1. Find the Laplace transform of +3 + et sin(4t) 2. Find the Laplace transform of (t - 34 3. Find the Laplace transform of : te4t sin(2t)
Answers
The Laplace transform of t ×\(e^{4t}\) × sin(2t) is (2 / s²) × (1 / (s - 4)) ×(1 / (s² + 4)).
To find the Laplace transform of the function f(t) = 3 + \(e^{t}\)× sin(4t), we can use the linearity property of the Laplace transform. The Laplace transform of a sum of functions is equal to the sum of their individual Laplace transforms.
Let's break down the function into its individual components:
f₁(t) = 3 (constant term)
f₂(t) = \(e^{t}\) (exponential term)
f₃(t) = sin(4t) (sine term)
The Laplace transform of f₁(t) = 3 is simply 3 multiplied by the Laplace transform of 1, which is 3/s.
The Laplace transform of f₂(t) = \(e^{t}\)can be found using the formula:
L{\(e^{at}\)} = 1 / (s - a)
Therefore, the Laplace transform of f₂(t) =\(e^{t}\)is 1 / (s - 1).
The Laplace transform of f₃(t) = sin(4t) can be found using the formula:
L{sin(at)} = a / (s² + a²)
Therefore, the Laplace transform of f₃(t) = sin(4t) is 4 / (s² + 16).
Now, we can combine the Laplace transforms of the individual components to find the overall Laplace transform of f(t):
L{f(t)} = L{f₁(t)} + L{f₂(t)} × L{f₃(t)}
= (3/s) + (1 / (s - 1)) × (4 / (s² + 16))
So, the Laplace transform of 3 + \(e^{t}\) × sin(4t) is (3/s) + (4 / ((s - 1)(s² + 16))).
To find the Laplace transform of f(t) = t - 34, we'll apply the linearity property of the Laplace transform.
The Laplace transform of t, denoted as L{t}, can be found using the formula:
L{t} = 1 / s²
The Laplace transform of a constant, such as -34, is simply that constant multiplied by the Laplace transform of 1, which is -34/s.
Therefore, the Laplace transform of f(t) = t - 34 is L{f(t)} = (1 / s²) - (34 / s).
To find the Laplace transform of f(t) = t× \(e^{4t}\) × sin(2t), we'll again use the linearity property of the Laplace transform.
Let's break down the function into its individual components:
f₁(t) = t (linear term)
f₂(t) = \(e^{4t}\) (exponential term)
f₃(t) = sin(2t) (sine term)
The Laplace transform of f₁(t) = t can be found using the formula:
L{tⁿ} = n! / \(s^{n+1}\)
Therefore, the Laplace transform of f₁(t) = t is 1 / s².
The Laplace transform of f₂(t) = \(e^{4t}\) can be found using the formula:
L{\(e^{at}\)} = 1 / (s - a)
Therefore, the Laplace transform of f₂(t) = \(e^{4t}\) is 1 / (s - 4).
The Laplace transform of f₃(t) = sin(2t) can be found using the formula:
L{sin(at)} = a / (s² + a²)
Therefore, the Laplace transform of f₃(t) = sin(2t) is 2 / (s² + 4).
Now, we can combine the Laplace transforms of the individual components to find the overall Laplace transform of f(t):
L{f(t)} = L{f₁(t)}× L{f₂(t)}× L{f₃(t)}
= (1 / s²) × (1 / (s - 4))×(2 / (s² + 4))
So, the Laplace transform of t ×\(e^{4t}\) × sin(2t) is (2 / s²) × (1 / (s - 4)) ×(1 / (s² + 4)).
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Related Questions
hii i’ll give brainliest please help thanks :)
Answers
Answer:
3,6,9
Step-by-step explanation:
123 456 789
Answer:
85
Step-by-step explanation:
hi plz mark brainlist
Does a traingel have to be congruent if the two congruency marks are on the same line but different triangles.
Answers
Answer:
If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
Step-by-step explanation:
2 1/3 +1/2{2 divided by 4/5}
Answers
Answer:
36/5
Step-by-step explanation:
36/5 is the answer.
21/3 +1/2*4/10
7+1/5
36/5
please mark me brainliest
Determine the discriminant for the quadratic equation -3=x^2+4x+1. Based on the discriminant value, how many real number solutions does the equation have ? Discriminant value = b^2-4ac
Answers
Answer:
One real root (multiplicity 2).
Step-by-step explanation:
-3=x^2+4x+1
x^2 + 4x + 4 = 0
Discriminant = 4^2 - 4*1*4 = 0
There is one real root (multiplicity 2).
The equation has 1 real solution.
The quadratic function is given as:
\(-3=x^2+4x+1\)
Add 3 to both sides of the equation
\(3-3=x^2+4x+1 + 3\)
This gives
\(0=x^2+4x+4\)
Rewrite the equation as:
\(x^2+4x+4 = 0\)
A quadratic equation is represented as:
\(ax^2+bx+c = 0\)
By comparison, we have:
\(a =1\)
\(b =4\)
\(c = 4\)
The discriminant (d) is calculated as:
\(d =b^2 - 4ac\)
So, we have:
\(d =4^2 - 4 \times 1 \times 4\)
\(d =16 - 16\)
Evaluate like terms
\(d = 0\)
Given that the discriminant value is 0, it means that the equation has 1 real solution.
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Which of the following best shows two elements combining to form a compound!? Explain...
Chemistry.
Answers
Answer:
C because elements are form by atoms and when we study about atom we draw atom like circle
so, that's why I think C is correct
Step-by-step explanation:
Option C best shows two elements combining to form a compound.
What is molecular structure?The term "molecular structure" refers to the structure of a molecule that merely consists of the arrangement of its atoms.
A chemical compound is a material made of several similar molecules that are linked together by chemical bonds and are made up of atoms from various elements.
Chemical compounds cannot be created when two atoms of the same element are bound together since this would need the presence of two distinct elements.
In diagram C it is obtained that atoms are combined to form the compound.
The finest example of two components combining to make a compound is in Option C.
Hence, option C is correct.
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Plan 2 is a better deal for more than 8 cards purchased
Plan 1 is a better deal for more than 8 cards purchased
Plan 1 is a better deal for more than 5 cards purchased
Plan 2 is a better deal for more than 5 cards purchased
Answers
Where the above conditions are given, the correct option is: Plan 1 is a better deal for more than 5 cards purchased.
How is this so?
To determine which pricing plan is a better deal,we need to compare the total cost for a certain number of game cards purchased.
Let's calculate the total cost for different numbers of game cards.
For Plan 1 -
- Admission fee - $5 (fixed)
- Cost per game card - $1
For Plan 2 -
- Admission fee - $2.50 (fixed)
- Cost per game card - $1.50
Now, let's compare the total cost for different numbers of game cards -
1. If you purchase 1 game card -
- Plan 1 - $5 (admission fee) + $1 (cost per game card) = $6
- Plan 2 - $2.50 (admission fee) + $1.50 (cost per game card) = $4
2. If you purchase 5 game cards -
- Plan 1 - $5 (admission fee) + $5 (cost for 5 game cards) = $10
- Plan 2 - $2.50 (admission fee) + $7.50 (cost for 5 game cards) = $10
3. If you purchase 8 game cards -
- Plan 1 - $5 (admission fee) + $8 (cost for 8 game cards) = $13
- Plan 2 - $2.50 (admission fee) + $12 (cost for 8 game cards) = $14.50
Based on these calculations, we can conclude that -
- Plan 1 is a better deal for more than 5 cards purchased.
- Plan 2 is a better deal for more than 8 cards purchased.
Therefore, the correct option is - Plan 1 is a better deal for more than 5 cards purchased.
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How would you use Math at six Flags ?
Answers
Answer:
To find the velocity of a ride and comparing how the height of a ride has to do with how fast the cart goes
Explanation:
At Six flags math can be used in a variety of ways.
For example: to find the price of a ticket that has a 5 percent tax or fiinding out how much of a difference a family package and buying individual tickets are
Pleaseeeeee help?????????????????
Answers
Answer:
x = 129°
Step-by-step explanation:
The sum of the angle with a measure of 51° and x° is equal to 180° because they are supplementary angles. Therefore:
m < 51° + x° = 180°
Subtract m < 51° from both sides to isolate x°:
m < 51° - m < 51° + x° = 180° - m < 51°
x° = 180° - m < 51°
x° = 129°
Therefore, m < x° = 129°
A certain recipe asks for a certain weight in butter. The ratio of butter to the rest of the recipe is 2 : 5. If the total weight of the recipe is 560g, how much butter must be added to the recipe?
Answers
We need 160g of butter for this recipe.
To solve this problem, we need to use the ratio of butter to the rest of the recipe, which is 2:5. This means that for every 2 parts of butter, there are 5 parts of the other ingredients.
To determine how much butter we need, we first need to find the total number of parts in the recipe. In this case, there are 2 parts butter and 5 parts other ingredients, making a total of 7 parts.
Next, we can use the total weight of the recipe (560g) to find out how much each part weighs. To do this, we divide 560 by 7, giving us 80g per part.
Now that we know that each part weighs 80g, we can find how much butter we need by multiplying the number of parts of butter (2) by the weight per part (80g).
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simplify the following
\( \frac{5 {ab } ^{2} + 10 {a}^{4} {b}^{3} - 15 {ab}^{3} }{5ab} \)
Answers
![simplify the following[tex] \frac{5 {ab } ^{2} + 10 {a}^{4} {b}^{3} - 15 {ab}^{3} }{5ab} [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/4MZdlTF0LiEscAyMt2Cgu6Ha5TWziXdj.png)
A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called?
Answers
A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.
We know that,
A dummy variable is a binary variable that takes a value of 0 or 1.
In regression analysis, a dummy variable is one that takes only the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.
The number of dummy variables we must create is equal to k - 1, where k is the number of different values that the categorical variable can take on.
It is an artificial variable created to represent an attribute with two or more distinct categories/levels.
These are being used in order to sort out data into mutually exclusive groups.
It is used typically in time series analysis, response modelling, bio-medical studies, economic forecasting and credit scoring.
Therefore, a variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.
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answer these 3 pls find the shaded region
Answers
7) 100in²
8) 56cm²
9) 51in²
Have a great day <3
Answer:
7. 100
8. 56
9. 51
Step-by-step explanation:
Area of triangle: Length × breadth ÷ 2
Area of rectangle/square: Length × breadth
7. Area of shaded region = (20 × 10) - (20 × 10 ÷ 2)
= 100
8. Area of shaded region = (8 × 8) - (4 × 4 ÷ 2)
= 56
9. Area of shaded region = (15 × 5) - (3 × 8)
= 51
anybody know ow to do this one
Answers
Answer:
b=10mm
Step-by-step explanation:
6x10=60÷2=30
(base x height)÷2
help me pleaseeeeeeeeeeeeeeeee
Answers
A +15-15=35-15
A=20
2b=20
2b/2=20/2
B=10
Britney is 10 years old
7. f(x)=x2 and g(x)=x-1 Evaluate f(g(3)) =
Answers
riddle: how can you take 2 from 5 and leave 4?
Answers
Answer:
The answer is IV.
Step-by-step explanation:
If you remove the first and last letter from the word FIVE, you are left with IV which is the roman number for 4.
Richard walked 15.74 miles and James walk 12.98 miles how many more miles did Richard walk then James.
Answers
Answer: He walked 2.76 more miles.
Step-by-step explanation: In this problem, we would subtract James' miles from Richard's miles to get the answer.
15.74 miles - 12.98 miles = 2.76 miles.
Therefore, Richard walked 2.76 more miles than James.
Santana has already downloaded 8 songs and will continue to download 3 songs per hour.
Answers
EX:
1st: 11
2nd: 14
3rd: 17
4th: 20
5: 23
So on…
Select the correct answer.
Consider figures 1 and 2 shown in the coordinate plane. Figure 1 has been transformed to produce figure 2.
-00
55-
N
2
N
ON
6
80
Which notation describes this transformation?
OA. (x,y) = (x,-)
OB. (x,y)=(x-4,y - 8)
OC. (x,y) = (x - 8,y - 8)
OD. (x,y)= (-2,-y)
9.
8.
Answers
Using translation concepts, the notation that describes this transformation is:
C. (x,y) -> (x - 8, y - 8).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
To generate figure 2 from figure 1, these following translations happened:
8 units left, hence x -> x - 8.8 units down, hence y -> y - 8.Thus the rule is given by:
C. (x,y) -> (x - 8, y - 8).
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Answer: (x',y') = (x - 4,y - 8)
Step-by-step explanation:
(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.
(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.
Answers
(a) We have shown that there exists an element b ∈ B that is an upper bound for A.
(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.
(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.
Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).
Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.
(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.
Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.
This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.
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In the number 2,222. 222, what is the difference between the 2 in the tens place and the 2 in the column to its left?.
Answers
The difference between the 2 in the tens place and 2 to its left column in the given number 2,222.222 is 180.
According to the number system, a number can be written in its expanded form according to their pace value in the chart.
2,222.222 can be written as 2×1000+2×100+2×10+2X1+2×1/10+2×1/100+2×1/1000
The place value of 2 in the tens place in given number 2,222.222 = 20
The place value of 2 in its left column in the given number 2,222.22 = 200
Difference between the place of 2 in tens place and 2 in its left column
= 200 - 20
= 180
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weight loss x runs a number of weight reduction centers within a large city. from the historical data it was found that the weight of the participants is normally distributed with a mean of 175 lbs and a standard deviation of 35 lbs. calculate the standard error of the average sample weight when 15 participants are randomly selected for the sample? enter your answer rounded to two decimal places. for example, if your answer is 12.345 then enter as 12.35 in the answer box.
Answers
The standard error of the average sample weight when 15 participants are randomly selected for the sample is 9.05 (rounded to two decimal places).
The standard error of the average sample weight when 15 participants are randomly selected for the sample can be calculated using the formula given below:SE = σ/√nWhere,σ = standard deviation of the populationn = sample sizeSE = standard error of the meansubstituting the given values,SE = 35/√15 = 9.05
Note:When using the given formula, it is important to note that it assumes a normal distribution of sample means. The standard error is used to estimate the true value of the mean from the sample data. The larger the sample size, the smaller the standard error. The smaller the standard error, the more precise the estimate of the true value of the mean.
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What is the 2-digit subtraction with regrouping worksheets?
Answers
Answer:
To subtract two-digit numbers, use column form. Subtract one column at a time, starting with the Ones column. We regroup, or borrow. To regroup, take 1 from the Tens column and add 10 to the Ones column.
Step-by-step explanation:
Tickets at an amusement park are $25 for children and $45 for adults, the Jones family has 4200 cash
and they have two children, what is the maximum amount of adult tickets they can purchase?
Answers
Step-by-step explanation:
$4200 - $50
= $4150
4150 divided by 45 = 92.222.......
92.222 is approximately 93
So you can purchase 92/93 tickets in total
Since tickets are physical things, I dont think you can approximate it but that's my answer
The maximum amount of adult tickets they can purchase are 92.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given are tickets at an amusement park that are $25 for children and $45 for adults. The Jones family has 4200 cash and they have two children.
Assume that they could purchase [n] number of adult tickets.
Cash remaining for adult tickets = 4200 - 2(25)
The total number of adult tickets that can be buyed are calculated as follows -
45n = 4200 - 2(25)
45n = 4200 - 50
45n = 4150
n = 4150/45
n = 92 (exact value)
Therefore, the maximum amount of adult tickets they can purchase are 92.
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What is 55 divided by 32
Answers
Answer:
1.71875
Step-by-step explanation:
Answer:
1.72 (rounded to the nearest hundredth)
Step-by-step explanation:
b) if the price of cigarettes increases by $1 (all else equal), then what will be the change in the odds of smoking?
Answers
However the exact change in the odds of smoking would depend on various factors such as individuals' preferences, income levels, and the price elasticity of demand for cigarettes.
If the price of cigarettes increases by $1 (all else equal), then the odds of smoking are likely to decrease. This is because an increase in price typically leads to a decrease in demand, and therefore a decrease in the likelihood that someone will choose to smoke cigarettes.
Specifically, the odds of smoking would decrease by a certain percentage that would depend on a variety of factors, such as the current price of cigarettes, the income level of individuals who smoke, and the availability of alternative products or behaviors. However the exact change in the odds of smoking would depend on various factors such as individuals' preferences, income levels, and the price elasticity of demand for cigarettes.
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Isaiah buys a hat that normally costs $17.There is a sale for 15% off. How much
does he pay for the hat?
+
Answers
Answer:
$14.45
Step-by-step explanation:
15% of 17 is 2.55. 17 - 2.55 is 14.45
what is the sum of the measures of the exterior angles of a decagon?
Answers
Answer:
360°
Step-by-step explanation:
The sum of the exterior angles of any polygon is 360°
sum of exterior angles of decagon = 360°
A pile of sand weighs 90kg. the sand is put into a small bag, a medium bag and a large bag in the ratio 2: 3: 7. work out the weight of each sand bag Please help!
Answers
Answer:
the first bag is 15 ,the second bag is 22.5 and the third bag is 52.5
Step-by-step explanation:
you take the ratios and add them together 2+3+7=12. then you take 2/12×90=15,3/12×90=22.5,7/12×90=52.5 I think I tried
Will make brainiest if 2 people answer :3
Answers
Answer:
1.6
Step-by-step explanation:
12.8/8 = 1.6
15.2/9.5 = 1.6
Scale factor = 1.6