The solution to the given initial value problem is y(t) = -e^(8t) + e^(9t)u(t-1).
To solve the given initial value problem using the Laplace transform, we first take the Laplace transform of both sides of the differential equation:
L[y''(t)] - 17L[y'(t)] + 72L[y(t)] = L[scripted capital u(t-1)]
Using the property L[derivatives of y(t)] = sY(s) - y(0) - y'(0)s and L[scripted capital u(t-a)] = e^(-as)/s, we get:
s^2 Y(s) - sy(0) - y'(0) - 17sY(s) + 17y(0) + 72Y(s) = e^(-s)/s
Substituting y(0) = 0 and y'(0) = 1, we simplify and solve for Y(s):
Y(s) = 1/(s-9)(s-8)
Using partial fraction decomposition, we can write Y(s) as:
Y(s) = -1/(s-8) + 1/(s-9)
Taking the inverse Laplace transform of Y(s), we get:
y(t) = -e^(8t) + e^(9t)u(t-1)
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Jada’s dog was 5 1/2 inches tall when it was a puppy. Now her dog is 14 1/2 inches taller than that. How tall is Jada’s dog now as a fraction?
Answer: 20 or 20/20
Step-by-step explanation: It equals a whole number.
Answer:
20/20
Step-by-step explanation:
so there is 5 1/2, you can add 14 1/2, 14 plus five equals 19, but you also have to add the two halves, which in total gives you 20/20.
Which are equivalent to 32 · 34 ? Check all that apply.
36
38
96
3-4 · 310
30 · 38
33 · 33
(3 · 2) · (3 · 4)
(3 · 3) · (3 · 3 · 3 · 3)
Using exponential properties, it is found that the equivalent expressions are given by:
[tex]3^6[/tex].[tex]3^{-4} \times 3^{10}[/tex][tex]3^0 \times 3^8[/tex].(3 · 3) · (3 · 3 · 3 · 3)What happens in the multiplication of two terms with the same base and different exponents?We keep the base and add the exponents, that is:
[tex]a^b \times a^c = a^{b + c}[/tex]
In this problem, we want an expression equivalent to:
[tex]3^2 \times 3^4 = 3^{2 + 4} = 3^6[/tex]
The equivalent expressions have the same result, hence, they are:
[tex]3^6[/tex].[tex]3^{-4} \times 3^{10}[/tex][tex]3^0 \times 3^8[/tex].(3 · 3) · (3 · 3 · 3 · 3)More can be learned about exponential properties at https://brainly.com/question/234372
3^6 Or A
3^-4 · 3^10 or C
3^3 · 3^3 Or E
(3 · 3) · (3 · 3 · 3 · 3) Or H
Pls consider me for Brainliest!!
why do the angles in a triangle add up to 180 degrees?
Answer:
Angles in a triangle add up to 180 degrees because triangles are have the measure and sizes of quadrilaterals, which have an angle measure of 360 degrees. If you divide 360 degrees by 2, you will get 180 degrees.
Step-by-step explanation:
Hope that helps!
Answer:
Let N equal the number of angles in the polygon
Use the formula:
(N x 180)-360 = the sum of all the angles in the polygon
A triangle has 3 angles so:
(3 x 180)-360=180 degrees
(this formula works for any polygon, regardless of the number of it's angles)
Damian’s computer repair shop earned $2,500 in income last week. Expenses were $2,750. What was Damian’s profit or loss for the week?
Answer:
2500-2750 = - 250
hence,he lost $250
If
f(x) = x^2 + 2x - 4
and
g(x) = 3x + 1
Find
f(g(x)) = ?
Answer;
f (x) = 2x-4g (x) =x^2
Step-by-step explanation:
The solution is 9x² + 12x - 1
The composition function f ( g ( x ) ) is 9x² + 12x - 1
What is Composition of functions?
Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
The value of f ( x ) = x² + 2x - 4
Let the second function be represented g ( x )
The value of g ( x ) = 3x + 1
Now , the composition function f ( g ( x ) ) is calculated by
Substitute the value of x as 3x + 1 , in f ( x ) , we get
f ( g ( x ) ) = f ( 3x + 1 )
f ( 3x + 1 ) = ( 3x + 1 )² + 2 ( 3x + 1 ) - 4
On simplifying the equation , we get
f ( 3x + 1 ) = ( 9x² + 6x + 1 ) + ( 6x + 2 ) - 4
f ( 3x + 1 ) = 9x² + 12x - 1
Therefore , the value of f ( 3x + 1 ) is 9x² + 12x - 1
Hence , the composition function f ( g ( x ) ) is 9x² + 12x - 1
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answer quickly and quietly incorrectly please
Answer:
Your answer is
A & E
Mark my answer as brainlist . I need that urgently . Folow me for more answer.
Step-by-step explanation:
what is domain and range because I got it wrong is not the right one
Answer:
You most likely got it wrong because you didn't plot all the points that are actually in the table, the domain and range are both right.
Find the slope!!!
Quickly please
Answer:
the slope is m= 2
Answer:
2
Step-by-step explanation:
Slope is (y1 - y2) / (x1 - x2) for any 2 respective x's and y's.
For any of the points here, you get 2.
Mark is reading a book with 96 pages. It takes him 4 days to read the book. He reads the same number of pages each day. How many pages does Mark read each day?
24
Step-by-step explanation:
he reads 24 pages a day
Answer:
24 pages per day
Step-by-step explanation:
Mark has a 96-paged book. It takes him 4 days to read the book.
[tex]\frac{pages}{day}=\frac{96}{4}= \frac{96/4}{4/4}= \frac{24}{1}=\boxed{24}[/tex]
Mark would read 24 pages per day.
Hope this helps.
6m+17-13+5n combine like terms
Answer:
hmmmm bilmim weantremlo ?
Step-by-step explanation:
= 6m +5n + 4
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you and plzzz.
Daniel debe $12.300 a Miguel y paga con un billete de $50.000 ¿cuanto dinero le devuelven ?
Answer:
37,700
Step-by-step explanation:
I believe that you do 50,000 - 12,300. That would get you to your final answer of 37,700. So Miguel has to give 37,700 back to Daniel.
Hope this helped you!
Answer:
Miguel devuelve a Daniel $ 37.70
Step-by-step explanation:
50 - 12.3 = 37.7
pls help it for math
The selling price of an item is $600. It is marked down by 30%, but this sale price is still marked up
from the cost of $350. Find the markup from cost to sale price.
The markup is $ (Round to the nearest dollar as needed.)
Answer:
7000
Step-by-step explanation:
divide 600 and 30 then multiply that answer by 350
Answer:
Correct answer is 70 trust me
Step-by-step explanation:
The translation shown in the graph moves the figure to the right. What kind of translation is shown?
the figure go to the left
The age at which a person can be tried as an adult
Answer:
giyi
Step-by-step explanation:
HELPPPPPPP pleaseeeee mathhhh
9514 1404 393
Answer:
y = 1/6x
Step-by-step explanation:
The constant of proportionality is the ratio of y to x:
k = y/x
Using the point you have circled, it is ...
k = 2/12 = 1/6
Then the equation y = kx can be written:
y = 1/6x
Which is Better Lion ling action movie or The Cartoon Version? Explain your answer gets 25 Points!
Answer:
Cartoon
Step-by-step explanation:
Answer:
The cartoon lion king is way better. I say this because the action one is kinda creepy. I feel like Disney tried too hard to make it great, that it ended up not as good as it could be.
Step-by-step explanation:
Hope this is good enough!
Plllzzzzz help quick
Answer:
also click the first choice. It has 10 sides.
Step-by-step explanation:
1440=(N-180)-360
N-180=1080
n=10 sides
Answer: The answers would be A
Step-by-step explanation- The sum of all angles in a decagon will always equal 1440 degrees. That is all. Plz mark brainliest?
You are raising money by holding a bake sale at school. You have a budget of $100 to set up the bake sale. You provide volunteers with $40 of materials. Each table that you plan to rent costs a flat rate of $10. How many tables can you rent?
Answer:
6 Tables
Step-by-step explanation:
100 = 10x + 40
60 = 10x
6 = x
good luck, hope this helps :)
6 tables
100-40=60
each table = 10
60 divided by 10=6
How many degrees
in 1/20 of a full turn?
Answer:
18 degerees
Step-by-step explanation: i am 100% sure have a nice day.
I need help with this please :(
Answer:
b
Step-by-step explanation:
b= luck
simplify this: (1/5^3)^4
Answer: The simplest form of (1/5^3)^4 is 1/244140625
Step-by-step explanation: Strange answer, huh?
The masses of 4 containers loaded on a ship are 28 tonnes,45 tonnes,16.8tonnesand 48500kg .What is 5he total mass in tones?
Step-by-step explanation:
first of all we have to change kg into ton= 48500kg into ton =53.462ton(48500/907.168)
after that we add all the weight of 4 container = 28+45+16.8+53.462
total will be his total mass of tones he had =143.262
z > 34. Which of the following statements is the best way to describe the value of z?
A. The value of z is less than 34.
B. The value of z is more than 34.
C. The value of z has a maximum of 34.
D. The value of z has a minimum of 34.
Answer:
B
Step-by-step explanation:
The open end is always going to be by the larger number.
Answer:
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
HAHAHA
Step-by-step explanation:
Help me plz i will give brainlest
Answer:
the answer should be (3,-2)
Find angle a.
You will get 20 points
Answer:
127
Step-by-step explanation:
15+38+a=180
a= 127
Please I need help
Write the equation for a parabola with a focus at (1,-4) and a directrix at x = 2.
X=?
Answer:
Step-by-step explanation:
The directrix is a vertical line, so the parabola is horizontal. The focus lies to the left of the directrix, so the parabola opens to the left.
For a left-opening parabola:
x = a(y-k)²+h,
a < 0,
vertex (h,k)
focal length p = 1/|4a|
focus (h-p, k)
directrix: x=h+p
Apply your data
focus (1,-4)
directrix x=2
vertex (1.5,-4).
focal length p = 0.5
a = -1/|4p| = -½
x = -½(y-2)²+ ½
The pair of figures is similar. Use proportions to find the value of each variable.
A computer store buys a computer system at a cost of $370.80. The selling price was first at $618 , but then the store advertised a 20% markdown on the system.
Answer:
The answer is 494.40 for the first question and then the second answer is 395.52
Step-by-step explanation:
Answer:
$494.40
Step-by-step explanation:
618 x 20% or .2 = $123.60.
$618 - $123.60= $494.40.
Hope this helps!
Solve for w.
-4(w+1) = -24
Answer:
w=5
Step-by-step explanation: