simplify to create an equivalent expression -4(z+3)-4(5-4z)
Find the inverse transform by convolution: 4 (s-3)(s-2) C.27.
I suppose you're asking about the inverse Laplace transform of
[tex]F(s)=\dfrac4{(s-3)(s-2)}[/tex]
by way of the convolution theorem.
The theorem itself says that
[tex]\mathscr L^{-1}\{A(s)B(s)\}=(a*b)(t)[/tex]
where [tex]A(s)[/tex] and [tex]B(s)[/tex] are the Laplace transforms of [tex]a(t)[/tex] and [tex]b(t)[/tex], respectively.
Let [tex]A(s)=\frac1{s-3}[/tex] and [tex]B(s)=\frac1{s-2}[/tex]. Then
[tex]a(t)=\mathscr L^{-1}\left\{\dfrac1{s-3}\right\}=e^{3t}[/tex]
[tex]b(t)=\mathscr L^{-1}\left\{\dfrac1{s-2}\right\}=e^{2t}[/tex]
So we have
[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=e^{3t}*e^{2t}[/tex]
Convolution is defined as
[tex](a*b)(t)=\displaystyle\int_0^t a(t-\tau)b(\tau)\,\mathrm d\tau[/tex]
The convolution of [tex]e^{3t}[/tex] and [tex]e^{2t}[/tex] is
[tex]e^{3t}*e^{2t}=\displaystyle\int_0^t e^{3(t-\tau)}e^{2\tau}\,\mathrm d\tau[/tex]
[tex]=\displaystyle e^{3t} \int_0^t e^{-\tau}\,\mathrm d\tau[/tex]
[tex]=e^{3t}(1-e^{-t})=e^{3t}-e^{2t}[/tex]
We end up with
[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=\boxed{4(e^{3t}-e^{2t})}[/tex]
scientific notation
Answer:
1.45
Step-by-step explanation:
not sure but trying to help :)
2/5 y - 4 + 7 - 9/10 y
Answer:
-1/2y +3
Step-by-step explanation:
2/5y -4 + 7 -9/10y=
combine like terms
-1/2y +3
What is the domain of the function f(x)=
Answer:
The domain of a function is the set of all possible inputs for the function.
Step-by-step explanation:the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
can someone help ASAP plzz
Answer:
c. 84 ft²
Step-by-step explanation:
lateral area = 1/2 * base perimeter * height
where
base sides = 6 ft.
height (L) = 7
lateral area = 1/2 x (4*6) * 7
lateral area = 84 ft²
LA = 1/2pl
p = base perimeter
l = length
p = (6 * 4)
p = 24
l = 7
Use the formula and solve.
LA = 1/2(24)(7)
LA = 1/2(168)
LA = 84
Therefore, the answer is C
Best of Luck!
Integers are ________ whole numbers. braineist for first person to get it right and hurry im on a time limit 20 points for it also
sometimes whole numbers
Step-by-step explanation:
maybe
Answer with proper units too!
Answer:
Step-by-step explanation:
1. Area of a parallelogram = base * height
area = 10 * 4 = 40 in squared
perimeter = 2(a + b)
perimeter = 2 * (5 + 10) = 2 * 15 = 30in
2. Area of triangle = 1/2 * base * height
area = 1/2 * 21 * 8 = 84 cm squared
perimeter = sum of outer perimeters
perimeter= 10cm + 17cm + 21cm = 48cm
3. area of trapezium = 1/2 * (a+b) * h
area = 1/2 * (6+12) * 4 = 36ft squared
perimeter = sum of outer perimeters
perimeter = 5ft + 6ft + 12ft + 5ft = 28ft
A car is traveling down a highway at a constant speed, described by the equation d=65t, where d represents the distance, in miles, that the car travels at this speed in t hours. How many miles does the car travel in 1.5 hours?
Answer:
A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels - 1138… ... How many miles does it take the car to travel 26 miles at this speed? c. ... the distance, in miles, that the car travels at this speed in t hours.
Step-by-step explanation:
Hope this helps
convert this statement into a conditional statement: 2 angles that add up to 180 degrees are supplementary
The sum of two numbers is 91.one is 37 more than the other.Find the numbers
Step-by-step explanation:
Hey there!!
Here, According to the question;
Let one number be x then another number will be x+37. (as one number is 37 more than other number. )
Now,
Their sum is 91.
It would be like;
[tex]x + (x + 37) = 37[/tex]
[tex]2x + 37 = 91[/tex]
[tex]2x = 91 - 37[/tex]
[tex]x = \frac{54}{2} [/tex]
Therefore the value of x is 27.
So, one number is 27 and another number is 64.
Hope it helps....
Solve the equation, 5- 2y = –8
Answer:
Step-by-step explanation:
5 - 2y = - 8
Subtract 5 from both sides
-2y = - 8 - 5
-2y = - 13
Divide by - 2
-2y/-2 = - 13/-2
y = 6 1/2 or 6.5
What number is 136% of 12.24?
Answer:
I really don't know but I'm trying to hurry for my quiz lol sorry
Answer:
cxcxcxcxcxgergddgg
Step-by-step explanation:
1. You want to purchase a car that costs $25,000. You must pay a 10% down payment. How much is this?
Answer: 2,500
2. What do you still owe?
Answer: 22,500
3. Determine the monthly payment for 60 months with an APR of 5.5%. Round to the nearest cent.
Answer: 22,500(0.055/12)/(1-(1+0.055/12)^(-60)= 429.78 rounded to the nearest cent.
4. How much do you pay all together at the end of the 60 months including the down payment and interest charges?
I need help with number 4. Please.
Answer: If interest is not given, it would be 25,000+ interest as your answer
Step-by-step explanation:
A clown uses canisters of helium to make balloons. The graph shows the number of canisters used and the number of balloons created. What does the point (0,0) represent? A It shows the number of balloons created using 1 canister of helium. B It shows that when 0 canisters of helium are used, 0 balloons are created. C It shows that when 0 canisters of helium are used, 5 balloons are created. D It shows the number of canisters needed to create 10 balloons.
Answer:
B It shows that when 0 canisters of helium are used, 0 balloons are created
Step-by-step explanation:
from the graph, we can see that point (0,0) means that when the number of canisters of helium used is 0, then the number of balloons created is also 0
the closest answer to this observation is:
B It shows that when 0 canisters of helium are used, 0 balloons are created
What is 45divided by 9 ?
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Step 1:
45 ÷ 9
Answer:
5
Hope This Helps :)
Dale made a model of a lighthouse using a 4 inches=50 feet if the lighthouse is 120 feet tall, how tall is his model
Answer:
8 2/5 inches!
Step-by-step explanation:
The lighthouse is 120 feet, and 4 inches of height on the model equals 50 feet of height on the lighthouse. 100 divided by 50 = 2, and 4 multiplied by 2 is 8. 20 divided by 50 = 2/5, so the answer is 8 2/5 inches. :)
Nick mowed about 3/5 of the school lawn yesterday. The mowed another 1/4 of the remaining portion of the lawn this morning. How much is left to mow?
find the first three terms of the sequence with nth term 3n-2
Answer:
To find out the first three terms of 3n - 2 substitute 1 ,2 and 3 into the equation.
so the three terms a
3(1)-2=1
3(2)-2=6-2=4
3(3)-2=9-2=7
As you can see the sequence goes up in 1,4 and 7.To find out the 10th term you also substitute 10 into the equation so 3(9)-2=18-2=16
so 16 is the tenth term
Hope this helped!
You pick a card at random 6,7,8,9. What is P (8)?
Answer:
1/4
Step-by-step explanation:
4|m-n| if m= -7 and n=2
Solve the following (x+y+z)(x-z)^2
Hey there!
ANSWER: [tex]x^2y-2xyz+yz^2+x^3-x^2z-xz^2+z^3[/tex]EXPLANATION:[tex](x+y+z)(x-z)^2[/tex]
Simplify.
[tex]x^2y-2xyz+yz^2+x^3-x^2z-xz^2+z^3(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
Step-by-step explanation:
x³+yx²+zx²-2x²z-2xzy-2xz²+x²z-z²y+z³
SOMEONE HELP PLEASE.............
What is the x-coordinate of the solution of the following system of equations?
3x + y = 6
x - y = 6
A. -3
B. 0
C. 3
Answer:
(3,-3) or x = 3
Step-by-step explanation:
I solved this problem with the help of graphing, you would start by sketching each equation. The x-value of the point where both equations intersect would be solution to your equations.
find the value power of 3^4
Answer:
81
Step-by-step explanation:
3 ^4 =3 ×3 ×3 ×3 =81
I need help and it’s due today
Answer: same bruh
Step-by-step explanation:
-7x+4y+9-4x=-7-5-5(-x-3y)
Answer:
for x = −11y/16+ 21/16
for y = 16x/11 +21/11
Step-by-step explanation:
Solve the equation . Check your solution
Answer:
x=48/8=6
Step-by-step explanation:
simple form
8x-48=0
fractionized
8(x-6)=0
What are the values of the two 3s in 3,435?
Answer:
The first 3 is in the thousandths place. it is worth 3 thousand. The second 3 is in the tenths place. It is worth 30.
Answer: 3,435
Least place value to largest largest place value-
5-ones place
3-tens place
4-hundreds place
3-thousands place
I hope that worked!
1.For this problem, 200 meters of fencing will all be used to place fence on all four sides of the rectangle. Your task is to write the area that can be enclosed as a function of the width, w, of the rectangle.
Area equation:
What is the domain for this function (what values do you expect the width to fall between)?
Answer:
Step-by-step explanation:
Given that:
the perimeter of the fencing (rectangle) = 200
Let recall that the area equation of a rectangle = L × w
The perimeter now = 2(L + w)
The perimeter = 2L + 2w
∴
200 = 2L +2w
Dividing both sides by 2
100 = L + w
Making Length L the subject; we have:
- L = -100 + w
L = 100 - w
Thus;
A(w) = (100 - w) w
and the domain of the function is (0,100)
Warren had d dollars. He bought 5 ice creams which cost x dollars each. How much money does he have left?
Answer:
The answer is: d-5x
Step-by-step explanation:
What I like to do is rewrite the problem with numbers instead of variables.
Example: Warren had 20 dollars. He bought 5 ice creams which cost 2 dollars each. How much money does he have left?
He has 20 dollars, 5x2=10 he spent 10$ on the ice cream so you have to subtract how much he had in the beginning to how much he spent, the answer with numbers would be: 20-5x2
With variables it would be d-5x