The inverse Laplace transform of [tex]-aa^2/(s+1)^2[/tex]is [tex]e^{(-t)} - ae^{(-at)}.[/tex]
What is the inverse Laplace transform of [tex]-aa^2/(s+1)^2[/tex]?[tex]e^{(-t)} - ae^{(-at)}.[/tex]To find the inverse Laplace transform of [tex]-aa^2/(s+1)^2[/tex].
We can use the property of the Laplace transform that states the Laplace transform of the derivative of a function f(t) is given by sF(s) - f(0), where F(s) is the Laplace transform of f(t).
In this case, let's denote the inverse Laplace transform of [tex]-aa^2/(s+1)^2[/tex] as g(t). We can rewrite the expression as [tex]-aa^2/(s+1)^2 = F(s) - a^2/s^2.[/tex]
Now, we know that the Laplace transform of [tex]e^{(-at) }[/tex]is given by 1/(s + a). Therefore, the Laplace transform of [tex]ae^(-at)[/tex] is [tex]a/(s + a).[/tex]
Comparing this with the expression [tex]F(s) - a^2/s^2,[/tex] we can deduce that F(s) must be equal to 1/(s + 1).
Hence, g(t) is the inverse Laplace transform of F(s), which is [tex]e^{(-t)}[/tex]. Adding the term [tex]ae^{(-at)}[/tex] to account for the constant a, the final inverse Laplace transform is [tex]e^{(-t)} - ae^{(-at)}[/tex].
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Which side lengths represent the sides of a right triangle?
A)
1, 1, 2
B)
2, 3,5
C)
5, 12, 13
D)
7, 23, 25
Answer: the answer is C
Step-by-step explanation:
My friend is a math teacher
Hope this helps
A can of soup has the shape of a cylinder.
The diameter of the base of the can is
3.4 inches, and the height of the can is
4.5 inches. What is the volume of the can
rounded to the nearest tenth of a cubic
inch?
Answer:
Step-by-step explanation:
Height h = 4.5 inches
Radius r = 3.4/2 = 1.7 inches
Area of base = πr² = 2.89π square inches
Volume of cylinder = πr²h = 2.89π4.5 = 13.0 cubic inches
Answer:
The answer is 40.8
Step-by-step explanation:
The volume of a cone equals the area of a circle multiplied by the height
[tex]v = \pi \times {r}^{2} \times h \\ = 3.14 \times 1.7 \times 1.7 \times 4.5 \\ = 40.8[/tex]
Is A PQR-AXYZ? If so, name which similarity postulate or
theorem applies.
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Answer:
D. Cannot be determined
Step-by-step explanation:
Similarly between given triangles can not be determined because given information are insufficient.
The correct option for the given triangles is D. Cannot be determined
What are similar triangles?Any two triangles will be considered as similar as they have congruent corresponding angles and the corresponding sides are in equal ratios.
Two shapes are Similar when one can become the other after a resize, flip, slide or turn.
Given are two triangle PWR and XYZ we need to determine whether they are similar or not,
So, we only have measurement of a pair of sides and measurement of an angle,
We have some similarity rules by which we can prove two triangles to be similar, they are :-
AA rule, Side Angle Side (SAS), Side Side Side (SSS) and Right-angle Hypotenuse Side (RHS)
Since, we do not enough information to conclude our discussion.
Hence, the correct option is D. Cannot be determined
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You are going on an expedition to dig for dinosaur fossils. In digging you come across a small trunk left by another archeologist. In the trunk is a paper that lists how deep you need to dig to reach dinosaur fossils. Unfortunately, something spilled on part of the paper and it is damaged.
Using your knowledge of mathematics, find the missing numbers in the
chart. Write a generalization or rule to determine any number of feet you
must dig given the number of years.
If the Jurassic period was 200 million years ago, how deep would you need
to dig at this location to uncover fossils of that era? Explain why your
answer is or is not reasonable.
Answer:
200,000 feet to dig
Step-by-step explanation:
We use a ratio for this problem
30,000 200,000,000
----------- = ---------------------
30 x
200,000,000 * 30
---------------------------- = 200,000 feet to dig
30,000
This answer is reasonable because 200,000,000 years ago was a long time ago so then the person must dig a reasonable amount of dirt. So then 200,000 feet is reasonable.
5 examples of theorems in math. :")
3/10 divided by 2/5?
Answer:
3/4 is your answer
Step-by-step explanation:
The area of a rectangle is 2x^2-11x+15 square feet. The length of the rectangle
is 2x - 5 feet. What is the width of the rectangle?
A) W = x + 5
B) W = x-1
C) W = x-3
D) W = 2x-5
Answer:
A
Step-by-step explanation:
6*10^5 is how many times as large as 3*10^3
Given A=
What is the value of matrix B if A + B = C
Answer:
A
Step-by-step explanation:
We know that 8+3x= x
solve for x
8= -2x
-4 =x
The only answer that has -4 is A
Verify that the given segments are parallel.
Answer:
Step-by-step explanation:
M and N and QR
Can someone pls help me with this?? I’m in a rush it’s due at 11:59 pm..pls help! And show work pls and thx
Answer:
D. 4.5
Step-by-step explanation:
<3
Answer:the answer will be D)4.5
Step-by-step explanation:
Determine a series of transformations that would map Figure G onto Figure H. I need help ASAPPP PLEASEEE
Answer:
A translation followed by a rotation would do it if they are congruent, which they should be.
Step-by-step explanation:
A transformation to move the corresponding points of each shape to the other, and a rotation to rotate the shape until the shapes map onto each other.
Can you conclude that these triangles are congruent?
Yes or no
Answer:
Yes
Step-by-step
If there flipped then they’re congruent
Answer:
Yes
Step-by-step explanation:
Here we get two triangles,
In triangle MNH. In triangle JKH
What is 73 x 4 + 13?
Answer:
73 x 4 + 13 is 305
Answer:
305
explaination:
73 x 4 = 292
292 + 13 = 305
A computer at an electronics store costs $2,893 The tax is 6% how much money will you spend total?
Answer:
$3066.58
Step-by-step explanation:
$2893 x 1.06= $3066.58
Hope this helps!
what is the distance between-2 and -5 on the number line?
Answer:
3
Step-by-step explanation:
on a number line, we use the absolute values to find the difference.
the absolute value of -2 is 2
the absolute value of -5 is 5
5-2=3
so, the distance between -2 and -5 on a number line is 3
three times the cost is 24$.
Answer:
72
Step-by-step explanation:
24 x 3 = 72
20 x 3 = 60
4 x 3 = 12
60+12= 72
Need help ASAP I’m on an exam there is a timer
Thankss + BRAINLIST only for correct answer
(question in the picture )
Answer:
it should be D
Step-by-step explanation:
Because shes going back home.
five yellow m&m for every 3 green. How many green m&m if there are 95 yellow ?
PLEASE HELP
1. Does the system of linear equations shown below have a solution? Explain.
Answer:
hb Step-by-step explanation:
Madison is starting her own sewing business. Madison has calculated that she needs to earn $840 per week to support her family. If she knows she will only be able to work 75 hours per week, what is the minimum amount of dollars per hour that she will need to charge her customers?
Answer:
$11.20 per hour
Explanation:
x = dollars per hour
75x = 840
x = 11.20
Proof that 1^√2 = 1 is true
Answer:
1^sqrt(2) = 1 is always true
Step-by-step explanation:
Step-by-step explanation:
it is always 1 because the teacher said.....lol
Me han descontado 10 euros en unos pantalones que estaban rebajados un 20 porciento .¿cuantos costaban los pantalones ?¿cuanto ha pagado por ellos ?
Answer:
los pantalones costaban 50 euros, y ha pagado 40 euros
The perimeter of a rectangular plot of land is 250 meters if the. Length of one side of the plot is 40 meters what is the area of the plot in square meters?
Answer:
3400 meters squared
Step-by-step explanation:
So if you know that one side 40 another has to be to. So those 2 sides add up to 80. 250-80= 170. Next, you divide 170 by 2 and get 85. Then you just multiply 40 by 85.
Please help ASAP I need this right now
Answer:
You have to look closely and you will find The letters D and C on the bottom of the triangle. D is kinda on the right and C is on the left. Hope this helps.
Step-by-step explanation:
Find the solution of y = –2x + 3 for x = 2.
A. (7, 2)
B. (2, [tex]\frac{1}{2}[/tex])
C. (2, –1)
D. (2, –10)
A store pays $11 for a set of spoons and marks the price up by 30%. What is the amount of the markup?
Answer:
[tex]\$3.3[/tex]
Step-by-step explanation:
Given:
Amount paid by a store for a set of spoons = $11
Percentage increase in price = 30%
To find: amount of the mark up
Solution:
To find amount of the mark up, find 30% of (amount paid by a store for a set of spoons)
Amount of the mark up = [tex]\frac{30}{100} (11)=\$3.3[/tex]
So is 0.147 a rational number?
Answer:
Yes because it is a terminating decimal.
Step-by-step explanation:
30 people liked Brand X. This is 20% of the people in a survey.
a) How many people were there in the survey?
b) What percent of the people did not like Brand X?
c) How many people did not like Brand X?
A newsstand seller sold a total of 68 magazines and newspapers, which brought in a total of $199 on a certain day. Newspapers sell for $2 per copy and magazines sold for $5 per copy. How many magazines were sold on that day?
Answer:
21
Step-by-step explanation:
Using inequality to solve this question, we say
Let the total number of newspapers sold be x
Let the total number of magazines sold by y
x + y = 68
Suppose 1x = $2 and 1y = $5, then
2x + 5y = $199
Solving both as a simultaneous equation, we get that
2(68 - y) + 5y = $199
136 - 2y + 5y = $199
136 + 3y = $199
3y = 199 - 136
3y = 63
y = 63/3
y = 21
Then solving for x, we have
x + 21 = 68
x = 68 - 21
x = 47
Therefore, a total of 21 magazines were sold that day