Solve By The Laplace Transform Of Y(T), If Y(T) Satisfies The Following Equation. G(T)+ Y(T) Cosh(T – T)Dt = T +Et
Answers
To solve the given differential equation using Laplace transform, we first take the Laplace transform of both sides with respect to t:
L[G(t)] + L[Y(t) cosh(t-T)] = L[t] + L[E(t)]
where L denotes the Laplace transform operator.
Using the properties of Laplace transform, we have:
L[G(t)] = G(s) (where s is the Laplace variable)
L[Y(t) cosh(t-T)] = Y(s) * L[cosh(t-T)] = Y(s) * [s/(s^2-1)]
L[t] = 1/s^2
L[E(t)] = E(s)
Substituting these values into the equation and solving for Y(s), we get:
Y(s) * [s/(s^2-1)] + G(s) = 1/s^2 + E(s)
Y(s) = [1/s^2 + E(s) - G(s)] * [(s^2-1)/s]
To obtain the solution in the time domain, we use partial fraction decomposition and inverse Laplace transform:
Y(s) = [A/s + B/s^2 + C/(s+1) + D/(s-1)]
where A = lim(s->0) sY(s), B = lim(s->0) ds/dt[Y(s)], C = Y(-1), D = Y(1).
After finding the values of A, B, C, and D, we can write the solution in the time domain as:
Y(t) = A + Bt + Ce^(-t) + De^(t)
where e^(-t) and e^(t) are the inverse Laplace transforms of 1/(s+1) and 1/(s-1), respectively.
Note that the Laplace transform solution assumes that the initial conditions are zero. If there are non-zero initial conditions, they need to be incorporated into the solution.
Related Questions
am I right for part A. And please help me with B
Answers
a) The radius of the sphere is given as follows: 27.13 ft.
b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.
How to obtain the surface area?The surface area for a sphere of radius r is given by the equation presented as follows:
S = 4πr².
The surface area for this problem is given as follows:
9244 ft².
Hence the radius is given as follows:
\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)
r = 27.13 ft.
More can be learned about the surface area of a sphere at https://brainly.com/question/32375678
#SPJ1
How many significant figures will the answer to the following problem have?You do not have to solve the problem.532.1*101
Answers
Find the number of significant figures of the given problem:
\(532.1\times101\)Number of significant figures in 532.1 is 4.
Number of significant figures in 101 is 3.
Since, the smallest number of significant figures in any number in the problem determines the number of significant figures as the answer.
Hence, the answer is 3.
What is the formula for net cost price
Answers
Answer:
Hope this helps lol !
Step-by-step explanation:
This is how to calculate net price. Start with the list price and add any taxes and other government-mandated charges. Then subtract any discounts, negotiated prices. The result you get will be the net price.
Roger and his sister started watching a cartoon movie at 2:45 P.M. The movie was 2 hours and 15 minutes long. After the movie, they played a card game for 45 minutes and then played soccer in the backyard for 2 hours and 30 minutes. What time was it when Roger and his sister finished playing soccer?
Answers
Answer:
08:15 pm
Step-by-step explanation:
2:45 + 2:15 + 0:45 + 2:30
=8:15
Does anyone know this answer??
Answers
Approximately 99.7% of scores lie in the shaded region.
We have,
The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.
According to this rule:
Approximately 68% of scores lie within 1 standard deviation of the mean.
Approximately 95% of scores lie within 2 standard deviations of the mean.
Approximately 99.7% of scores lie within 3 standard deviations of the mean.
Now,
In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.
This encompasses the area within 3 standard deviations of the mean.
And,
Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.
Therefore,
Approximately 99.7% of scores lie in the shaded region.
Learn more about normal distribution here:
https://brainly.com/question/31327019
#SPJ1
Angle between two lines What is the size of the angle between the two lines 3x-2y+1=0 and x-3y=0 (answer in degrees and minutes)
Answers
Answer:
hiiiiiiiiiiiiiiiiiiiiiiiiii
Please help is due tonight
Answers
The linear function that has the greatest initial value is Function C.
Function B has the greatest rate of change.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Function A:
The initial value is o.
f(0) = 0
The rate of change.
= (f(4) - f(2)) / 4 - 2
= (10 - 5) / 2
= 5/2
= 2.5
Function B:
The initial value is
y = 3x - 1
y = 3 x 0 - 1 = 0 - 1 = -1
Let y = f(x)
The rate of change.
= (f(2) - f(1)) / (2 - 1)
= (5 - 2) / 1
= 3
Function C:
The initial value is 2.
(0, 2) is considered as when x = 0, y = 2.
Take two coordinates from the graph.
(3, 3) and (6, 4)
The rate of change.
= (4 - 3) / (6 - 3)
= 1/3
= 0.33
Thus,
Function C has the greatest initial value.
Function B has the greatest rate of change.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
pls help help help help
Answers
Answer:
D
Step-by-step explanation:
We can plug in the numbers (15, 23, 25, 38, 53) into the equation for x, and see if we get the values given for the number of hits (4, 12, 14, 27, 47)
Please only answer if u actually know pls!
Answers
At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.
To find the total revenue at each price, we can multiply the price by the corresponding quantity.
Price Quantity Total Revenue
$6 0 $0
$5 1 $5
$4 2 $8
$3 3 $9
$2 4 $8
$1 5 $5
To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.
In this case, the highest total revenue is $9, which occurs when the price is $3.
At a price of $3, the company will sell 3 units (as indicated in the Quantity column).
To learn more on Revenue click:
https://brainly.com/question/14952769
#SPJ1
With a discount of 60 percent, the cost of a bracelet is $17.99. What is the price before the discount
Answers
28.78
Explanation:
If you want to save your total contribution for all 4 years before you start attending college, how much do you need to save each month if you have 4 years to accomplish your goal?
Answers
The solution is:
If my parents are going to pay the 5%, then, they will pay: $2979.
I will need to save $62.06 each month to accomplish my goal.
Here,
I'm going to a 4-year college that will cost $14895/year.
It means that I will need to pay: 14895*4 = $59.580
If my parents are going to pay the 5%, then, they will pay: $2979.
Now, if I want to save my total contribution for all four years, and I have four years to accomplish the goal, then:
Then, if I have 4 years to pay it. It means I have 4*12 = 48 months.
Then I will need to save $2979./48 = $62.06 each month to accomplish my goal.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ1
complete question:
You are going to a 4-year college in 4 years that will cost $14,895.00/yr. Your parents expect you to pay 5% of the total cost.
How much do you need to pay for each year of attending?
If you want to save your total contribution for all four years before you start attending college, how much do you need to save each month if you have four years to accomplish your goal?
There are 26 boys and 20 girls in a class.
The boys and the girls have some counters.
The mean number of counters that the boys have is 28.
The mean number of counters that the girls have is 19.
Work out the mean number of counters the 46 children have.
Answers
Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.
What is the mean?The mean refers to the average value.
The average is the quotient of the total value divided by the number of items in the data set.
The number of boys in the class = 26
The number of girls in the class = 20
The total number of boys and girls in the class = 46
The mean number of counters that the boys have = 28
The total number of counters that the boys have = 728 (28 x 26)
The mean number of counters that the girls have =19
The total number of counters that the girls have = 380 (19 x 20)
The total number of counters that the class has = 1,108 (728 + 380)
The average or mean number of counters in the class = 24 (1,108 ÷ 46)
Learn more about the average at https://brainly.com/question/130657.
#SPJ1
4.
If 75 persons can perform a piece of work in 12 days of 10 hours, how many men will
perform a piece of work twice as great in tenth part of time, if they work the same
number of hours a day, supposing that two of the second set can do as much work as
three of the first set?
1
n.1.1
Answers
Answer: dont know
Step-by-step explanation:
NO LINKS OR FILES THINGS LIKE THAT!!!!!!
DUE TODAY!!!!!!
Write format:
(Quarters,Dimes)
No spaces
Example:
5 quarters, and 2 dimes should be written as (5,2)
Answers
Answer:
(4,8)
Step-by-step explanation:
One of the marked points on the black line is (4,8).
__
You will notice that the only combination worth $3.00 is (12,0).
A 12-ounce soda can has a height of 4.875 inches. What is its average diameter in
inches?
8 ounces = 1 cup, 16 cups = 1 gallon,
7.48 gallons = 1 ft3, 1 foot = 12 inches.
Answers
The average diameter of a can in inches is 2.4 inches.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, a 12-ounce soda can has a height of 4.875 inches.
We know that, 1 ounce = 1.805 cubic inches
Here, 12 ounce = 21.6563 cubic inches
As we know, volume of cylinder is πr²h.
Now, 21.6563 = 3.14×r²×4.875
21.6563 =r²×15.3075
r²=21.6563/15.3075
r²=1.414
r=1.2 inches
Then, diameter = 2.4 inches
Therefore, the average diameter of a can in inches is 2.4 inches.
To learn more about the volume visit:
https://brainly.com/question/13338592.
#SPJ1
what is the correct evaluation of 15-3x, when x is equal to -2?
-15
21
15
-21
Answers
Answer:
Step-by-step explanation:
15-3x
15-3(-2)
15+6
21
Answer:
21 is the correct answer
in how many ways can a family of four be seated at a round table if two brothers must sit together a)1 b)8 c)2 d)4
Answers
Answer:
8
Step-by-step explanation:
i think this is right if not it would be 2
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer:
C
Step-by-step explanation:
cot²θ = 1/tan²θ
plug this in to get
1/(1/tan²θ + 1)
1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ
we then have
1/((1+tan²θ)/tan²θ)
1/(x/y) = y/x, so this is equal to
tan²θ/(1+tan²θ)
tan²θ = sin²θ/cos²θ, so plug this in to get
(sin²θ/cos²θ)/(1+sin²θ/cos²θ)
1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ
sin²θ + cos²θ = 1, so we have
(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get
(sin²θ/cos²θ)/(1/cos²θ)
(a/b)/(c/d) = (d/c) * (a/b), so we have
(sin²θ/cos²θ)/(1/cos²θ) = cos²θ/1 * sin²θ/cos²θ = sin²θ
An athlete runs 3 mi in 24 min. Is the rate of this athlete greater than, less than, or equal to the rate of an athlete who runs 4 mi in 33 min?
Answers
The rate of the first athlete is greater than the rate of the second athlete.
To determine if the rate of the first athlete is greater than, less than, or equal to the rate of the second athlete, we need to compare their average speeds.
The average speed of an athlete is calculated by dividing the distance traveled by the time taken.
For the first athlete who runs 3 miles in 24 minutes, the average speed can be calculated as:
Speed1 = Distance1 / Time1 = 3 miles / 24 minutes = 1/8 miles per minute.
For the second athlete who runs 4 miles in 33 minutes, the average speed can be calculated as:
Speed2 = Distance2 / Time2 = 4 miles / 33 minutes.
To make a comparison, we need to convert both rates to a common unit. Let's convert both rates to miles per minute:
Speed2 =\((4 miles / 33 minutes) * (24 minutes / 24 minutes)\) = (96 miles / 792 minutes) ≈ 0.1212 miles per minute.
Comparing the two rates, we see that Speed1 (1/8 miles per minute) is greater than Speed2 (0.1212 miles per minute). The rate of the first athlete is greater than the rate of the second athlete.
For more such questions on rate
https://brainly.com/question/119866
#SPJ8
825 use each digit once. make the smallest 3digit number
Answers
Step-by-step explanation:
Given: To make smallest 3-digit number of 825.
To find: The smallest 3-digit number of 825.
Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...
Final answer: The smallest 3-digit number of 825 is 258.
hope it helps
Answer:
258
Step-by-step explanation:
We are given 3 numbers:
8 2 5
And we are asked to find the smallest 3 digit number using those 3 digits above.
To make the smallest number, place the numbers in value from least to greatest:
2 5 8
This is your 3 digit number: 258.
Hope this helps! :)
A salesperson earns a commission of $322 for selling $2300 in merchandise.
Find the commission rate. Write your answer as a percentage.
Answers
The commission rate for the given amount will be 14%.
What is the percentage?According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.
To find the commission rate, we need to divide the commission earned by the amount of merchandise sold, and then express the result as a percentage.
The commission rate is given by:
Commission rate = (commission earned / amount of merchandise sold) x 100%
Substituting the given values, we get:
Commission rate = (322 / 2300) x 100%
Commission rate ≈ 0.14 x 100%
Commission rate ≈ 14%
Therefore, the commission rate is 14%.
To know more about the percentage follow
https://brainly.com/question/21290758
#SPJ2
Find the slope of the line graphed below.
Answers
Answer:-3 over 7
Step-by-step explanation:
rise over run
Explain how to translate the phrase into an algebraic
expression
a number squared decreased by ten
Answers
Answer:
I think the answer is 1^2 - 10
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of -2,-1, and 5, and a y-intercept of -10.
Answers
Answer:
y = x³ -2x² -13x -10
Step-by-step explanation:
You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.
Polynomial factorsA polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...
p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)
Expanding this gives ...
p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10
This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.
The polynomial function is ...
y = x³ -2x² -13x -10
si ABCD son los vertices de un cuadrado y A(2,2) y C (10,8) 2 vertices opuestos. Hallar los otros dos vertices, dar como respuesta la mayor de las ordenadas
Answers
The area of the square is given as 100 square unit
How to determine the area of square?You should be aware that the square has all its sides equal
The perpendicular from opposite vertices represent distance
The given vertices are
(2,2) and (10,8)
Using the formula for distance between two points
d=√(10-2)²+(8-2)²
d=√8²+6²
d = √64+36
d=√100
This implies that d=10
The area of a square is given as s²
Area = 10²
Atrea = 100 square units
In conclusion, the area of the square is 100 square units
Learn more about area of square on https://brainly.com/question/27683633
#SPJ1
Translated question:
The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square
The exchange rate for US dollars to Canadian dollars is 0.77. What is value of 200 US dollars?
Answers
The value of 200 US dollars into canadian dollars is 259.74
What is an example of a unitary method?
A single or unique unit is referenced to using the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
Given That:
1 Canadian dollar is = 0.77 US dollar
So 1 US dollar is = 1/0.77 canadian dollar
So 200 US dollar is = 1/0.77 * 200 = 259.74 canadian dollar
Hence the answer is 259.74 dollar
Learn more about unitary method at
brainly.com/question/19359186
#SPJ1
If the the price of a pair of shoes is 35$ before tax and the tax is 20% what will the final price of the shoes be
Answers
Answer:
$42
Step-by-step explanation:
You want the price with tax of a $35 pair of shoes subject to a 20% tax.
Price with taxThe tax is the cost of the shoes multiplied by the tax rate. The final price is the sum of the cost of the shoes and the tax:
final price = price + price × tax rate
final price = price × (1 + tax rate) = $35 × 1.20 = $42
The final price of the shoes is $42.
Answer:
42$
Step-by-step explanation:
tax increase will be
20% of 35$
= 20/100 × 35
= 7$
Final price = Old price + Tax
= 35 + 7
= 42$
identify the relationship that does not represent a direct variation
Answers
Remember that
In a direct variation
we have an equation of the form
y=kx
where
k is the constant of proportionality o slope of the linear equation
so
Verify each table
N 1
Find out the value of k
k=y/x
(5,1) ----> k=1/5
(7,2) ----> k=2/7
the values of k are not equal
that means
not represent a direct variation
N2
(6,3) -----> k=3/6=1/2
(12,6) -----> k=6/12=1/2
(18,9) ----> k=9/18=1/2
the values of k are the same
so
represent a direct variation
N 3
(2,10) -----> k=10/2=5
(4,20) ----> k=20/4=5
(8,40) ----> k=40/8=5
the values of k are the same
so
represent a direct variation
N 4
(4,2) ----> k=2/4=1/2
(8,4) -----> k=4/8=1/2
(12,6) ----> k=6/12=1/2
the values of k are the same
so
represent a direct variation
therefore
the first table does not represent a direct variationFind the measure of the indicated angle.
Answers
Answer:
I believe it could be 25
Step-by-step explanation:
Eight angle = 90
1. 38 + 27 = 65
2. 90 - 65 = 25
I haven't done angles for a long time, but I hope my memories serves well. Sorry if it may be wrong, but this is what I remember from doing angles in Year 7
3. The fuel economy of a car, measured in miles per gallon, is modeled by the function f(s) = -0.009s² +0.699s +12 where s represents the speed of the car, measured in miles per hour. What's the fuel economy of the car when it
travels at an average of 20 miles an hour?
O A. 20 miles per gallon
O B. 26.63 miles per gallon
4
O C.-10.02 miles per gallon"
O D. 22.38 miles per gallon
O Mark for review (Will be highlighted on the review page)
Answers
Answer:
The Answer Will Be D
Step-by-step explanation:
The fuel economy of a car is modeled by the function f(s) = -0.009s² +0.699s +12 where s represents the speed of the car, measured in miles per hour.We need to find the fuel economy of the car when it travels at an average of 20 miles an hour.f(20) = -0.009(20)² +0.699(20) +12f(20) = -0.009(400) +13.98f(20) = 9.6The fuel economy of the car when it travels at an average of 20 miles an hour is 9.6 miles per gallon.Therefore, the answer is option D. 22.38 miles per gallon.