The Laplace transform is a mathematical technique used to convert a function of time, f(t), into a function of a complex variable, s. The transform is defined by an integral that takes the function f(t) and transforms it into the function F(s) defined by:
We can use the definition of Laplace transform to find L{f(t)}:
L{f(t)} = ∫₀^∞ e^(-st) * f(t) dt
For 0 ≤ t < 1, f(t) = t, so we have:
L{f(t)} = ∫₀¹ e^(-st) * t dt
Integrating by parts with u = t and dv/dt = e^(-st), we get:
L{f(t)} = [-te^(-st)/s]₀¹ + ∫₀¹ e^(-st)/s dt
= [-te^(-st)/s]₀¹ + [-e^(-st)/(s^2)]₀¹
= [e^(-s) - 1 + s]/(s^2)
For t ≥ 1, f(t) = 2 - t, so we have:
L{f(t)} = ∫₁^∞ e^(-st) * (2 - t) dt
Integrating by parts with u = 2 - t and dv/dt = e^(-st), we get:
L{f(t)} = [(2 - t)*e^(-st)/s]₁^∞ - ∫₁^∞ (-e^(-st)/s) dt
= [(2 - e^(-s))/s] - [e^(-s)/s^2]
Therefore, the Laplace transform of f(t) is:
L{f(t)} = [e^(-s) - 1 + s]/(s^2) for 0 ≤ t < 1
= [(2 - e^(-s))/s] - [e^(-s)/s^2] for t ≥ 1
Note: The square brackets [] indicate the limits of integration.
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Tell weather each pair is parallel, perpendicular, or neither: y= 3x + 2 2y= 6x -6
8r2 in fraction form
8r^2 eight r squared hope this is right
It is the simplest fraction form
What is the next term of the geometric sequence?
20, -10,5,
Answer:
0
Step-by-step explanation:
Answer: -2.5
Step-by-step explanation:
filipino.munting gamogamo.malaking gamugamo
Answer:
i Don't understand what ur saying
Step-by-step explanation:
Answer:
Nagtatanong ka ba? kung ganun ano yun
There are 9 counters in a bag.
7 of the counters are green.
2 of the counters are blue.
Ria takes at random two counters from the bag.
Work out the probability that Ria takes one counter of each colour.
What is the volume of this?
Answer:
270 m³
Step-by-step explanation:
[tex]A_{triandle}[/tex] = [tex]\frac{5*12}{2}[/tex] = 30 m²
[tex]V_{triangular prism}[/tex] = 30 × 9 = 270 m³
In the figure shown the sum of the measures yxz and wxv is 75 degrees . what is the measure of zxw
Answer: 105 = WXZ
Step-by-step explanation:
180 = WXZ + 75
subtract both sides by 75 and you get WXZ is equal to 105
I'm not 100% sure, lmk if I'm wrong
Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 per job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this.
30 + 15 x greater-than-or-equal-to 90
Which best describes the restrictions on the jobs Deepak will accept?
He only accepts jobs that last 4 or more hours.
He only accepts jobs that last 5 or more hours.
He only accepts jobs that last 8 or more hours.
He only accepts jobs that last 9 or more hours.
Answer:
4 or more hours
Step-by-step explanation:
I just took the test
Please help:
Find the class width of this graph
Answer:
The biggest one is 32 to 38
Step-by-step explanation:
hope it helps
Was wondering if anyone knows the answer to part A and B for this question?
Answer:
no idea
Step-by-step explanation:
Answer:
k so from my opinion
I think the answer is gonna be a
You deposit $1,600 in a bank account. The account pays 3% annual Interest compounded monthly. Find the balance after 5 years
Step-by-step explanation:
step 1. let's call the amount of money A, the initial amount P, the yearly rate r, the number of compounds per year n.
step 2. A = P(1 + r/n)^(nt)
step 3. A = 1600(1 + .03/12)^((12)(5)
step 4. A = 1600(1.0025)^(60)
step 5. A = $1858.59
Order the angles in each triangle from smallest to largest.
Mrs. Hanson has a potato salad recipe that calls for 238 pounds of potatoes, but she wants to make 112 times as much as the recipe calls for.
The diagram represents the number of pounds of potatoes that Mrs. Hanson needs.
How many pounds of potatoes does Mrs. Hanson need?
Enter your answer as a mixed number in simplest form by filling in the boxes. please hurry dont say what to add or mutply say the answer i am on k12
Answer:
3 9/16 lbs
Step-by-step explanation:
took quiz
Perry's bikes rent bikes for $18 plus $4 per hour. Lea paid $42 to rent a bike for how many hours did she rent the bike?
Answer:
10.5 hours!
Step-by-step explanation:
-2x + 4 = -3x + 4
3
One Solution
No Solution
Infinite Solutions
Answer:
X=0 or no solution
Step-by-step explanation:
-2x+4=-3x+4
cancel equal terms on both sides of the equation
-2x=-3x
move the variable to the left-hand side and change its sign
-2x+3x=0
collect like terms
x=0
A medical provider is doing a study to determine the average time spent waiting before an appointment. The current average wait time is 34 minutes, which is 15% shorter than the average was when the study started. What was the average wait time then?
Answer:
39.1 minutes
Step-by-step explanation:
Given that:
Current wait time = 34 minutes
Current wait time is 15% shorter than average wait time when study started.
Average wait time when study started :
15% of current wait time :
0.15 * 34
= 5.1 minutes
Average wait time when study started :
34 minutes + 5.1 minutes
= 39.1 minutes
please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! will give brainliest!!!!!!
Answer:
X is 40
Step-by-step explanation:
Look it up
how to the medium in the dot line????!! I don't want my mom to be mad at my grade please!!!!!!
Thank you whoever helps me!
Answer: To find the median, count the dots from left to right until you find the middle value.
Step-by-step explanation:
Ok so first it's not a dot line it's a dot plot. Second, let's define what a medium is. The medium is the "middle" of a sorted list of numbers. To find the Median, place the numbers in value order and find the middle number. Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. The middle number is 15, so the median is 15. Tip to find the median from a list of value ordered numbers every time cross a number from each side. For example, if you cross 13 from above also cross 26 and if you cross 23 then also cross 10.
Back to your original question of how to find the medium on a dot plot you need to take all the numbers from your dotted line put them in order even if they are repeated and then cross each one on each side from right to left. Also remember if you cross out all the numbers right and left and end up with two numbers left then take them and add them and then divide by 2 and that will be the median.
An example is attached on here in order to help you understand what I am saying. Hope this helps. Your welcome and I hope you make your mama proud.
What is the difference from congruent figures and similar figures
Answer:
similar = only the angles are the same
congruent = angles and sides are the same
The candy store has a stock of candy. They have 15 bags of tootsie rolls, 10 boxes of nerds, 12 bags of gummy
bears, 5 bags of M&M's and 22 bags of skittles. Find the ratio of tootsie rolls to total candy in the store. Be sure
to simplify
Answer:
15:49
Step-by-step explanation:
15 : 10+12+5+22
15 : 49
Can't be simplified further.
Find the length of y
Answer:
25 cm
Step-by-step explanation:
Find the surface area of the
triangular prism.
10 ft.
3 ft.
3 ft
Given:
The figure of a triangular prism.
To find:
The surface area of the triangular prism.
Solution:
We know that, a triangular prism contains 2 congruent triangular surface and 3 rectangular surface.
Triangles have base 3 ft and height 2 ft.
Area of a triangle is
[tex]Area=\dfrac{1}{2}\times base\times height[/tex]
[tex]A_1=\dfrac{1}{2}\times (3)\times (2)[/tex]
[tex]A_1=3[/tex]
Area of congruent triangles are congruent. So,
[tex]A_1=A_2=3\text{ sq. units}[/tex]
Now the three rectangular surface have dimensions 10 by 3, 10 by 3 and 10 by 3 because the triangles are equilateral and the length of the prism is 10 ft.
Area of a rectangle is
[tex]Area=Length\times width[/tex]
[tex]A_3=10\times 3[/tex]
[tex]A_3=30[/tex]
Dimensions of all three rectangles are same, therefore there areas are equal.
[tex]A_3=A_4=A_5=30[/tex]
Now, the total surface area of the prism is
[tex]A=A_1+A_2+A_3+A_4+A_5[/tex]
[tex]A=3+3+30+30+30[/tex]
[tex]A=96[/tex]
Therefore, the total surface area of the prism is 96 sq. ft.
a²-a² what is the answer
Answer:
a² - a² = 0
hope it helps
Answer:
a ² - a ²= 1 a ² - 1 a ² = 0
you understand ?
Maria ha invitado a 18 de sus compañeros de clase a su fiesta de cumpleaños .Si en total tiene 30 compañeros ,¿que porcentaje de la clase ha ido a su fiesta?
Answer:
59.9%
Step-by-step explanation:
100/30 = 3.3
3.3*18 = 59.9%
Your class earned $120.00 Saturday afternoon by washing cars to raise money for the class trip. This is 1/4 of the money needed for the trip. What is the total amount needed?
Answer:
$360.00
(I hope this was helpful)
Tyler has $415 in his savings Tyler has $415 in his savings account account. He earns $45 a week mowing lawns. Write and solve an equation.using b for the variable to find how many weeks will he to work to have $1315 saved?
Answer:
20 weeks
Step-by-step explanation:
1315$-415$=900$
900/45=20
Hence 20 weeks
Answer: 45b
Step-by-step explanation: Divide 1315 with 45xb.
rewrite 1/2 3/4 as a unit rate
Answer: 3 / 8
Step-by-step explanation:
Answer:
The answer is 6:1
Step-by-step explanation:
5/2k+1=-9
What does k equal?
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
If you mean,
[tex] \frac{5}{2k} + 1 = - 9[/tex]
Then the answer would be,
[tex]k = - \frac{1}{4} [/tex]
But, if you mean
[tex] \frac{5}{2} k + 1 = - 9[/tex]
Then the answer would be,
[tex]k = - 4[/tex]
Factor the following expression completely.
2x^2y-18y
Answer:
Since both terms are perfect squares, factor using the difference of squares formula,
a2-b2=(a+b)(a−b) where a=x and b=3.2y(x+3)(x−3)
Step-by-step explanation:
hope this helps!!!
¿Sera cierto que existe una fraccion con numerador 20 equivalente a la fraccion 100/55?Justifica tu respuesta
Answer:
si porq si porq si si dices si es si