Plsss help me ASAP plss
Answer: x gte -6 if not try -6 lte x
Step-by-step explanation:
Tito builds a model of the solar system. In his model, the diameter of the sphere representing Jupiter is 7
inches. What is the circumference of a cross section through the center of the model of Jupiter? Use 3.14
for π
Answer:
21.99
Step-by-step explanation:
C = 2 * Pi * (r)
Diameter = 7
Radius = 3.5
Pi
21.99
2x - 5y = - 15
I need to rewrite it in the terms of “y” an I need the steps on how to do it thanks
Answer:
2x+15=5y
y=(2x+15)/5
hope this helps
Answer:
[tex]y = \frac{2}{5} x + 3[/tex]
Step-by-step explanation:
2x - 5y = -15
Firstly, you will need to isolate the variable you are solving for, in this case, y.
2x - 2x - 5y = -15 - 2x
-5y = -15 - 2x
-5y/-5 = -15/-5 - 2x/-5
A negative divided or multiplied by a negative is positive.
[tex]y = 3 + \frac{2}{5} x[/tex]
Rearrange.
[tex]y = \frac{2}{5} x +3[/tex]
Find the equation of the line with slope −15 and y-intercept (0,−2).
Answer:
y = -15x - 2
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
two adjacent angles of a rhombus as in the ratio 2:3. Eind all the a angles of the rombus
Answer:
Let the adjacent angles of the rhombus be 2x and 3x. We know that the sum of the measures of the adjacent angles is equal to 180°. AD = DC = 3 × 36° = 108°. Hence , the angles of the rhombus are 72° , 108° , 72° and 108°.
Step-by-step explanation:
Answer:
Let the adjacent angles of the rhombus be 2x and 3x.
we know that the sum of the measures of the adjacent angles is equal to 180°.
2x+3x=180
=5x=180
=x=180/5
=x=36°
Hence,AB =BC=2×36°=72°
AD=DC=3×36°=108°
Hence,The angles of the rhombus are 72°,108°, 72°and108°.
I hope it's helpful!
Jasmine had some candy to give to her three children. She first took four pieces for herself and then evenly divided the rest among her children. Each child received two pieces. With how many pieces did she start?
Answer:
10 pieces
Step-by-step explanation:
She gave herself 4 pieces, and each child 2 pieces. If she has 3 children, she gave them 6 pieces.
(3*2=6) and then you add with the amount she gave herself, (6+4) that would be 10. She started with 10 pieces.
An equation would be:
x= 4+(2*3)
I hope this helps!
(Also this equation seems a bit easy, am I reading it wrong? If I am be sure to correct me :) )
jane spend $42 for her for shoes this was $14 less than twice what she spent for a blouse how much was the blouse
40. Which two are equivalent to 4?
A A √2
BV8
C V16
D V12
E V64
Answer:
a or b
Step-by-step explanation:
HELP ANSWER FAST!!!!
In 1995, there were 85 rabbits in Central Park. The population increased by 8.5% each year. How much rabbits were in Central Park in 2005
==============================================
Work Shown:
A = P*(1+r)^t
A = 85*(1+0.085)^10
A = 192.183592562981
A = 192
-----------
Notes:
P = 85 is the starting population.r = 0.085 is the decimal form of 8.5%, so we can say 8.5% = (8.5)/100 = 0.085t = 10 years have elapsed from 1995 to 2005.The formula shown above helps with exponential growth and decay problems.The rabbit population in Central Park in 2005 is 192 rabbits.
To find the rabbit population in Central Park in 2005, we need to calculate the growth from 1995 to 2005.
From 1995 to 2005, there is a total of 10 years.
Using the growth rate of 8.5% per year, we can calculate the population in 2005:
Population in 2005 = 85 rabbits(1 + 0.085)¹⁰
Calculating this expression:
Population in 2005 = 85 rabbits(1.085)¹⁰
= 85 rabbits × 2.2609
= 192 rabbits
Therefore, the estimated rabbit population in Central Park in 2005 is 192 rabbits.
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Omg pls help in my math. It is 6th grade
Answer:
1. You have to shade 38/100 squares
2. You have to shade 65/100 squares
3. 3/5=15/25, 6/10, 9/15
answer choices:90ft square inches, 45ft square inches, 80ft square inches
Answer:
CAUSE I FEEL THE BREK FEEL THE BREK FELLLLLLL THE BREKK
Step-by-step explanation:
Please help answer all please thank you
Answer:
The answers are, in order:
1. Isolate
2. substitute
3. variable
Step-by-step explanation:
You're welcome :)
If m+6 divided by 2 is 4 less than 4m. What is the value of m?
Answer:
Ok
Step-by-step explanation:
find an equation of line containing (3, -4) and having slope -2. if this line contains the points (a, 8) and (5, b) find a and b
Answer:
a = -3
b = -8
Step-by-step explanation:
Equation for a line is:
y-coordinate = (slope * x-coordinate) + y-intercept
For (3, -4): -4 = (-2 * 3) + y-intercept
y-intercept = 2
Equation for all points on this line is:
y = -2*x + 2
For (a, 8): 8 = (-2 * a) + 2
For (5, b): b = (-2 * 5) + 2
Which triangle makes this statement true?
Answer:
Step-by-step explanation:
The question is kind of confusing but I think the answer is A.
Answer:
C is the correct answer
Step-by-step explanation:
I did this exact one and it was right I hope this helps! Have a good day! :)
Proof:
Jimmy invests $2500 in an account with a 5% interest rate, making no other deposits or withdrawals. What will Jimmy’s account balance be after 8 years if the interest is compounded 6 times each year?
URGENT PLEASE
Answer:
We conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.
Step-by-step explanation:
Given
Principle P = $2500
Interest rate r = 5% = 0.05
Time period t = 8 years
To determine
Accrue Amount A = ?
Using the compound interest equation
[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]
where:
A represents the Accrue Amount
P represents the Principal Amount
r represents the interest rate
t represents the time period in years
n represents the number of compounding periods per unit t
Important tip:
Given that the interest is compounded 6 times each year, therefore, the value of n = 6.now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation
[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]
[tex]A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}[/tex]
[tex]\:A=2500\left(1+\frac{0.05}{6}\right)^{48}[/tex]
[tex]A=2500\times 1.48935[/tex] ∵ [tex]\left(1+\frac{0.05}{6}\right)^{48\:\:}=1.48935[/tex]
[tex]A=\:3723.38[/tex] $
Therefore, we conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.
Enter a digit in each box to complete the division problem.
Please answer i’ll give brainliest
Step-by-step explanation:
2527 is the first line so 5 in the box
then 47 so a 4 in that box
top answer row
315 E7 so a 5 in that box.
pls help soon reward brainiest
Answer:
x=-6
Step-by-step explanation:
Enola surveyed 300 of the students in her school about their favorite color. 78 students said their favorite color was purple. What percentage of the surveyed students said their favorite color was purple?
Answer:
26%
Step-by-step explanation:
I did some simple math here: a percentage represents a number over 100.
To find the percentage, I just divided 78 by 300 and got 0.26
I then multiplied by 100 to get 26%
Hope this helps! Have a great day!
2
1
X 46
7. Find the m 2 JKL
in rhombus JKLM
Step-by-step explanation:
since KLJ is a parallelogram, it can be split into 2 congruent triangles, as seen above. The angles remain the same, so we know angle KJL is also 25 degrees. Using the triangle angle sum theorem (all sides of a triangle add up to 180 degrees), we can determine the missing angle measure is 25 degrees. It would have been nice if the question told us JKLM was also a rhombus.
What is the distance between the points (2, 3) and (5, -4)?
PLEASE HELP ASAP!!
Answer:
7 point 6
Step-by-step explanation:
A store wants to mark up
their prices by 12%.
What would the markup
be on a $40 lamp?
What is the final price?
And how did you solve it
Answer:Plus, calculate your profit margins, total revenue and more with FreshBooks ... Whether you sell online or in a retail store, you can set the perfect price for each ... service sold, you want to charge a price that's a percentage above how much it costs ... If Product A costs $10, the marked-up selling price would be $15 ( $10 x .50 ...
Step-by-step explanation:
Plus, calculate your profit margins, total revenue and more with FreshBooks ... Whether you sell online or in a retail store, you can set the perfect price for each ... service sold, you want to charge a price that's a percentage above how much it costs ... If Product A costs $10, the marked-up selling price would be $15 ( $10 x .50 ...
Answer:
$44.80
Step-by-step explanation:
Here' s an equation to help you with percent problems: part %
------- = -----
whole 100
Because you want to find 12%, the % in the equation would be replaced with 12. The part would be x because that's what u need to find. The whole would be 40. Cross multiply to get 100x = 480. Divide 480 by 100 to get x = 4.80. Add 4.80 to 40.00 to get the final price. The final price is $44.80.
please help me solve this problem
Step-by-step explanation:
it seems the answer is four (option a)
I need help with this assignment please help me
Answer:
Step-by-step explanation:
a. 7*7*7= 7 cubed(when we divide powers we subtract them)