Hãy tìm hàm gốc f(t) có hàm ảnh Laplace như dưới đây:
F(p)=6/p(2p^2+4p +10)

Answers

Answer 1

It looks like we're given the Laplace transform of f(t),

[tex]F(p) = L_p\left\{f(t)\right\} = \dfrac6{p(2p^2+4p+10)} = \dfrac3{p(p^2+2p+5)}[/tex]

Start by splitting up F(p) into partial fractions:

[tex]\dfrac3{p(p^2+2p+5)} = \dfrac ap + \dfrac{bp+c}{p^2+2p+5} \\\\ 3 = a(p^2+2p+5) + (bp+c)p \\\\ 3 = (a+b)p^2 + (2a+c)p + 5a \\\\ \implies \begin{cases}a+b=0 \\ 2a+c=0 \\ 5a=3\end{cases} \implies a=\dfrac35,b=-\dfrac35, c=-\dfrac65[/tex]

[tex]F(p) = \dfrac3{5p} - \dfrac{3p+6}{5(p^2+2p+5)}[/tex]

Complete the square in the denominator,

[tex]p^2+2p+5 = p^2+2p+1+4 = (p+1)^2+4[/tex]

and rewrite the numerator in terms of p + 1,

[tex]3p+6 = 3(p+1) + 3[/tex]

Then splitting up the second term gives

[tex]F(p) = \dfrac3{5p} - \dfrac{3(p+1)}{5((p+1)^2+4)} - \dfrac3{5((p+1)^2+4)}[/tex]

Now take the inverse transform:

[tex]L^{-1}_t\left\{F(p)\right\} = \dfrac35 L^{-1}_t\left\{\dfrac1p\right\} - \dfrac35 L^{-1}_t\left\{\dfrac{p+1}{(p+1)^2+2^2}\right\} - \dfrac3{5\times2} L^{-1}_t\left\{\dfrac2{(p+1)^2+2^2}\right\} \\\\ L^{-1}_t\left\{F(p)\right\} = \dfrac35 - \dfrac35 e^{-t} L^{-1}_t\left\{\dfrac p{p^2+2^2}\right\} - \dfrac3{10} e^{-t} L^{-1}_t\left\{\dfrac2{p^2+2^2}\right\} \\\\ \implies \boxed{f(t) = \dfrac35 - \dfrac35 e^{-t} \cos(2t) - \dfrac3{10} e^{-t} \sin(2t)}[/tex]


Related Questions

A) -0.25(O)=-1.753 +2.25

Answers

Answer:

If you are trying to find O, then O would be

-1.988

Step-by-step explanation:

First, add -1.754 and 2.25, then divide by -0.25 which results in O=-1.988

Which of the following theorems verifies that AABC - ASTU?
A. AA
B. HL
C. HA
D. LL

Answers

Answer:

AA

Step-by-step explanation:

See In Triangle ABC and Triangle STU

[tex]\because\begin{cases}\sf \angle A=\angle S=90° \\ \sf \angle B=\angle T=31°\end{cases}[/tex]

Hence

[tex]\sf \Delta ABC~\Delta STU(Angle-Angle)[/tex]

By AA similarity  triangle ABC is similar to triangle SUT. Therefore, option A is the correct answer.

What are similar triangles?

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

In the given triangle ABC, ∠C=180°-90°-31°

∠C=59°

In the given triangle SUT, ∠U=180°-90°-31°

∠U=59°

Here, ∠B=∠T (Given)

∠C=∠U (Obtained using angle sum property of a triangle)

So, by AA similarity ΔABC is similar to ΔSUT.

Therefore, option A is the correct answer.

To learn more about the similar triangles visit:

https://brainly.com/question/25882965.

#SPJ7

Which of the following statements accurately describes the period of a trigonometric function?

Answers

Answer:

b

Step-by-step explanation:

b is  correct.

2. Solve the following:
a. When six is added to four times a number the result is 50. Find the number.
b. The sum of a number and nine is multiplied by -2 and the answer is -8. Find the
number.
c. The length of a rectangular map is 37,5 cm and the perimeter is 125 cm. Find the
width.​

Answers

Answer:

a = 11

b = -5

c = 25

Step-by-step explanation:

a.

6 + 4x = 50

50 - 6 = 44

4x = 44

x = 11

b.

(x+9) * -2 = -8

(x+9) = 4

x = -5

c.

2(37.5) + 2(x) = 125

75 + 2x = 125

125 - 75 = 2x

50 = 2x

x = 25

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K


Plz help quick quick quick

Answers

Step-by-step explanation:

[tex]\angle 3[/tex] and [tex]\angle 16[/tex] are alternate exterior angles so they are equal to each other, which means

[tex]5x - 30 = 3x + 10 \Rightarrow x = 20[/tex]

Solving for the measure of [tex]\angle 16[/tex], we get

[tex]m\angle 16 = 5(20) - 30 = 70°[/tex]

Since [tex]\angle 12[/tex] and [tex]\angle 16[/tex] are supplementary,

[tex]m\angle 12 = 180° - 70° = 110°[/tex]

Answer:

ur image wont load

Step-by-step explanation:

find the three consecutive 0dd integers such that two is less than 15 than 5 times the firs​

Answers

Step-by-step explanation:

Find three consecutive odd integers such that the sum of the last two is 15 less than 5 times the first.

let the consecutive odd integers are :- x , x + 2 and x + 4.

According to question :-

the sum of the last two is 15 less than 5 times the first.

It means that

the sum of ( x + 2 ) and ( x + 4 ) is 15 less than 5 times the x .

( x + 2 ) + ( x + 4 ) = 5x - 15

x + 2 + x + 4 = 5x - 15

2x + 6 = 5x - 15

6 + 15 = 5x + 2x

21 = 7x

or ;

7x = 21

x = 21 / 7

x = 3

So, the consecutive odd numbers are :-

x = 3

x + 2 = 3 + 2 = 5

x + 4 = 3 + 4 = 7

=> 3 , 5 and 7

hope this helps you

Devaughn is 6 years older than Sydney. The sum of their ages is 56 . What is Sydney's age?

Answers

Answer:

Devaughn = 31, Sydney = 25

Step-by-step explanation:

(56-6)÷2= 25

So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31

Age of Sydney=xAge of Devaghn=x+6

ATQ

[tex]\\ \sf\longmapsto x+x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x=56-6[/tex]

[tex]\\ \sf\longmapsto 2x=50[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]

[tex]\\ \sf\longmapsto x=25[/tex]

What is the equation of the line that passes through (4,3) and (2, -1)?

y = 4x -13
y = 6x+4
y = 2x-5
y = 1/2 x -2

Answers

Answer:

y=2x-5

Step-by-step explanation:

By using two-points form:

y-y1/y2-y1=x-x1/x2-x1

p(x1,y1)=(4,3)

p(x2,y2)=(2,-1)

Subtitute points in formula:

y-3/-1-3=x-4/2-4

y-3/-4=x-4/-2

y-3/-2=x-4/-1

1(y-3)=2(x-4)

y-3=2x-8

y=2x-8+3

y=2x-5

Note:if you need to ask any question please let me know.

Graph the function f(x) = 1/2(2)^x

Answers

Answer; Down

Step-by-step explanation:The graph of the squaring function has the shape of a parabola that opens up. Its vertex is at (0,0). The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2).

Here u gooo i have more ok

Answers

1: b
2: D
3: A
4: C
Hope this helps
Sorry if it’s wrong

a hexagon has angles that measure 90º, 120º, 150º, 145º, 65º, and t. what is t?

Answers

Answer:

150°

Step-by-step explanation:

Sum of all angles in a hexagon = 720°

90° + 120° + 150° + 145° + 65 ° = 670°

720° - 570° = t

t = 150°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

solve 3/4(2/3m)=24. use the properties of equality first. justify each step.

pls help urgent​

Answers

Answer:

m = 48

Step-by-step explanation:

3/4(2/3m)=24

Multiply each side by 4/3 using the multiplication property of equality

4/3*3/4(2/3m)=24*4/3

2/3m = 32

Multiply each side by 3/2 using the multiplication property of equality

3/2*2/3m = 32*3/2

m = 48

The highest attendance at this stadium was in 2007 when 91,547 people attended. The average cost of a ticket was $57. How much money was made on ticket sales for that game?

Answers

Answer:57*91547

Step-by-step explanation:

Solve each equation for the given variable

1.3(2x+4)=54

2.4+(5x+5)54

Please

Answers

Answer:

1. x = 7

2. 270x+274

Explanation:

see attached filed for step by step reasoning

Answer:

1. x = 7

2. x = 9

Step-by-step explanation:

1. 3(2x + 4) = 54

Multiply 3 by the numbers in “( )”

6x + 12 = 54

Subtract 12 from both sides

6x = 42

x = 42/6

x = 7
****************************************
2. 4 + (5x + 5) = 54

Subtract 4 from both sides

5x + 5 = 50

Subtract 5 from both sides

5x = 45

x = 45/5

x = 9

Mila wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments


1) How much money does mila take as loan from the bank?

a) Rs 62,000
b) Rs 44,000
c) Rs 45,000
d) Rs 43,000​

Answers

Answer:

Scheme a 45000 is the answer

Answer is D Rs.43,000I hope this answer may be right

Which point should be removed for the graph to represent a table of equivalent ratios?
A. (2, 10)
B. (3, 15)
C. (4, 20)
D. (5, 15)

Answers

Answer:  D.   (5,15)

===========================================================

Explanation:

As the graph shows, three of the four points are on the same line. That line being y = 5x. This line has slope 5 and y intercept 0.

The point not fitting this pattern is the point (5,15), so that is the final answer.

For the other three points, note that the jump from x to y coordinate is "times 5". For example, y = 5x = 5*2 = 10 for point A. In contrast, point D has a jump of "times 3" when going from x to y.

--------------

Alternatively, you can divide each y coordinate by its corresponding x coordinate.

For choice A, we have y/x = 10/2 = 5Choice B has y/x = 15/3 = 5Choice C has y/x = 20/4 = 5

All results are 5 so far. Choice D doesn't follow the trend and instead has y/x = 15/5 = 3. This is another way to show that choice D is the answer.

Answer:

D

Step-by-step explanation:

A recipe says to use 2/3 cup milk to make 4/5 serving of pudding. How many cups of milk are in one serving?

Answers

Answer:

[tex]\frac56[/tex] cups

Step-by-step explanation:

The serving size is proportional to the amount of milk used, so we have

[tex]\frac{2/3}{4/5}=\frac x1[/tex]

where [tex]x[/tex] is the amount of milk needed for 1 serving. The right side is simply [tex]x[/tex]. We now simplify

[tex]x=\frac23\cdot\frac54=\frac{10}{12}=\frac56[/tex]

Therefore [tex]\frac56[/tex] cups of milk are needed for 1 serving.

Does anyone know this?

Answers

Answer:

the first term is -4

the difference is 3.

*notice how each term increases by 3:

-4 + 3 = -1

-1 + 3 = 2

2 + 3 = 5

Step-by-step explanation:

Here’s the answers to your question…
Hope you understand it!!

Find a formula for a function f that satisfies the following conditions. lim x→±∞ f(x) = 0,   lim x→0 f(x) = −∞,  f(2) = 0 lim x→7− f(x) = ∞,   lim x→7+ f(x) = −∞​

Answers

9514 1404 393

Answer:

  f(x) = (x -2)/(x²(7-x))

Step-by-step explanation:

The horizontal asymptotes of zero mean the denominator degree needs to be greater than the numerator degree. The zero at x=2 means (x-2) will be a factor in the numerator. The limit at x=0 means there will be a factor of x² in the denominator. Since the numerator term is negative at x=0, the signs of the terms so far do not need modification.

The vertical asymptote at x=7 means there will be a factor of (x-7) in the denominator. In order for the limits to be correct, it must have a negative sign:

  -(x -7) = (7 -x)

Then the function with these characteristics can be written ...

  f(x) = (x -2)/(x²(7 -x))

evaluate the function f(x)=4x^2-7x+7 find f(7)​

please I need the answer soon!

Answers

9514 1404 393

Answer:

  f(7) = 154

Step-by-step explanation:

The basic idea is you put 7 where x is and do the arithmetic.

Polynomial evaluation is sometimes easier if you rewrite it to Horner form.

  f(x) = (4x -7)x +7

  f(7) = (4·7 -7)(7) +7 = 21(7) +7 = 147 +7

  f(7) = 154

Can someone help me with this

Answers

Answer:

Step-by-step explanation:

If two triangles have two congruent sides and a congruent non included angle, then triangles are not necessarilly congruent.



The sum of 3 times a number and 4 is 9.

Answers

Answer: x = 5/3

Step-by-step explanation:

Let the number be x

Then

3x + 4 = 9

3x = 9-4

3x = 5

x = 5/3

please click thanks and mark brainliest if you like :)

Answer:

x = 5/3 or 1.6

Step-by-step explanation:

The sum of 3 times a number and 4 is 9

Step 1. Write the phrase as an expression

3x + 4 = 9

Step 2. Solve for x

3x + 4 = 9

Step 3. Subtract 4 from 9

3x = 9 - 4

3x = 5

Step 4. Isolate the variable

x = 5/3

Select the correct answer from each drop-down menu. Complete the statement. The solutions of sin2x= √3/2

are : 30 / 120 / 150 / 330

and

45 / 60 / 105 / 135

What are the correct solutions?

Answers

Answer:

henc X = 30°

Step-by-step explanation:

here is the proof

when X=30° then

sin2x = sin2×30

=sin 60°

= √3/2

or else,

putting value of X = 30° then

sin2x= 2sinxcosx

= 2×sin30°×cos30°

=2×1/2×√3/2

= 2√3/4

= √3/2

hence proved sin2x= √3/2.

−5x−9y=3 added to 5x−9y=−2


Answers

Answer:

the 5s cancel out the -9s become -18y and 3-2 is 1

Step-by-step explanation:

so -18y=1

Answer From Gauth Math

8.113 as a fraction PLEASE HELP ME ​

Answers

Answer:

8113/1000

Step-by-step explanation:

12/1,000 into decimal​

Answers

0.012 is the answer!

I hope this helps you out! :D

[tex]\\ \sf\longmapsto \dfrac{12}{1000}[/tex]

1000 has 3zeros hence decimal will go 3 points left

[tex]\\ \sf\longmapsto 0.012[/tex]

More:-

[tex]\\ \sf\longmapsto \dfrac{1}{10}=0.1[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{100}=0.01[/tex]

5. Determine the formula for the following arithmetic sequence: 4, 7, 10, 13, ...

Answers

Answer:

[tex]a_{n}[/tex] = n + 3

Step-by-step explanation:

Each number increases by 3. Therefore, n+3.

1. Convert a distance of 54 feet into yards

Answers

Answer:

18 yards

Step-by-step explanation:

54/3 = 18

3 feet = 1 yard

rewrite the following statements into algebraic expression
the sum of x and y
5 is subtracted from y​

Answers

x+y

5-y

i really hope this is it.

The sum of a number and its inverse is 3 29 / 52. Find the number?​

Answers

What does the inverse mean in this scenario
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