I suppose you're asking about the inverse Laplace transform of
[tex]F(s)=\dfrac4{(s-3)(s-2)}[/tex]
by way of the convolution theorem.
The theorem itself says that
[tex]\mathscr L^{-1}\{A(s)B(s)\}=(a*b)(t)[/tex]
where [tex]A(s)[/tex] and [tex]B(s)[/tex] are the Laplace transforms of [tex]a(t)[/tex] and [tex]b(t)[/tex], respectively.
Let [tex]A(s)=\frac1{s-3}[/tex] and [tex]B(s)=\frac1{s-2}[/tex]. Then
[tex]a(t)=\mathscr L^{-1}\left\{\dfrac1{s-3}\right\}=e^{3t}[/tex]
[tex]b(t)=\mathscr L^{-1}\left\{\dfrac1{s-2}\right\}=e^{2t}[/tex]
So we have
[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=e^{3t}*e^{2t}[/tex]
Convolution is defined as
[tex](a*b)(t)=\displaystyle\int_0^t a(t-\tau)b(\tau)\,\mathrm d\tau[/tex]
The convolution of [tex]e^{3t}[/tex] and [tex]e^{2t}[/tex] is
[tex]e^{3t}*e^{2t}=\displaystyle\int_0^t e^{3(t-\tau)}e^{2\tau}\,\mathrm d\tau[/tex]
[tex]=\displaystyle e^{3t} \int_0^t e^{-\tau}\,\mathrm d\tau[/tex]
[tex]=e^{3t}(1-e^{-t})=e^{3t}-e^{2t}[/tex]
We end up with
[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=\boxed{4(e^{3t}-e^{2t})}[/tex]
An airplane flying with the wind takes 2 hours to travel a distance
of 600 miles. The return trip takes 3 hours flying against the
wind. What is the speed of the airplane in still air and how fast is
the wind blowing?
I need to know this I don’t understand and it is last one
Answer:
The answer is 4x
Step-by-step explanation:
Hope this helped
1. Original numbers are rounded to the nearest hundred and to the nearest thousand. The
original numbers are different from all the rounded numbers in the table.
Complete the table with possible original numbers.
Original Number
Rounded to the Nearest
Hundred
13,600
Rounded to the Nearest
Thousand
14,000
2,400
2,000
Answer:
Your answer would be 14,000
Answer:13,555
Step-by-step explanation: because in order for it to be rounded to the nearest 100 of 600 it would have to be over 550. If it was 550 or lower it would be rounded to 500. And in order for it to be rounded to the nearest thousand of 14,000 it would have to be a higher number than 13,550.
when 560000 is written in notation, what is the power of 10 a 4, b 5, c 6, d 7
Answer:
a : 4
Step-by-step explanation:
56*10^4 = 56*10000=560000
What fraction is equivalent to 2 31/32
Answer:
95/32
Step-by-step explanation:
You can multiply 32 by two, 64, then add 31, 95
Answer:
95/32
Step-by-step explanation:
yea i checked and it is 95/32
George Foster had a batting
average of .323 one season. Pete
Roses' average was .306 that same
season. How much better was
George Foster's average?
Answer:
.17 better average
Step-by-step explanation:
.323 - .306 = .17
8. Kathy is painting the outside of her
house. Its area is 2,250 square feet. Each
gallon of paint covers 250 square feet
and costs $19.90. How much money is
she going to spend on paint to cover the
outside of her house?
Answer:
$179.1
Step-by-step explanation:
Total area to be painted = 2,250 sq.ft
area covered by per gallon of paint = 250 sq.ft
Hence, gallons of paint required to paint 2,250 sq.ft is...
2250/250 = 9
so, 9 gallons of paint are required to paint 2,250 sq.ft
cost per gallon of paint = $19.90
so, cost of 9 gallons is...
19.90*9 = 179.1
The total money that Kathy will spend for painting the outside of her house is $179.1.
What is Unitary Method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given is the Kathy who is painting the outside of her house. Its area is 2,250 square feet. Each gallon of paint covers 250 square feet and costs $19.90.
Area of the outer house = [A] = 2250 ft²
Area covered by 1 gallon of paint = [a] = 250 ft²
Therefore, the total gallons of paint needed = (2250/250) = 9 gallons.
Cost of 9 gallons of paint will be = 19.90 x 9 = 179.1
Therefore, the total money that Kathy will spend for painting the outside of her house is $179.1.
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Help ASAP I will give 20 pionts!
Marco sorted these solid figures into two groups. What is true about the groups?
Group 1
Group 2
All figures in Group 2 appear to have at
least one triangular face.
<) All figures in Group 1 are rectangular
prisms
)) All figures in Group 2 are triangular
prisms
1) All figures in Group 1 appear to have at
least one square face,
Answer:
All figures in Group 1 appear to have at
least one square face
Step-by-step explanation:
Let us examine each statement and see whether they are true or not.
The first statement is not true. Only one of the figures (square pyramid) has at least one triangular face. It has 4 triangular faces, actually.
The second statement is not true. Only one of the figures is a rectangular prism. The remaining two are triangular pyramid and triangular prism respectively.
The third statement is not true also. Only 1 figure is a triangular prism.
The fourth statement is correct. In group 1, all the figures has at least one square face.
How many square inches are in 60 square feet?
Answer:
8640
Step-by-step explanation:
Answer:
8640
There is 8640 square inches in 60 square feet.
40.4 x 18=? Please help
Answer:727.2
Step-by-step explanation:40.4x18=727.2
What’s the area of the walk?
A circular flower bed is 21 m in diameter & has a circular sidewalk around it 2 m wide. (Use pi as needed in answer)
A survey at a bake-off showed that 32% of children chose strawberry cake as their favorite cake. A total of 750 children took the survey. How many children chose strawberry cake
Someone please help!!
Harper scores 24 points per coin. In all, how many coins does Harper have to collect to
score a total of 48 points?
Answer:
2
Step-by-step explanation:
1 coin = 24 points
2 coins = 48 points
3 coins - 72 points
~theLocoCoco
Which of the following is most likely the next step in the series
Answer:
The answer is C
Step-by-step explanation:
You have to find the pattern, in this case it's 4,5,6, then 7
Hope this helps! :)
Answer:
its actualy D
Step-by-step explanation:
jim's bookshelf has 24 inches remain in. each of his notebooks is 3/4 inches wide. how many notebooks will fit in the remaining space
Answer:
32 notebooks will fit.
Step-by-step explanation:
Please help me out!!!!!
Inverse of [tex] {12}^{2} [/tex] is [tex] {12}^{ \frac{1}{2} } [/tex]
Explanation:Because [tex] {12}^{ \frac{1}{2} } = \sqrt[2]{12} [/tex]Which is the inverse of [tex] {12}^{2} [/tex]
Answer:Option C. Is the correct answer.
During a science experiment, Daniel noted the starting
temperature of a -4°F. At the end of the experiment, the
change in temperature was -5°F. What was the final
temperature?
A.-1 B.1 C.9 D.-9
Answer: D. - 9
Step-by-step explanation:
Give the following :
Starting temperature = - 4°F
At the end of the experiment, the change in temperature was -5°F
What was the final temperature?
Taking the difference of the starting temperature and the final temperature should give the change in temperature over the course of the experiment.
Δtemperature = (final temperature - initial temperature)
Δtemperature = - 5°F
Initial /starting temperature = - 4°F
Hence,
-5 = final temperature - (-4)
-5 = final temperature + 4
Final temperature = - 5 - 4
Final temperature = - 9
A 12-inch candle burns at a rate of 2 inches per hour. What is the graph of the equation that models the height of the candle over time?
The candle burns at a rate of 1 inch per hour.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
here, we have,
Given,
A 12-inch candle burns down in 12 hours.
∴ The rate at which it burns per hour is the total length of the candle divided by the total time it brunt for which is,
= (12/12) inch/hr.
= 1 inch/hr,
Hence, The candle burns at a rate of 1 inch per hour.
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complete question:
A 12 inch candle burns down in 12 hours. at what rate does the candle burns, in inches per hour?
need help asap (8u^9)^2 must have only one exponent plssss help me
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ {8u}^{18}}}}}} [/tex]
Step-by-step explanation:
Using the power to power law of indices
i.e When an algebraic term in the index form is raised to another index , the base is raised to the product of two indices.
Now, Let's simplify
[tex] \star \: \sf{({8u}^{9})^{2} }[/tex]
[tex] \dashrightarrow{ \sf{(8 {u})^{9 \times 2}}} [/tex]
[tex] \dashrightarrow{ \boxed{ \sf{ {8u}^{18}}}} [/tex]
Hope I helped!
Best regards! :D
Question
Community Gym charges a $40 membership fee and a $65 monthly fee. Workout Gym charges a $210
membership fee and a $55 monthly fee. After how many months will the total amount of money paid to
both gyms be the same?
i think the answer is at 15 months
The Lions won 35 out of 40 games this season. What fraction of the games did the Lions win?Write your answer in simplest form.____________________________
Answer:
操你bit子
-by-step explanation: fjrfr gtger 操你bit子
Answer:
7/8 of their games
Step-by-step explanation:
35 divided by 5 is 7 and 40 divided by 5 is 8
A forensic accountant usually takes additional coursework in which field?
Answer:
law enforcement
Step-by-step explanation:
can yall please start answering more questions about the subject
What does this say? Please Help me!
Answer:
That is a child mom with triplets.
Step-by-step explanation:
Name the property illustrated by each equation.
(6.8)x5 = 6x(8.5)
Answer:
Commutative Property Of Multiplication
6 + 4 x 3 +7}
Pls helpppp
Answer:
25
Step-by-step explanation:
none
Answer:
6+4×3+7=37
Step-by-step explanation:
6+4= 10
3x10=30
30+7=37
HELPPPPPP ASAP . Which triangle represents the reflection ABC across the y-axis ?
Answer:
The answer above me is wrong, it is C, red triangle.
Step-by-step explanation:
Got it right on a school test.
The red triangle represents the reflection ABC across the y-axis. Option C is correct.
What is geometric transformation?It is described as the modification of both the geometric body's coordinates and form. A two-dimensional transformation is another name for it. Geometric transformations allow for the rotation, translation, reflection, and glide translation of the geometry.
We have to find the triangle that represents the reflection ABC across the y-axis.
A flip is a term for a reflection in geometry. The form is mirrored in a reflection. The line of reflection is a line across which an image will reflect. Every point in a figure is said to mirror the other figure if and only if it is equally spaced from every corresponding point in the other figure.
Since the green and blue triangles are equidistant from the y-axis. The red triangle will represent the reflection ABC across the y-axis
Thus, option C is correct.
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What is the least common multiple of these two denominators 3/6 2/12
Answer:
1 1/2 = 36/24
3/8 = 9/24
5/6 = 20/24
3 = 72/24
Step-by-step explanation:
if this answers it or it is just 12
The least common multiple of these two denominators 6 and 12 is 2.
To find the least common multiple (LCM) of the denominators 6 and 12, follow these steps:
Step 1: Prime factorize each denominator.
6 = 2 × 3
12 = 2 × 2 × 3
Step 2: Identify the highest power of each prime factor.
In this case, the highest power of 2² is 2 and the highest power of 3 is 3.
Step 3: Multiply the highest powers of all prime factors.
[tex]2^2 * 3^1 = 4 * 3 = 12[/tex]
Therefore, the LCM of the denominators 6 and 12 is 2.
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If QR = 18, RS = x -11, and QS = 2x - 11, what is QS?
Answer:
QS =25
Step-by-step explanation:
QR + RS = QS
18 + (x-11) =2x-11
7 +x =2x -11
18=x
Plug in x
2(18) -11
36-11
QS=25
18 + (18-11) = 2(18)- 11
18+ 7 = 36 -11
25= 25
True
Answer:
QS=QR+RS
2x-11= 18+x-11
2x-x= 18
x= 18
QS=2*18-11
=36-11
=25