use laplace transforms to solve the integral equation y(t) 16∫t0(t−v)y(v)dv=12t. the first step is to apply the laplace transform and solve for y(s)=l(y(t))

Answers

Answer 1

The solution to the integral equation using Laplace transform is:

y(t) = (1/16)e^2t - (1/16)e^-2t + (1/4)

To solve the integral equation y(t) 16∫t0(t−v)y(v)dv=12t using Laplace transforms, we need to apply the Laplace transform to both sides and solve for y(s).

Applying the Laplace transform to both sides of the given integral equation, we get:

Ly(t) * 16[1/s^2] * [1 - e^-st] * Ly(t) = 1/(s^2) * 1/(s-1/2)

Simplifying the above equation and solving for Ly(t), we get:

Ly(t) = 1/(s^3 - 8s)

Now, we need to find the inverse Laplace transform of Ly(t) to get y(t). To do this, we need to decompose Ly(t) into partial fractions as follows:

Ly(t) = A/(s-2) + B/(s+2) + C/s

Solving for the constants A, B, and C, we get:

A = 1/16, B = -1/16, and C = 1/4

Therefore, the inverse Laplace transform of Ly(t) is given by:

y(t) = (1/16)e^2t - (1/16)e^-2t + (1/4)

Hence, the solution to the integral equation is:

y(t) = (1/16)e^2t - (1/16)e^-2t + (1/4)

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Related Questions

HELP PLEASE!! WILL GIVE BRAINLIEST!!!

Answers

The slope is 5/7

Step-by-step explanation:

When you find slope you need to find both points and use the ordered pairs and subtract y1 - y2 and x2 - x1 and then you get your slope which is 5/7

sorry im bad at explaining

Enter the value of n so that the expression (3y + 1) + (2y + 8) is equivalent to (ny + 9).

Answers

Answer:

Step-by-step explanation:

3y+1+2y+8=ny+9

5y+9=ny+9

5y=ny

n=5

can someone tell the answers?

Answers

Answer:

IT B

Step-by-step explanation:

BECAUSE IT B

Answer:

A. B and D

Step-by-step explanation:

A because: X can be the minutes she goes over

B because: X can be the customers coming in for breakfast

D because: X can be every ticket

it can't be C because you would take away the eggs not add

Show that the line 3y = 7 + 5x is perpendicular to the line 5y = 4 - 3x.

Answers

Answer:

Proven Below

Step-by-step explanation:

If we rearrange these equations, we get that 3y = 5x + 7 and that 5y = -3x + 4. Next, to find what y equals on both equations, we divide by 3 on both sides of the first equation, where we would get that y = 5/3x + 7/3, and then divide by 5 on both sides of the second equation, where we would get that y = -3/5x + 4/5. Now, to see if two lines are perpendicular to each other, we have to see if the slopes (The number being multiplied by x. Ex.) In the equation y = 3/4x + 4, the slope is 3/4) are opposite reciprocals (If you multiply them and they are equal to -1. Ex.) 3/4 * -4/3 is equal to -1, so they are opposite reciprocals). In this case, we have -3/5 and 5/3 as slopes, and -3/5 * 5/3 is equal to -1, so they are perpendicular.

Answer:

The slope of the first line is 5/3

The slope for the second one is -3/5

If you multiply the 2 slope you have to end up with - 1

So 5/3*(-3/5)=-15/15 which is - 1

So yes the lines are perpenducular

porfis ayúdenme es para hoy ​

Answers

Answers:

1. V=triangle area × length

V=1/2×8×12×20

V=960in³

2. triangle area × length

Area of the triangle=1/2×4×11

A=22ft²

V=22×6

V=132ft³

3. b, volume always have cubic power (³)

4. d, same reason of question 3

a line passes through the points (4,23) and (8,27). write a linear funtion rule in terms of x and y for this line

Answers

Answer:

Step-by-step explanation:

(27 - 23)/(8 - 4)= 4/4= 1

y - 23 = x - 4

y = x + 19

Given the following data set: 111, 122, 133, 149, 126, 117, 101, 121
Find the values of the upper and lower quartiles.​

Answers

Answer:

the upper is 149

and the lower is 101

Step-by-step explanation:

sana makatulong

Can you help me please

Answers

Answer:

D?

Step-by-step explanation:

if i got it wrong im truly sorry

The answer is A the common ratio is 2

Rizwan has 100 ruppees . He spent rs 25 in ice cream . Rs 45 on pizza, and the rest on other things . What percantage did he spend on other things .

Answers

Answer:percantage spent on other things = 30%

Step-by-step explanation:

Percentage spent on other things = Money spent on other things/ Total money x `100/ 1

Money spent on rest things = Total money - ( Money spent on ice cream + Money spent on pizza)

100 -(25+ 45)

100-70= Rs 30

Percentage spent on other things = Money spent on other things/ Total money x `100/ 1

= Rs 30/ Rs 100 x 100

0.3 x 100 = 30%

if you can help me i’ll make brainliest

Answers

Answer:

help me

Step-by-step explanationok so

Answer:

pts

Step-by-step explanation:

X and Y
-5x+5y=-25
3x+2y=10

the X and Y is (4,-1) i need to know how to get the answer ​

Answers

Step-by-step explanation:

just substitute X and Y by their numerical values.

a) -5(4)+5(-1)=-25

-20-5= -25

-25= -25. true

b) 3(4)+2(-1) = 10

12 -2 =10

10=10. true

3. The functions f and g are defined by f: x → ax – b where a and b are constants and g: x → X+4.
Given fg(2) = 9 and gf (1/2) = 2, find the value of a and of b. ​

hiii this is adddmath can anyone help with this please

Answers

Answer:

fg(2) = 9 means that f(g(2)) = 9

We know that g(2) = 6

So f(6) = 9 which means that

6a - b = 9 (note 1)

And we know that g(f(1/2)) = 2

And we know that f(1/2) = 1/2(a) - b

So g(1/2(a) - b) = 2

Meaning that 1/2(a) - b + 4 = 2

So 1/2(a) - b = - 2 (note 2)

Using note 1 and 2 we can solve the equation

11/2(a) = 11 so a = 2 and b = 3

Please help will give brainliest!

Answers

Answer:

Should be 1 if im not wrong Then Mark Me brainliest

Step-by-step explanation:

a negative times a neg equals a posative

Neg x pos = neg

pos x neg = neg

pos x pos = pos

neg x neg = pos

so if there greater then over neg<, >,=

You would look at the problem for given f(x)=

x → -1 and neg times neg more or less

-1 x -1 = 1

what is the sum of 3 + 6 + 5

Answers

Answer:

The answer is 14

Step-by-step explanation:

3 + 6 = 9

9 + 5 = 14

The answer is 14 this is easy

A batch of 26 television sets are being checked by two supervisors. Both start from the same end. One supervisor checks every
2nd set and puts a blue mark on it. Another supervisor checks every 3rd set and puts a green mark on it. How many television
sets will have BOTH a blue and a green mark on them​

Answers

Answer:

4

Step-by-step explanation:

Total number of television sets = 26

With the condition given that; every 2nd set had blue mark on it, and every 3rd set had green mark on it.

The number of only blue marked set is 8, while the number of only green marked set is 4.

So that, the number of television sets with both blue and green mark on them is 4.

-30=5(x+1) x=?

please help ​

Answers

Answer:

x = -7

-30 = 5(x + 1)

5(x + 1) = -30

5(x + 1)/5 = -30/5

x + 1 = -6

x + 1 - 1 = -6 -1

x = -7

Choose the two number sentences that are true.
A. 5+7= 11+2
B. 3 + 3 = 20 - 9
C. 5+9 = 19 - 4
D. 12 +7 = 5 + 14
E18 - 6 = 15 - 1

Answers

Answer:

D

because 12+7=19

5+14=19

If f(x) = x2, and
g(x) = x - 1, then
f(g(x)) = ?

Answers

Answer:

f(g(x))=1x^2 +-2x+1

Step-by-step explanation:

your inputs should be

1

-2

1

If f(x) = [tex]x^{2}[/tex], g(x) = [tex]x -1[/tex] then f(g(x)) = [tex]1x^{2} -2x+1[/tex].

What is a function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given

f(x) = [tex]x^{2}[/tex]

g(x) = [tex]x -1[/tex]

f(g(x)) = [tex](x-1)^{2}[/tex]

It is in the form of [tex](a-b)^{2}=a^{2} -2(a)(b) +b^{2}[/tex]

= [tex]x^{2} -2(x)(1) +1^{2}[/tex]

= [tex]x^{2} -2x+1[/tex]

f(g(x)) = [tex]1x^{2} -2x+1[/tex]

Hence, If f(x) = [tex]x^{2}[/tex], g(x) = [tex]x -1[/tex] then f(g(x)) = [tex]1x^{2} -2x+1[/tex].

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what is the answer to this problem if you need to find out the area?

Answers

Answer:

17.28in

Step-by-step explanation:

To find the area of a triangle, multiply the base by the perpendicular height (the length from the point opposite the base, to the base, which makes a 90-degree angle with the base), and half it:

7.2*4.8=34.56

34.56/2=17.28

Jada sister Earns a commission. She makes 3.5 of them out she sells. Last week she sold, 7000 Worth of furniture. How much was her commission?

Answers

Answer:

$245

Step-by-step explanation:

3.5% of 7000 = 0.035 × 7000 = 245

why is it so hard like math in general is hard has been for years

Answers

Answer:

Tell me about it..

Step-by-step explanation:

Step-by-step

explanation:

math is hard because is hard

a tree is broken at a height of 6 cm from the ground and its top touches the ground at a distance of 8cm from the base of the tree . find the original height of the tree pls do to step to step explaination ​

Answers

Answer:

I guess its 16

Step-by-step explanation:

Because

Hieght =6cm

Base = 8cm

Hypotenuse=?

by pythagoras formula = a^2+b^2=c^2

6 *6 + 8*8 =c^2

36 + 64 = c^2

100 =c^2

Root of 100 is 10

so the whole tree is = to 10 +6 =16

At Franklis Incorporated, during the month of January, the direct labor rate variance was $3,000 unfavorable, and the direct labor efficiency variance was $5,000 favorable. Actual direct labor costs during January were $100,000. What was the standard direct labor applied to production at Franklis during the month of January?

Answers

Answer:

50

Step-by-step explanation:

Direct labour rate variance is $3,000

Direct labour efficiency variance is $5,000

Actual direct labour costs is $100,000

Therefore the standard direct labour production during the month of January can be calculated as follows

= 100,000/5,000-3,000

= 100,000/2,000

= 50

Help meh ill mark 1 and 1/2 +2/5 PLZZZZZZZZZZZZZZZZ

Answers

Answer:

1 9/10

Step-by-step explanation:

AYO HELP A MAN OUT PLEASE

Answers

Answer:

I think it's A I'm not sure tho

Step-by-step explanation:

the answer is A and I think C I don't know though ur welcome!:)

An airplane on autopilot took 9 hours to travel 6,471 kilometers. What is the unit rate for kilometers per hour?

Answers

Answer:

719 kilometers

Step-by-step explanation:

6,471/9 = 719

that's the unit rate

Answer:

719

Step-by-step explanation:

6,471/9=719

719*9=6,471

which means the correct answer is 719

YW!!

You purchased a car for $56,843. After
one year, the car is worth $51,474. How
much is the car worth in 4 years?

Answers

Answer:

$35,367

Step-by-step explanation:

The bag has 2 yellow cubes, 5 green cubes, and 3 red cubes. Without replacing the yellow cube, what is the probability of selecting a red cube at random?

Answers

32% chance of selecting red at random.

B. 13 (x - 10) = -4

Answer: x =
Its a neg #

Answers

X=9.69
you have to distribute the 13 to x and -10 which gives you 13x-130=-4 then you add 130 to -4 because your going over the equal sign and it gives you 126 next you divide 126 by 13 which gives you 9.69

If you did not learn a different method for unit conversion in a previous class, respond to the following statement.

Explain how to use the unit-factor method to convert 120 pounds to kilograms.
Hint: 1 kilogram=2.2 pounds
To write the unit factors, use the / symbol, like this: 1 gallon/3.79 liters.

Answers

Answer:

120 pounds = 54.5 kilogram

Step-by-step explanation:

We know that,

1 kilogram=2.2 pounds

or

1 pound = (1/2.2) kilogram

We need to convert 120 pounds to kilograms.

[tex]120\ \text{pounds}=\dfrac{120}{2.2}\ \text{kilogram}\\\\=54.5 \text{kilogram}[/tex]

So, there are 54.5 kilograms in 120 pounds.

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