Use appropriate algebra and theorem 7. 2. 1 to find the given inverse laplace transform. (write your answer as a function of t. ) ℒ−1 2 s − 1 s3 2
Answers
The inverse Laplace transform of \(L^{-1}[(\frac{2}{s} -\frac{1}{s^3})^2]\) is:
\(L^{-1}[(\frac{2}{s} -\frac{1}{s^3})^2] =4t -\frac{4t^3}{3}+\frac{t^5}{120}\)
The inverse Laplace transform is given as follows as:
\(L^{-1}[(\frac{2}{s} -\frac{1}{s^3})^2]\)
As per the question, We have to determine the given inverse Laplace transform.
We can use the formula for the square of a binomial to simplify the expression inside the Laplace transform as follows:
\((\frac{2}{s} -\frac{1}{s^3})^2 = \left(\frac{2}{s}\right)^2 - 2\left(\frac{2}{s}\right)\left(\frac{1}{s^3}\right) + \left(\frac{1}{s^3}\right)^2\)
\(= \frac{4}{s^2} - \frac{4}{s^4} + \frac{1}{s^6}\)
Now, we can use the linearity property of the inverse Laplace transform and Theorem 7.2.1 to find the inverse Laplace transform of each term separately:
\(L^{-1}[\dfrac{4}{s^2}] = 4t\\L^{-1}[-\frac{4}{s^4}] = -4t^3/3\\L^{-1}[\frac{1}{s^6}] = t^5/120\)
Therefore, the inverse Laplace transform of \(L^{-1}[(\frac{2}{s} -\frac{1}{s^3})^2]\) is:
\(L^{-1}[(\frac{2}{s} -\frac{1}{s^3})^2] = L^{-1}[\frac{4}{s^2} - \frac{4}{s^4} + \frac{1}{s^6}] = 4t -\frac{4t^3}{3}+\frac{t^5}{120}\)
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Related Questions
2. How long will it take for $6,500 to grow to $85,000 at an interest rate of 8% if the
Interest is compounded continuously?
Answers
Sam found a tent in his garage, and he needs to find the center height. the sides are both 5 feet long, and the bottom is 6 feet wide. what is the center height of sam’s tent, to the nearest tenth? 3 feet 4 feet 5.5 feet 7.8 feet
Answers
The centre height of Sam's tent to the nearest tenth = 7.8 feet.
Calculation of the center heightThe length of both sides of the tent (a) = 5ft
The base of the tent is (b)= 6ft
The centre height (c) = ?
Using the Pythagorean theorem
c² = a² + b²
c² = 5² + 6²
c² = 100 + 36
c² = √136
c² = 7.8 feet
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in a field hockey championship, 120 matches were played. every pair of team played one match with each other. the number of teams in the tournament is therefore:
Answers
The number of teams in the field hockey championship tournament is 16.
The total number of matches played in the field hockey championship are 120 matches.
Each pair of team played one match with each other.
So, let us say that there are N teams in the tournament.
So, we can chose any two teams for a match,
So, applying the permutation formula,
ⁿC₂ = 120
Solving further,
N!/2!(N-2)! = 120
N(N-1)/2 = 120
N(N-1) = 240
On observing closely and applying hit and trial method,
16(15) = 240
So, the values of N is 16.
Hence, 16 teams participated in the tournament.
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Developing spiritual wellness includes:
A.
Finding an inner peace
B.
Participating in self-nurturing activities
C.
Respecting other people
D.
All of the above
Answers
Answer:
The answer is D all of the above
Step-by-step explanation:
Being spiritually well means to be clean and pure thus meaning having inner peace, participating in self nurturing activities and being respectful of others.
Onyx surveys students at his school and finds that 80% have a pet. He wants to estimate the probability that, if he randomly selected 4 students, at least one student would NOT have a pet.
To estimate this probability, he lets the numbers 1, 2, 3, and 4 represent a student who HAS a pet and 5 represent a student who does NOT have a pet. He then has a computer randomly select 4 numbers and repeats this 20 times.
Based on this simulation, what is the estimated probability that at least one student who have NO PETS?
Represent your answer as a decimal and show your work as to how you determined the answer. pls help this one will give you 50 points
Answers
The estimated probability that at least one student who have NO PETS is 1/4.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Onyx surveys students at his school and finds that 80% have a pet.
He wants to estimate the probability that, if he randomly selected 4 students, at least one student would NOT have a pet.
lets the numbers 1, 2, 3, and 4 represent a student who HAS a pet, and 5 represent a student who does NOT have a pet.
He then has a computer randomly select 4 numbers and repeats this 20 times.
The estimated probability that at least one student who have NO PETS
= 1/4
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Which statement about f(x)=x^2+16x+3 is true?
A. The function has a maximum value of 3
B. The function has a maximum value of 16
C. The function has a maximum value of -8
D.The function has a maximum value of -61
Answers
Answer:
I think D the function has a maximum value of -61
Step-by-step explanation:
Sixteen times a number x is less than -2.
Answers
Answer:
16x<-2
Step-by-step explanation:
twice the difference of a number and 2 is 9
Answers
The difference of a number and 2: x-2
Twice the difference of a number and 2: 2(x-2)
Is 9.
2(x-2) = 9
2x - 4 = 9
2x = 13
x = 13/2 = 6 1/2
Slope = -2/3, y-intercept = 1
Write the slope-intercept form of the equation of each line given the slope and y-intercept ?
Answers
Answer:
The answer is y=-2/3x+1
Step-by-step explanation:
Remember the slope intercept is y=mx+b
m = slope, b = y intercept
Plug those in
Answer: y = -2/3x + 1
Write the fraction which corresponds to the part no shaded
Answers
Answer:
1/8 not shaded, 7/8 shaded
Step-by-step explanation:
At the grocery store, 4 pints of ice cream cost $8.24. How much would 30 pints of ice cream cost
Answers
Answer:
$61.80
Step-by-step explanation:
you first want to find out how much one pint costs so you do 8.24/4 which is 2.06 then you multiply it by 30 to get 61.80
Answer: I believe it would cost $61.8
Step-by-step explanation:
\(\frac{4}{8.24} x \frac{30}{x}\)
8. 24 x 30 = 247.2
247.2 / 4 = 61.8
the curve passes through the point (1,7) and is tangent to the line yx at the origin. find a, b, and c.
Answers
The solution to the problem as given is not possible and there may be a typo or mistake in the problem statement.
To solve this problem, we need to use the equation of the tangent line at the origin and the fact that the curve is tangent to it at that point. The equation of the tangent line at the origin is y = x since it passes through the origin and has a slope of 1.
Let's assume that the equation of the curve is y = ax^2 + bx + c. We know that it passes through the point (1,7), so we can substitute these values into the equation to get 7 = a(1)^2 + b(1) + c, which simplifies to 7 = a + b + c.
Next, we need to find the derivative of the curve in order to find the slope of the curve at the point (1,7). The derivative of y = ax^2 + bx + c is y' = 2ax + b. We know that the curve is tangent to the line y = x at the origin, so the slope of the curve at the origin is 1. Therefore, we have 1 = y'(0) = b.
Now we can substitute a and b into the equation we found earlier: 7 = a + b + c. Simplifying, we get 7 = a + c + 1.
We have two equations with two variables, so we can solve for a and c:
a + c = 6
a + c = 6 - 1 = 5
Therefore, a = 5 - c. Substituting into the first equation:
(5 - c) + c = 6
5 = 6
This is a contradiction, so there is no solution for a, b, and c that satisfies all the conditions. There may be a typo or mistake in the problem statement.
In conclusion, the solution to the problem as given is not possible and there may be a typo or mistake in the problem statement.
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HELP MATH SUCKSSSSSS 7 and 8
Answers
Answer:
Step-by-step explanation:
The diagram shows the shape of a putting green in a miniature golf course. One part of the green is a sector of a circle. To the nearest square foot, what is the area of the putting green?
Answers
Given the diagram shows the shape of a putting green in a miniature golf course.
We will find the area of the putting green by dividing it into 3 sections as shown in the following figure:
Area (1) is the area of a rectangle with dimensions 4.5 and 8 feets
so, the area (1) = 4.5 x 8 = 36 feet²
Area (2) is the area of a square with a side length of 4.5 feet
So, the area (2) = 4.5 x 4.5 = 20.25 feet²
Area (3) is the area of the sector of a circle with a radius = 4.5 feet
The sector represents the quarter of the circle
so, Area (3) =
\(\frac{1}{4}\pi *r^2=\frac{1}{4}*\pi *4.5^2=15.9043\text{ }feet^2\)So, the total area is the sum of the three areas:
\(Total\text{ }Area=36+20.25+15.9043=72.1543\)Rounding to the nearest square foot
So, the answer will be: Area = 72 feet²
What is associative property example?
Answers
The example of an associative property is a+(b+c) = (a+b) + c for additional operation and a × (b × c) = (a × b) × c for the multiplication operation. The associative property is used to solve an equation or expression of real numbers.
What are the properties of real numbers?
In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.
The four primary characteristics of real numbers are as follows:
Commutative property
Associative property
Distributive property
Identity property.
Associative property: The associative property is applicable on two arithmetic operations. They are multiplication and addition.
For multiplication operations: a × (b × c) = (a × b) × c
For additional operation: a+(b+c) = (a+b) +
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15 POINTS!! NUMBER 40-45 NO EXPLANATION NEEDED (will get brainliest!!)
Answers
Answer:
Leo shared 112 tom thumb drops, 220 micro mints, and 164 tiny tots. He has 140 tom thumb drops, 275 micro mints, and 205 tiny tots remaining.
Hope this helps !! :D
Answer:
Sweets shared
> 112
> 220
> 164
Sweets remaining
> 140
> 275
> 205
3 to the power of a+4
Answers
The word description "3 to the power of a + 4" should be written as 3^{a + 4}.
What is an exponent?In Mathematics, an exponent is sometimes referred to as power and it can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;
bⁿ
Where:
the variables b and n represent numerical values or an algebraic expression.
By applying the property of exponents based on the law of indices for powers, we have the following:
Expression = 3^{a + 4}.
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Complete Question:
What is 3 to the power of a+4?
Knowing that Mountain McKinley is above sea level and death valley is below sea level. What integer would be used to represent sea level. Explain
Answers
we can use integer 0 as a sea level.
does anything in the plot of the semimajor axis versus the period change when the eccentricity is changed?
Answers
Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.
What is eccentricity?In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.
Here,
In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.
As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.
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on a girls volleyball team 9 out of 12 team members have played in previous years based on this information if 80 girls are in a volleyball league than how many could be expected to have played the year before?
Answers
Answer: I believe the answer is 60
Step-by-step explanation:
9/12 = 3/4
If we do cross multiplying x over 80 times 3/4 it equals 60.
I am sorry if it is not correct I'm not fully sure but I hope this helped!!
• Choose a topic from the list below: Argue why Josef Pieper conception of leisure is the best one in modernity, or instead why it might be a limited conception in comparison to another theory of leisure. • Argue why a life is better with leisure today, and why for the classical Greeks, an absence of leisure meant an absence of a happy life. • Argue why John Dewey and modern liberal thinkers did not agree with Aristotle's ideas on education or on leisure generally. • Argue how modern psychological conceptions of happiness and the classical idea of happiness in Aristotle differ. What was the "Greek Leisure Ideal" and how would it manifest today according to Sebastian De Grazia? What happened to it? • Argue why the liberal arts are so important in education and leisure, and explain its Greek origin and how that is received today. • You must choose from this list, but it can be modified slightly if you have an idea you wish to pursue. The main requirement is that you must contrast at least one ancient thinker and one modern one. • The paper must be well researched and contain a minimum of 6 sound academic sources. • Textbook or course readings may be used, but do not count in this total. DETAILS SCALCET8 1.3.039. 0/1 Submissions Used Find f o g o h. f(x) = 3x - 8, g(x) = sin(x), h(x) =x^2
Answers
To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.
The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.
The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.
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If the relationship between total cost and number of units made is linear, and if cost increases by $1.4 for each additional unit made, and if the total cost of 24 units is $55, find the equation of the relationship between total cost (y) and number of units made (x).
Answers
Answer:
y = 1.4x + 21.4
Step-by-step explanation:
Given :
Total cost and number of units made have a linear relationship
Mathematically,
Total cost, y = b * number of units made, x + c
If cost increases by $1.4 for each additional unit, the slope, b = 1.4
If total cost of 24 units = $55
Total cost = 1.4 * number of units made + c
55 = 1.4*24 + c
55 = 33.6 + c
c = 55 - 33.6
c = 21.4
c = intercept
The linear relationship between total cost and number of units made is :
y = 1.4x + 21.4
if olive construction company gets the job, what is the probability that base construction company did not bid?
Answers
If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.
The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
So, the probability that the base construction company did not bid:
\(\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}\)
Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.
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Help finding angle 1,2,3
Answers
2= 52
3=65
I think but idrk
20 points for who ever get it right someone who knows what they doing please
Answers
Answer:
F is greater than 25
F is positive
Step-by-step explanation:
You know that F must be positive, since a number is subtracted from it and then another number is multiplied by that difference. Since a positive number multiplied by a negative number is negative, F must be positive.
You also know that F is greater than 25, because a number is subtracted from it and it is multiplied by a fraction between 0 and 1, meaning that that difference is further reduced.
Hope this helps!
The sum of two rational numbers is 4. If one of the numbers is 2/3, then what is the other number
Answers
Answer:
10/3
Step-by-step explanation:
Let x be the value of the second rational number. The first rational number is 2/3, and we are told that the sum of these numbers is 4:
x + 2/3 = 4
Therefore:
x + 2/3 = 4
x = 4 - 2/3
x = 12/3 - 2/3
x = (10/3)
Mr. Wise is ordering a set of books for his class. Each book costs $6. There is a flat shipping fee of $5. The table below shows the relationship between the total cost, c, and the number of books, b. Fill in the blanks to complete the table. Number of Book, b 2 [a] 6 [b] 10 Total Cost ($), c 17 29 [c] 53 65
Answers
Filling the table to show the relationship between the total cost, c, and the number of books ordered is as follows:
Number of Books Total Cost ($)
2 $17 ($6 x 2 + $5)
6 $41 ($6 x 6 + $5)
10 $65 ($6 x 2 + $5)
What is the total cost?The total cost is a function of the number of units and the variable cost per unit plus the fixed costs.
For instance, the total cost of 9 books, in this scenario, is $59 ($6 x 9 + $5).
Data and Calculations:Cost per book = $6
Shipping fee = $5
Number of Books Total Cost ($)
2 $17 ($6 x 2 + $5)
6 $41 ($6 x 6 + $5)
10 $65 ($6 x 2 + $5)
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\(-2\leq 3x+1\)
Answers
Answer:
\(x\geq -1\)
Step-by-step explanation:
![[tex]-2\leq 3x+1[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/KO4tTGPgkI4uI2Fj7im84TMqlIMRvntB.png)
I dont know pls help me
Answers
In Close Encounters of a Bear Kind, the statement that represents the author's primary attitude towards John's work is that C. John's work is dangerous.
How to illustrate the information?According to the author, he stated that people don't usually realize that bears
can be very dangerous.
He further stated that they will reap people apart of they e the chance. The narrator gave an example about how he walked out at night and had to run back home for his dear life. This was why he stated that the job of John whom was a photographer was a dangerous one.
In conclusion, the correct option is C.
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What is the range in the following data? 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4 Your Answer:
Answers
The range or the given data is calculated as 10.2 . Range is the difference between minimum value and maximum value.
To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we can make use of the formula for range in statistics which is given as follows:[\large Range = Maximum\ Value - Minimum\ Value\]
To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we need to arrange the data in either ascending or descending order, but since we only need to find the range, it is not necessary to arrange the data.
From the data given above, we can easily identify the minimum value and maximum value and then find the difference to get the range.
So, Minimum Value = 1.0
Maximum Value = 11.2
Range = Maximum Value - Minimum Value
= 11.2 - 1.0
= 10.2
Therefore, the range of the given data is 10.2.
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