The solutuion to the given differntial equation is: f(t) = -1/4 e^(2t) + t e^(2t) + 3/4 sin(t)
How can we factor the denominator of the fraction?ℒ{f(t)}(s) = 1/(s^2 - 4s + 5)
We can factor the denominator of the fraction to obtain:
s^2 - 4s + 5 = (s - 2)^2 + 1
Using the partial fraction decomposition, we can write:
1/(s^2 - 4s + 5) = A/(s - 2) + B/(s - 2)^2 + C/(s^2 + 1)
Multiplying both sides by the denominator (s^2 - 4s + 5), we get:
1 = A(s - 2)(s^2 + 1) + B(s^2 + 1) + C(s - 2)^2
Setting s = 2, we get:
1 = B
Setting s = 0, we get:
1 = A(2)(1) + B(1) + C(2)^2
1 = 2A + B + 4C
Setting s = 1, we get:
1 = A(-1)(2) + B(1) + C(1 - 2)^2
1 = -2A + B + C
Solving this system of equations, we get:
A = -1/4
B = 1
C = 3/4
Therefore,
1/(s^2 - 4s + 5) = -1/4/(s - 2) + 1/(s - 2)^2 + 3/4/(s^2 + 1)
Taking the inverse Laplace transform of both sides, we get:
f(t) = -1/4 e^(2t) + t e^(2t) + 3/4 sin(t)
Therefore, the solution to the given differential equation is:
f(t) = -1/4 e^(2t) + t e^(2t) + 3/4 sin(t)
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What is the length of AB?
Answer: 6 units
Step-by-step explanation:
I know that in a triangle, there's two angles that have equal measures, then the sides opposite to them are equal in length. Thus, the length of side AB is 6 units.
Answer:
AB = 38.64 m
Step-by-step explanation:
[tex] \cos \: 75 \degree = \frac{10}{x} \\ \\ x = \frac{10}{ \cos \: 75 \degree } \\ \\ x = 38.637033052 \\ \\ x \approx \: 38.64[/tex]
AB = 38.64 m
choose the graph that solves system of equations.y=2x-6 y=-4x+3
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
HELP please can you answer this please
Answer:
1. 2x² - 8x - 7
2. x³+ x + 30
Step-by-step explanation:
[tex]2 {x}^{2} - 9x - 2 +x - 5[/tex]
[tex]2 {x}^{2} - 8x - 7[/tex]
2x² has no other like terms to add or substract with so it stays as is.
(-9x) + x = -8
(-2) - 5 = -7
or
(-2) - (-5) = 3
Watch out for the ones on top. I'm a bit confused about them but those ones are your possible options.
//
[tex] {x}^{3} + 27 + x + 3[/tex]
[tex] {x}^{3} + x + 30[/tex]
x³ stays as is and so does x.
27 + 3 = 30
Need help ASAP
Thankss + BRAINLIST only for correct answer
Answer:
(2, 0)
Step-by-step explanation:
Given the simultaneous equation
2x-y = 4
3x+y = 6
Add both equation
2x+3x = 4 + 6
5x = 10
x = 10/5
x = 2
Substitute x = 2 into equation 1
From1 ;
2x-y = 4
2(2) - y = 4
4 - y = 4
y = 4-4
y = 0
Hence the solution to the system of equation is (2, 0)
What is the value of x?
Answer:
x = 22
Step-by-step explanation:
hope I helped!!
Need help with the rule transformation
[tex]T(x,y)=(x+3,y-2)[/tex]
Hope this helps.
At 6:00 A.M., the temperature was 10º below zero. During the day, the temperature rose an average of 2º per hour. If h represents the number of hours since 6:00 A.M., which equation represents the temperature T?
Answer:
t=-10+2h
Step-by-step explanation:
Ashley and Carmen are both saving money for college. They each deposit a constant amount from their paychecks into their savings accounts. Which girl saves more money per paycheck? Explain how you know.
You have to use slopes
A rectangular path 60m and 3m is covered with square tiles of 25 cm. How many tiles wil be used to cover the path ?
Answer:
2880 tiles
Step-by-step explanation:
A rectangular path has dimensions 60 m and 3 m.
Area of a rectangular path = length × breadth = 60 × 3 = 180 [tex]m^2[/tex]
Use [tex]1\,m^2=10000\,cm^2[/tex]
So,
Area of a rectangular path = 180(10000) = 18,00,000 [tex]cm^2[/tex]
Side of a square tile = 25 cm
Area of a square tile = side × side = 25(25) = 625 [tex]cm^2[/tex]
Number of square tiles = Area of a rectangular path ÷ Area of a square tile
= [tex]\frac{1800000}{625} =2880[/tex] tiles
what is the slope intercept form
Answer:
5.8
Step-by-step explanation:
5.8 is the correction
angles
B
D
The AAS Triangle Congruence sch
Theorem can be used to show that ABE CDE
Choose...
Vertical Angles
Alternate Interior Angles
AAS Triangle Congruence
SSS Triangle Congruence
Answer:
Using the right angles, we can establish AAS making the triangles congruent. Or using the Pythagorean Theorem, we can find the missing side, and then use SSS, SAS, or ASA to make the triangles congruent.
Step-by-step explanation:
X+ 6
X+ 3
=
x + 2
x-5
a.
I = x
c.
X= -9
b.
S = x
d. x= -8
Step-by-step explanation:
x+6/x+2=x+3/x-5 x<>2 and x<>5
(x+6)(x-5)=(x+3)(x+2)
x2-5x+6x-30=x2+2x+3x+6
-5x+6x-30=2x+3x+6
x-30=5x+6
x-5x=6+30
-4x=36
x=-9
Note* x2=x in the power of 2
HELP PLS I WILL GIVE BRIANLY!
The students will paint 4 rooms on the first floor and the conference room on the second floor. Each room on the first-floor room is 4m x 5m.
1. Calculate the area of one of the rooms.
Answer:
20m
Step-by-step explanation:
The rooms are 4m x 5m.
To find the area, multiply length by width: 4*5=20
The Area of one room is 20 m².
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
Given:
First, Area of one room= lw
= 4 x 5
= 20 m²
Now, Area of four room = 4 x 20
= 80 m²
Thus, area of one room is 20 m².
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HELP ASAP
Will GUVE BRAINLIEST!!
Jayla and Brian are both selling cookie dough for a fundraiser. Although, Jayla has already sold 4 tubs, brian haven’t sold any yet. If jayla starts selling 1 Tun per day and brian begins selling 2 tubs per days, they will eventually sell the same amount of cookie dough, how many days will that take?
Write the expression. And solutions written as an ordered pair.
Answer:
cookie dough fundraiser is a great way to raise money for your school, team, ... selling large or small cookie dough tubs, or pre-portioned cookie dough trays.
Answer:
4 days
Step-by-step explanation:
If we say d = number of days passed, j = tubs sold by jayla and b = tubs sold by brian
j = 4 + d
because when d = 0 j must equal 4, then it goes up by 1 each day
b = 2d
because when d = 0 b must be 0, then it goes up by 2 each day
set them to be equal and solve for d
4 + d = 2d
d = 4
so after 4 days they sell the same amount which is 8
If we solve h(x) = 36, one of the possible values of x is 1
What is the other possible value of x?
Answer:
Step-by-step explanation:
(x+5)² = 36
x+ 5 = ±√36 = ±6
x = -5 ±6 = 1, -11
9) 5xy+10x ??????????????????
Answer:
5x(y+2)
Step-by-step explanation:
Answer:
You cannot add them because they both don't have the same like terms.
But if you just straight out add your answer would either be 15xy or just 15x
Step-by-step explanation:
Sorry hope this helped in someway
15 metre long ladder reached the a window 12 metre height from the ground and placing it against a wall and distance a find the distance of photo of the letter from the wall
Answer:
this is the answer of the required questions
thank you
please Mark this as brainlist answer
The number of branches of an oak tree and a birch tree since 1950 are represented by the following tables:
Determine whether the data described in the tables is best modeled by a linear function or an exponential function
Answer:
oak tree is a linear function and birch tree is exponential
Step-by-step explanation:
cuz i just did it
The oak tree have a liner function and the birch tree have exponential function .
What is linear function?Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
What is exponential function?An exponential function is a mathematical function of the following form:
f ( x ) = [tex]a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
According to the question
The number of branches of an oak tree and a birch tree since 1950 are represented by the following tables:
Number of Oak trees (x) Number of branches f(x)
0 34
3 46
6 59
9 70
12 82
So in this table we can see that there is increment in number of branches but in a pattern approx.
i.e
f(x) = 34 + 4(x)
where x will be Number of Oak trees
therefore it is a Linear function
Number of Birch trees (x) Number of branches f(x)
0 8
10 33
20 128
30 512
40 2049
So , in this table is increasing in a very fast pace but in a pattern approx.
i.e
f(x) = [tex]8*4^{\frac{x}{10} }[/tex]
Therefore it is an exponential function
Hence, The oak tree have a liner function and the birch tree have exponential function .
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Michael is going to invest in an account paying an interest rate of 5.8% compounded
monthly. How much would Michael need to invest, to the nearest dollar, for the value
of the account to reach $260 in 12 years?
Answer:
P=130
Step-by-step explanation:
Record sales are increasing by 5% each year. If 800,000 records were sold this year, what will annual sales be in 3 years?
Answer:
120000
Step-by-step explanation:
There are 50 students in a class and their annual result is presented in the following table:
Result
fail , 7 students
pass, 43 students
If a student is selected at random find the probability that the student has passed the examination.
factors of -135 that equal to -7
Answer:
Need more information.
Step-by-step explanation:
3(x+5)+3(x+5) help! Please
Answer:
=6x+30
Step-by-step explanation:
happy to help ya :)
What is the NPV of (x-5)
I’ll mark branliest!
2. Lindsay is financing $350,000 to purchase a house. How much money will she save over the life of a 30-
year, fixed-rate loan by buying 3 points with a rate of 6.375% instead of not buying points with a rate of
6.75%?
A. $2,596.50
B. $13,096.50
C. $20,658.00
D. $31,158.00
Answer:
D
Step-by-step explanation:
How to solve this system of equations?
y = 7x + 10
y = -4x - 23
x=
y=
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Answer:
x = - 3, y = - 11
Step-by-step explanation:
Given the 2 equations
y = 7x + 10 → (1)
y = - 4x - 23 → (2)
Substitute y = 7x + 10 into (2)
7x + 10 = - 4x - 23 ( add 4x to both sides )
11x + 10 = - 23 ( subtract 10 from both sides )
11x = - 33 ( divide both sides by 11 )
x = - 3
Substitute x = - 3 into either of the 2 equations and evaluate for y
Substituting into (1)
y = 7(- 3) + 10 = - 21 + 10 = - 11
9 - x < -11 lololol help
Answer:
Hey! Your answer is , x >20
Step-by-step explanation:
Hope this helps! :)
Have a nice day!
please help
How are transformations related to congruence?
Answer:
Congruence transformations
transformations that are performed on an object that can create a congruent object
Kevin can travel 24 1 4miles in 1 3hour. What is his average speed in miles per hour?
Answer:
The answer is about 331 miles.
Step-by-step explanation:
I took the test and the answer is correct <3!
Answer:
deeznuts
Step-by-step explanation:
ha got tem
The graph shows a function. Is the function linker or non linear?
Answer:
It is linear since it is a straight line.