The solution to the initial value problem is:
y(t) = 3t - cos(3t) + y(0)cos(3t) + y'(0)sin(3t)/3
To solve the initial value problem:
y'' + 9y = 9 + 3t
We can use the Laplace transform, which is a mathematical tool that transforms a function from the time domain to the complex frequency domain.
Taking the Laplace transform of both sides, we have:
[tex]s^2 Y(s) - s y(0) - y'(0) + 9Y(s) = 9/s + 3/s^2[/tex]
where y(0) and y'(0) are the initial conditions for y(t).
Rearranging terms and simplifying, we get:
[tex]Y(s) = [9/s + 3/s^2 + s y(0) + y'(0)] / (s^2 + 9)[/tex]
Now, we need to find the inverse Laplace transform of Y(s) to obtain the solution y(t).
We can do this using partial fraction decomposition and standard Laplace transform table:
[tex]Y(s) = [9/s + 3/s^2 + s y(0) + y'(0)] / (s^2 + 9)[/tex]
[tex]= (3/s^2) + (9/(s(s^2 + 9))) + (s y(0) + y'(0))(1/(s^2 + 9))[/tex]
Taking the inverse Laplace transform of each term using the Laplace transform table, we get:
y(t) = 3t - 3cos(3t)/3 + y(0)cos(3t) + y'(0)sin(3t)/3.
For similar question on Laplace transform.
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To solve the initial value problem y'' + 9y = 9 + 3(t), we can use the Laplace transform. Taking the inverse Laplace transform, we get the solution y(t) = 3cos(3t) + 3t*sin(3t)/2 + y(0)cos(3t) + y'(0)sin(3t)/3. Therefore, the initial values y(0) and y'(0) determine the solution uniquely.
To solve the initial value problem y'' + 9y = 9 + 3t using the Laplace transform, follow these steps:
1. Take the Laplace transform of the entire equation: L{y''} + 9L{y} = L{9} + L{3t}.
2. Apply the Laplace properties to get: (s^2Y(s) - sy(0) - y'(0)) + 9Y(s) = 9(1/s) + 3(1/s^2).
3. Insert the initial values, assuming y(0) and y'(0) are both 0: (s^2Y(s)) + 9Y(s) = 9/s + 3/s^2.
4. Solve for Y(s): Y(s) = (9/s + 3/s^2) / (s^2 + 9).
5. Apply the inverse Laplace transform to find y(t): y(t) = L^{-1}{Y(s)}.
The final solution y(t) is obtained by performing the inverse Laplace transform on Y(s).
To learn more about Laplace transform click here : brainly.com/question/31987705
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What is another way of writing the following expression?
4 + 5 + 2
Answer:
2+4+5 or 5+4+2 it functions in all the ways Simce it is sum XD
Find the elapsed time.
from 2:08 A.M. to 11:03 A.M.
3 h 5 min
8 h 55 min
8 h 45 min
9 h 5 min
Subtract -2x^2-6x+10−2x^2+9.
Answer:
−4x^2−6x+19
Step-by-step explanation:
this should be right
If Maria makes $40 each day at her job, and she gets paid $20 for a training course
Answer:
Where is the rest of the question?
Step-by-step explanation:
40x +20
Type the correct answer in the box.
V12 V5
The value of V10 V6 is closest to the whole number
Answer:
the nearest whole number is one i took the test
Step-by-step explanation:
what is the factored form of -1/2(32x - 40) - (20x - 4)?
Answer:
12(-3x + 2)
Step-by-step explanation:
-1/2 ( 32x - 40) - (20x - 4) = -16x + 20 - 20x + 4 = -36x + 24 = 6(-6x + 4) = 12(-3x + 2)
Find the value of x
A. 5 square root 2/2
B 5
C 10
D 10 square root 2
Answer:
The answer is C
Step-by-step explanation:
That side with the 5 is equal to 7.071067812.... (irrational number)
To get x you need to use the equation a^2 + b^2 = c^2
A^2 and B^2 will both be the same thing. The red line indicates they are the exact same length.
7.071037812.... ^2 is 50
Now your equation would be 50+50= c^2 (which is the same as x^2)
100= c^2 is simplified by finding the square root of 100.
Your answer is 10 for side X because the square root of 100 is 10.
This problem was solved using the Pythagorean Theorem.
The hypotenuse x of the right triangle is (c) 10
Finding the hypotenuse, x of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where, we have
Leg a = 5√2
Leg b = 5√2
The hypotenuse of the right triangle can be calculated using the following Pythagoras theorem
h² = a² + b²
Using the above as a guide, we have the following:
x² = (5√2)² + (5√2)²
Evaluate
x² = 100
Take the square roots
x = 10
Hence, the hypotenuse of the right triangle is (c) 10
Read more about right triangle at
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Plss help (IF ITS BOTH OR NEITHER PLS TELL ME) Zoom in to see full pic!!
to find the missing length for the equation you would use b.
Can someone plz help me with these. Will chose Brainlist.
Answer:
19= 11
20= 33
21= 22
22= 38
23= 74.8
Step-by-step explanation: if it's correct can i get brainliest.... hopes this helps.
what are two numbers that share a product of -24 and a sum of 5
[tex] - 3 \: and \: 8[/tex]
//
[tex] - 3 + 8 = 5[/tex]
[tex] - 3 \times 8 = - 24[/tex]
Work out the values of a and b in the identity
4(9x + 11)+5(3x+b)
A=
B=
Answer:
=36x+44+15x+5bƩƩƩƩ
=51x+44+5b ƩƩƩƩƩ
!!!!!!Plss Help Me!!!!!!!
Write the problem as an equation:
5n <65
Solve for n by dividing both sides by 5:
n <13
Because the inequality does not contain an equal sign, n (13) is not included in the answer so there would be an open circle on the number 13
The correct answer would be A.
A child wants to fill up a box with snow he can only carry the box if it weighs under 30 pounds the dimensions of the box are 30in by 24 inches by 24 inches each cubic inch of snow weighs .004 pounds if the child fills the box entirely with snow will he be able to carry the box?
Answer:
As a rule of thumb, snow weighs approximately 20 pounds per cubic foot, or 1.25 pounds per inch of depth. Depending on moisture content, snow can weigh from 1 pound per cubic foot to over 21 pounds per cubic foot. NOTE: Any ice build-up on the roof would need to be added to this formula.
Step-by-step explanation:
Sam wants to make a sketch of the white house with a scale factor of 2 inches to 15 feet. She knows that the white house is about 85 feet wide and 152 feet long. What will the width and height of her model be?
Answer: The width of the model = 11.33 inches and the height of the model = 20.27 inches.
Step-by-step explanation:
Given: Scale factor: 2 inches in model = 15 feet in actual.
White house is about 85 feet wide and 152 feet long.
Width of model = [tex]\dfrac2{15}\times85=\dfrac{34}{3}=11.33\text{ inches}[/tex]
Height of model = [tex]\dfrac{2}{15}\times152\approx20.27\text{ inches}[/tex]
Hence, the width of the model = 11.33 inches and the height of the model = 20.27 inches.
Urgent please hell..
What is the value of Z?
Answer:
21
Step-by-step explanation:
Answer:
The first option is the answer
hola cual es la raiz cuadrada de √639+(393)
Answer:
393 + 39√6
Step-by-step explanation:
√639 + (393)
Simplify
393 + 39√6 (Answer)
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Solve the following system of equations graphically on the set of axes below.
y= 2x-2
y= -x+7
Answer:
x=y + 2
2
y=2(x - 1)
Step-by-step explanation:
y=2 x -2
swap sides so that all variable terms are on the left hand side
2x - 2 =y
add 2 to both sides
2x = + 2
Divide both sides by 2.
2 x = y + 2
2. 2
Dividing by 2 undoes the multiplication by 2.
x = y + 2
2
Divide y +2 by 2.
x = y + 1
2
Can somebody pls help me with problems 16 and 17? I’m in a rush...thx
A family of four bought 6 bags of peanuts to share equally. If
each bag contained 36 peanuts, how many did each family
member receive?
Answer:
54
Step-by-step explanation: 36 * 6 = 216
216 divided by 4 = 54
A five feet tall man casts a shadow rhat is 4 1/3 feet long. A telephone pole casts a shadow that is 25.5 feet long. How tall is the telephone pole in inches
Answer:
22.1 inches
Step-by-step explanation:
The shadow is formed at a specific factor of the original image hence if a 5 feet tall man casts a shadow rhat is 4 1/3 feet long then a telephone pole casts a shadow that is 25.5 feet long must have a length
5 / 4 1/3 = x / 25.5
where x is the length of the pole
5 / 13/3 = x/ 25.5
15/13 = x/25.5
cross multiply
15 * x = 13 * 25.5
Divide both sides by 15
x = 13 * 25.5 / 15
x = 22.1 inches
The telephone pole in inches is 22.1 long
A flying squirrel lives in a nest that is 9 meters high in a tree. To reach a fallen acorn that is 4 meters from the base of the tree, how far will the flying squirrel have to glide? If necessary, round to the nearest tenth.
Answer:
Flying squirrel have to glide is for 9.8 meters approximately.
Step-by-step explanation:
Here we can use Pythagoras theorem.
Height is 9 , base is 4.
We need to find the hypotenuse measure.
So, let's use Pythagoras theorem [tex]a^{2} +b^{2}= c^{2}[/tex]
Plug in a as 9 and b 4.
[tex]9^{2} +4^{2}=c^{2}[/tex]
Simplify the left side of the equation
[tex]81+16=c^{2}[/tex]
[tex]97=c^{2}[/tex]
Take square root on both sides.
c=9.8 meters.
Sam is saving for a guitar. He already has $50 saved and intends to save $30 each week. Sam found a guitar that costs $410. After how many weeks will Sam have saved enough money to buy the guitar?
Answer:
12 weeks
Step-by-step explanation:
30 x 12 = 360
which equals 12 weeks in this case and 360 + 50 equals 410 the 50 came from the 50 he already had
I hope this helps!!
A 12-inch diameter pizza has 22 calories per square inch.
About how many calories are in the entire pizza?
Use 3.14 for pi.
Select from the drop-down menu to correctly complete the statement.
There are about
Choose...
calories in the pizza. optains : 264, 414, 2487, 9948
Answer:
2486.88
Step-by-step explanation:
Find the area of the pizza. A=πr²
the radius is half the diameter so here it's 6.
A= π6²
6²=36
36 × 3.14= 113.04
the pizza is 113.04 in². multiply that by 22.
Answer:
2487
Step-by-step explanation:
This is correct for k12 people
Jean needs 2 gallons of olive oil to make a recipe. If the olive oil 8:00 a quart how much money will she need to buy the olive oil
Answer:
$64
Step-by-step explanation:
Given that :
Required amount of olive oil = 2 gallons
Cost per quartz = $8
Recall:
1 quartz = 0.25 gallons
Amount of quartz in 2 gallons :
2 / 0.25 = 8 quartz
Cost of olive oil needed :
8 quartz * $8
= $64
I GIVE BRAINIEST
Can someone help me with questions 4,5, and 6? pls show all work pls.
Answer:
4. 3,4
5. 0,4
6. -8, -1
Hope that helps!
Step-by-step explanation:
How do I expand this
Step-by-step explanation:
We have
[tex](sc^2x-1)^2[/tex]
Which is the same as
[tex](sc^2x-1)(sc^2x-1)[/tex]
To expand this polynomial, we can use the FOIL method. Meaning that we multiply the Fronts, Outsides, Insides, and Lasts together and then add each of these products.
The two fronts are [tex]sc^2x[/tex] and [tex]sc^2x[/tex],
[tex](sc^2x )(sc^2x )=s^2c^4x^2[/tex]
The two Outsides are [tex]sc^2x[/tex] and [tex]-1[/tex],
[tex](sc^2x )(-1)=-sc^2x[/tex]
The two Insides are [tex]-1[/tex] and [tex]sc^2x[/tex],
[tex](-1)(sc^2x )=-sc^2x[/tex]
The two lasts are [tex]-1[/tex] and [tex]-1[/tex],
[tex](-1)(-1)=1[/tex]
Now we just need to add these together to get
[tex]s^2c^4x^2-sc^2x-sc^2x+1\\\\s^2c^4x^2-2sc^2x+1[/tex]
Answer:
[tex]cot^{4} x[/tex]
Step-by-step explanation:
graph the line please help
This is for one person (you know who you are) lol
Answer:
Nope...
Step-by-step explanation:
Check out my profile for [tex]incredible \lim_{n \to \infty} a_n[/tex] answers!
Answer:
Step-by-step explanation:
S+f=24 s=3f
I need this now
Answer:
f=6 and s=18
Step-by-step explanation:
Let's solve your system by substitution.
s+f=24;s=3f
Rewrite equations:
s=3f;f+s=24
Step: Solves=3ffor s:
s=3f
Step: Substitute3fforsinf+s=24:
f+s=24
f+3f=24
4f=24(Simplify both sides of the equation)
4f
4
=
24
4
(Divide both sides by 4)
f=6
Step: Substitute6forfins=3f:
s=3f
s=(3)(6)
s=18(Simplify both sides of the equation)
Answer:
f=6 and s=18