its complex functions subject 2 EXERCISE7: a/ Find Laplace transform of : f(t) = cos 7t + e-7t + e4fsh3t b/ Find Inverse Laplace transform of: F(s)= sl + (-3)3+25 + 25 EXERCISE8:Lety3+=0withu0=0.0)=0and0= a/ Find Laplace transform of this differential equation. Isolate Y(s) b/ From question a, find y(t).
Answers
a) To find the Laplace transform of the function f(t) = cos(7t) + e^(-7t) + e^(4sinh(3t)), we can use the linearity property of the Laplace transform.
The Laplace transform of cos(7t) can be found using the formula: L{cos(kt)} = s/(s^2 + k^2), where k is the constant coefficient.
So, the Laplace transform of cos(7t) is s/(s^2 + 7^2) = s/(s^2 + 49).
The Laplace transform of e^(-7t) can be found using the formula: L{e^(-at)} = 1/(s + a), where a is the constant coefficient. Therefore, the Laplace transform of e^(-7t) is 1/(s + 7). The Laplace transform of e^(4sinh(3t)) is not a standard function in the Laplace transform table. However, we can use the definition of the Laplace transform and perform the integration:
L{e^(4sinh(3t))} = ∫[0 to ∞] e^(4sinh(3t)) * e^(-st) dt.
The exact integral cannot be easily solved analytically, so it may require numerical or approximate methods to obtain the Laplace transform of e^(4sinh(3t)).
b) To find the inverse Laplace transform of F(s) = sl + (-3)^3 + 25 + 25, we need to use the inverse Laplace transform formula or table to identify the function that corresponds to F(s).
Using the linearity property of the inverse Laplace transform, we can break down F(s) into three terms: L^{-1}{sl}, L^{-1}{(-3)^3 + 25}, and L^{-1}{25}. The inverse Laplace transform of sl can be found using the formula: L^{-1}{s^nf(t)} = (-1)^n * d^n/dt^n[f(t)].
So, the inverse Laplace transform of sl is (-1)d/dt(l).
The inverse Laplace transform of (-3)^3 + 25 is simply (-3)^3 + 25 = -27 + 25 = -2. The inverse Laplace transform of 25 is 25. Therefore, the inverse Laplace transform of F(s) is (-1)d/dt(l) - 2 + 25, which simplifies to -d/dt(l) + 23.
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Related Questions
Apply the 30°-60°-90° Triangle Theorem to find the length of the longer leg of a triangle if the length of the shorter leg is 5√3 inches.
Answers
Answer:
15 inches
Step-by-step explanation:
The shortcut for finding the side lengths on a 30°-60°-90° triangle is that the long leg is
the short leg × √3.
So for your question:
5√3 × √3
= 5 × √3 × √3
= 5 × 3
= 15
Just in case it comes up next, the other shortcut is that the hypotenuse is double the short leg. Hypotenuse =
2 × 5√3 = 10√3
pls help due soon if your right ill mark you brainliest asap
Answers
Answer:
D
Step-by-step explanation:
Find all the trigonometric functions given csc θ=2 and θ is in quadrant 2
show all steps and work
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Answers
The trigonometric functions for θ in quadrant 2, given csc θ = 2, are:
sin θ = 1/2
cos θ = √3/2
tan θ = √3/3
csc θ = 2
sec θ = (2√3)/3
cot θ = √3.
Given that csc θ = 2 and θ is in quadrant 2, we can find all the trigonometric functions using the following steps:
1. Start with the given information: csc θ = 2. The cosecant function is the reciprocal of the sine function, so we can rewrite this as sin θ = 1/2.
2. In quadrant 2, the sine function is positive, so sin θ = 1/2. This means that the opposite side of the triangle is equal to 1 and the hypotenuse is equal to 2.
3. To find the adjacent side, we can use the Pythagorean theorem. Since the opposite side is 1 and the hypotenuse is 2, we have a^2 + 1^2 = 2^2. Solving for a, we get a^2 + 1 = 4, which gives us a^2 = 3. Taking the square root of both sides, we find that a = √3.
4. Now we have the values for the opposite side, adjacent side, and hypotenuse. We can use these values to find the other trigonometric functions:
- The cosine function is the ratio of the adjacent side to the hypotenuse. So cos θ = a/h = √3/2.
- The tangent function is the ratio of the opposite side to the adjacent side. So tan θ = o/a = 1/√3 = √3/3.
- The secant function is the reciprocal of the cosine function. So sec θ = 1/cos θ = 2/√3 = (2√3)/3.
- The cotangent function is the reciprocal of the tangent function. So cot θ = 1/tan θ = √3.
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PLEASE HELP AND SHOW WORK
Answers
Answer:
n ≥ -4 or n < -1
Step-by-step explanation:
Flip the sign with the -4 n thing and that's it for that side of the or. Then you subtract the 1 from -2. So, then you are left with 3n< -3 then you divide both sides by 3 and get n < -1.
Answer:
that's hard
Step-by-step explanation:
I can't answer
what is 4,234 dekaliters converted to milliliters
Answers
Answer:
4,234 dekaliters converted to milliliters is 42340000.
Step-by-step explanation:
Answer: Your answer is going to be 42340000 millimeters.
Step-by-step explanation:
Find out how much one dekaliter is worth; multiply by that amount.
simplify \(12 {a}^{4} {b}^{ - 3} \div 15 {a}^{ - 2} b\) I don't understand what the lesson is trying to teach me.
![simplify [tex]12 {a}^{4} {b}^{ - 3} \div 15 {a}^{ - 2} b[/tex] I don't understand what the lesson is](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/B4fUB4V0IDVGjK4b2XB48sw4PoW0ty4M.jpeg)
Answers
We have to simplify the expression:
\(\frac{12a^4b^{-3}}{15a^{-2}b}\)We have the variables a and b with different exponents, that we can simplify applyinf the rules of the exponents.
For example, we can do this:
\(\begin{gathered} \frac{12a^4b^{-3}}{15a^{-2}b} \\ \frac{12}{15}a^{4-(-2)}b^{-3-1} \\ \frac{4}{5}a^6b^{-4} \\ \frac{4}{5}\frac{a^6}{b^4} \end{gathered}\)Answer: (4/5)*a^6/b^4
To do the divisions, we divide all the same terms together.
12 : 15 = 4/5
a^4 : a^-2 = a^4 - (-2) = a^6
b^-3 : b = b^-3 - (1) = b^-4
And do the last step of moving the terms with negative exponents, we get the result shown in the picture.
There are 12 boys and 12 girls in Ms. Mooney’s homeroom class. Ms. Mooney will randomly pick 1 student to take attendance today.
Which statement explains how to find the probability that Sara, a student from Ms. Mooney’s homeroom class, will be the student picked?
PLEASE HELP
Answers
Answer:
There is a \(\frac{1}{24}\) chance that Sara will be picked.
There is a 4.16% chance that Sara will be picked.
Step-by-step explanation:
there are 12 boys + 12 girls in Mooney's class => 24 total students
Sara is ONE out of those students
Sara is \(\frac{1}{24}\).
\(\frac{1}{24}\) as a percent is 4.16%.
You deposit $2500 into a bank account that pays 7.5% annual interest, compounded continuously. Find
the amount in the account after 6 years?
Answers
Answer:
16,125
Step-by-step explanation:
what is this answer5+(−4)=
Answers
Answer:
Hello!
____________________
5+(−4)= 1
Step-by-step explanation: Simplify the expression.
Hope this helped you!
Answer:
5+(-4)=1
Step-by-step explanation:
2: Evaluate:
42.43
Please help me fast
Answers
Show work:
Write the fraction or mixed number as a percent.
1 13/20
this is for a test!! aghh
Answers
Answer: 165%
Step-by-step explanation:
1 = 100%
13/20 = 65%
1 13/20 = 165%
Problem #10: Find the value of y' when x = 0 if xy2 + ey/3 + / = e Problem #10: Enter your answer symbolically, as in the examples Just Save Submit Problem #10 for Grading Problem #10 Attempt #1 Attem
Answers
The equation, we have:
y^2 + (e/3)(1/y)(dy/dx) + ∞ = 0
We cannot determine the value of y' when x = 0 from the given equation since it leads to an indeterminate form.
To find the value of y' when x = 0, we need to take the derivative of the given equation with respect to x and then substitute x = 0.
The given equation is:
xy^2 + ey/3 + √x = e
Differentiating both sides with respect to x using the chain rule, we get:
y^2 + 2xyy' + (e/3)(1/y)(dy/dx) + (1/2√x) = 0
Now, substitute x = 0 into the equation:
y^2 + 0 + (e/3)(1/y)(dy/dx) + ∞ = 0
Since x = 0, the term (1/2√x) becomes ∞.
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A chain is formed of n links. The strengths of the links are mutually independent, and the probability that any one link fails under a specified load is q. What is the probability that the chain fails under that load?
Answers
The question is asking for the probability of the chain failing under the given load. The strength of the links is independent of each other. We can use Bernoulli's trial to solve this problem.
Let's define the probability of any one link not failing under the given load as `p = 1 - q`. Here, q is the probability that any one link will fail under the given load.
The probability that all n links will not fail under the load can be calculated as `P(success) = p^n`. Here, we multiply the probability of success of one link by the probability of success of another link and so on until the nth link.
The probability of the chain failing is the complement of the probability that all the links will not fail. Hence, `P(failure) = 1 - P(success) = 1 - p^n`.
Therefore, the probability of the chain failing under the given load is `1 - p^n` or `1 - (1 - q)^n`.
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How else can we express P(A) / P(A Ì)
Answers
P(A) / P(A|B) can be expressed as P(A and B) / P(B).
The expression P(A) / P(A|B) represents the ratio of the probability of event A occurring to the conditional probability of A given that event B has occurred.
Using Bayes' theorem, we can express P(A|B) in terms of P(A and B) and P(B) as:
P(A|B) = P(A and B) / P(B)
Rearranging this equation, we get:
P(A and B) = P(A|B) * P(B)
Substituting this expression for P(A and B) in the original ratio, we get:
P(A) / P(A|B) = P(A) / (P(A and B) / P(B))
= P(A) * P(B) / P(A and B)
Therefore, we can express P(A) / P(A|B) as P(A and B) / P(B).
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We know that the worst case for Insertion Sort is about n^2/2n 2 /2, while the average case is about n^2/4n 2 /4. This means that:
Answers
The statement suggests that the worst-case time complexity of Insertion Sort is approximately proportional to n²/2, while the average-case time complexity is approximately proportional to n²/4.
What does the statement meanThe worst-case and average-case time complexities of Insertion Sort indicate that the algorithm's performance is quadratic, with the average case being more efficient than the worst case due to a smaller constant factor.
The worst-case time complexity refers to the scenario where the input array is in reverse order or nearly sorted in reverse order. While the average-case time complexity represents the average performance of the algorithm over all possible inputs.
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A plane can fly 640 miles in the same time as it takes a car to go 240 miles. If the car travels 100 mph slower than the plane, find the speed (in mph) of the plane.
Answers
Answer:
Let s be the speed of the plane. Then s - 100 is the speed of the car.
640/s = 240/(s - 100)
640(s - 100) = 240s
8(s - 100) = 3s
8s - 800 = 3s
5s = 800, so s = 160 mph
The speed of the plane is 160 mph, and the speed of the car is 60 mph.
20 Points.
Thomas has some leftover paint that he would like to sell. He mixes 4 3/8
gallons of blue paint with 6 5/8
gallons of white paint. Then, he pours this light-blue mixture into 1/4
gallon containers. To find out how many of these 1/4
gallon containers he can fill, which two equations would you need?
Reminder: It says 2 answers are needed
Answers
Answer:
d and b
Step-by-step explanation:
d and b
Help!!!
If AB=4 feet & AD=10 feet & m What is DC?
What is BD?
Answers
BD= 10
Hope it’s right
Best luck with your studying
Answer:
DC=4 feet
Step-by-step explanation:
Opposite sides of a rectangle are equal.
Determine the mean of the following set of numbers: 40, 61, 95, 79, 9, 50, 80, 63, 109, 42
Round to the nearest tenth place. The mean is
Answers
Step-by-step explanation:
work is shown and pictured
here are the score that Jenna has received on her seven quizzes 16 13 20 16 12 17 18 what is the mean
Answers
Answer:
so you're adding up all the numbers together so 16+13+20+16+12+17+18=112
then you are dividing it by how many numbers there are so there are 7 numbers in total 112÷7=16
a metric is a single, quantifiable type of data that can be used for what task?
Answers
A metric is a single, quantifiable type of data that can be utilized for various tasks in different domains. Metrics serve as essential tools for measuring progress, assessing performance, and making informed decisions.
By converting complex information into manageable and comparable units, metrics enable individuals and organizations to monitor their objectives and drive improvement.
In business, metrics are often employed to evaluate the success of marketing campaigns, employee performance, or financial growth. They assist in identifying trends, pinpointing areas that need attention, and guiding strategic planning. Key performance indicators (KPIs) are a common type of metric used to measure the effectiveness of business processes and track progress toward organizational goals.
In scientific research, metrics provide valuable insight into the progress and impact of studies. For example, citation metrics measure the influence of a published work within a given field. Metrics also facilitate the assessment of experimental results and the development of new theories, ultimately advancing scientific knowledge.
In education, metrics serve as essential tools for gauging student performance and the quality of educational programs. They provide data on student learning outcomes, helping educators refine their teaching methods and tailor instruction to the needs of individual learners.
Overall, a metric is a versatile, quantifiable data type that plays a vital role in assessing and improving various aspects of performance across multiple domains. By offering concrete, measurable information, metrics empower decision-makers to make informed choices and drive progress.
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Determine whether the given lines are parallel, perpendicular or neither.
2x + 3y = 1
3x – 2y = 1
Answers
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
These two equations are perpendicular it's pretty tough to figure it out with the only the equations like last time but if you graph it's more easier because it's visual.
So the equations solved for y is...
\(y=-\frac{2}{3} x+\frac{1}{3}\)
\(y=\frac{3}{2}x-\frac{1}{2}\)
NEED HELP ASAP!!!¡!
A laser tag arena offers two payment plans for laser tag games.Plan A charges $6 per game plus a one-time membership fee of $35.Plan B offers unlimited games for a year for a one-time membership fee of $149. What is the minimum number of games you would have to play in order for the unlimited plan to be tha best deal?
Answers
Answer:
25 games
Step-by-step explanation:
We need to write an inquality to figure out how many games (which costs $6 with Plan A), you would need to play for that to have cost more than unlimited play for $149
\(6a > 149\)
$6 for a game for Plan A versus $149 set fee
Solve for a by diving by 6
It comes to 24.833 (repeating), but since this is a word problem, we need to round up
edit: i have no idea why it formatted weird ahhh sorry
Combine like terms
1) -2(x+6)
2) 10-4(6-x) + 5x
Answers
Answer:
1) -2x-12
2) 9x-14
Step-by-step explanation:
1). We use distributive property. We have to multiply -2 by x and 6. This means that the expression is -2x-12.
2). We use the distributive property again. We have to multiply -4 by 6 and x. Therefore, the equation will be 10-24+4x+5x. Then, we have to combine like terms. 10-24 is equal to -14 and 4x+5x is equal to 9x. Therefore, it is equal to 9x-14.
If this has helped please mark as brainliest
can someone help me please
Answers
Answer:
B) Y = 5x - 10
Step-by-step explanation:
m = y2-y1 / x2-x1
Hope this helps. Pls give brainliest.
7. Find the coordinates of a point on a circle with radius 20 corresponding to an angle of \( 305^{\circ} \)
Answers
Given that a circle with radius 20 has a corresponding angle of 305°.
To find the coordinates of a point on the circle, we use the formula:`(r cos (θ), r sin (θ))`Here, `r = 20` and `θ = 305°`.
Substituting the values of `r` and `θ` in the formula, we get:`(20 cos (305°), 20 sin (305°))`
Using the values of trigonometric ratios, we can write:cos(305°) = cos(360° - 305°) = cos(55°) ≈ -0.5736sin(305°) = sin(360° - 305°) = sin(55°) ≈ 0.8192
Hence, the coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`.
The coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`
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Type the correct answer in the box. Use numerals instead of words.
For this item, if the answer is not a whole number, enter it as a fraction in simplest form using / as the fraction bar.
Isolde is stacking books. The stack of books forms a rectangular prism.
Each book is the same size. Isolde knows the area of the base of one book is 22 1/2 square inches and each book is 3/4 inch thick.
The volume of a stack of 9 books is cubic inches.
Answers
The volume of a stack of 9 books is 1368.75 cubic inches.
Volume of a book stackTo find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.
Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.
Therefore, the volume of the stack of 9 books is:
Volume = Area of base x heightVolume = (202 1/2 square inches) x (6 3/4 inches)Volume = 1368.75 cubic inchesMore on volume of stacked books can be found here: https://brainly.com/question/1058070
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Craig wants to use an elevator to carry identical packages having the same weight each package weighs 4 pounds and Craig weighs 90 pounds if the elevator can carry a maximum of 330 pounds at a time which NE quality shows the maximum number of packages in that crag can carry with him self in the elevator if he is the only passenger
Answers
Answer:
He can carry 60 packages
Answer:
he can carry 60 packages with him if hes the only passenger
Step-by-step explanation:
HELP ME ASAPPP
Write the standard equation of a circle with center (2, 1) and radius 8.
Answers
Answer:
C
=
(
a
,
b
)
the center coordinates of circle
a
=
2
,
b
=
−
1
,
r
=
8
Step-by-step explanation:
Which of the following statements is not true about chi-square distributions? The mean decreases as the degrees of freedom increase. OPG? < 0) = 0 O PU2 > 3) is larger for a chi-square distribution with df = 10 than for df = 1 There are an infinite number of chi-square distributions, depending on degrees of freedom. They are always skewed to the right Previous Only saved at 4:44pm
Answers
The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.
Is it true that the mean of a chi-square distribution decreases as the degrees of freedom increase?In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.
The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.
Regarding the other statements:
The statement "OPG? < 0) = 0" is true. The probability of a chi-square random variable being less than zero is always zero, as chi-square values are non-negative.The statement "OPU2 > 3) is larger for a chi-square distribution with df = 10 than for df = 1" is true. As the degrees of freedom increase, the right-tail probability of a chi-square distribution also increases.The statement "There are an infinite number of chi-square distributions, depending on degrees of freedom" is true. The number of chi-square distributions is infinite because the degrees of freedom can take any positive integer value.The statement "They are always skewed to the right" is generally true. Chi-square distributions tend to be skewed to the right, especially when the degrees of freedom are small.In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.
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