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

.Part D. Analyze the residuals.
Birth weight
(pounds)
Adult weight
(pounds)
Predicted
adult weight
Residual
1.5
10

3
17

1
8

2.5
14

0.75
5

a. Use the linear regression equation from Part C to calculate the predicted adult weight for each birth weight. Round to the nearest hundredth. Enter these in the third column of the table.

b. Find the residual for each birth weight. Round to the nearest hundredth. Enter these in the fourth column of the table.

c. Plot the residuals.

d. Based on the residuals, is your regression line a reasonable model for the data? Why or why not? ​

Answers

Answer:

Hi there! The answers will be in the explanation :D

Step-by-step explanation:

a) I'll attach a doc for the table so it'll basically answer a and b.

c) I'll also attach the graph.

d) I'm not entirely sure for this question, but I'll do my best to answer it correctly for you. I would say no, because we can see that the residuals are all positive, but the graph we're looking is going down which means it's negative. We can also see the table is increasing a bit so it doesn't really make any sense...

Hope this helped you!

100 x 20 + 30 help me

Answers

[tex]\boxed{\underline{\bf \: Answer}}[/tex]

[tex] \sf100 \times 20 + 30[/tex]

First multiply 100 & 20 together.

[tex] \sf= 2000 + 30[/tex]

Now add 2000 & 30. You'll get :-

[tex]= \boxed{ \bf 2030}[/tex]

____

Hope it helps.

RainbowSalt2222

[tex]\\ \rm\longmapsto 100\times 20+30[/tex]

[tex]\\ \rm\longmapsto (100\times 20)+30[/tex]

Solve bracket

[tex]\\ \rm\longmapsto 2000+30[/tex]

[tex]\\ \rm\longmapsto 2030[/tex]

Piecewise functions alg1

Answers

Answer:

C. 0

Step-by-step explanation:

Since we are finding f(-4), we use the first function since -4 is less than -2.

f(-4) = (-4) + 4 = 0

Therefore, the answer is C.

Write an expression for the baseball team’s Purchase.

Answers

Sorry I do not get what you are asking

anyone know the answers for the final exam for part one of algebra 2 on edg?

Answers

Answer:

just show the questions i will help

Step-by-step explanation:

complete the table below?

Answers

ABC = $425

Load = 0

Total Cost = $425

Sales Price = $850

Sales price ÷ total cost = 850/425

= 2%

DEF = $600

Load = $375

Total Cost = $975

Sales Price = $1200

Sales Price ÷ Total cost = 1200/975

= 1% (Nearest 1%)

Must click thanks and mark brainliest

a number t is less than 7

Answers

Answer:

6 or 5 or 4...........

Step-by-step explanation:

Answer:

x=N :x<7

Step-by-step explanation:

123456

hope it's helpful

(Kind of urgent!) Using the figure below, find the value of a. Enter your answer as a simplified radical or improper fraction (if necessary)

Answers

Answer:

15/4

Step-by-step explanation:

sin60 =z/15

z=15sin60 =(15√3)/2

cos30 =b/z

b = zcos30 = (15√3)/2 * √3/2 = 45/4

a = 15-b = 15-45/4 = 15/4

The value of a is 15/4

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

According to the given figure,

Here is a right triangle

Let, The hypotenuse = 15

perpendicular = z and base = 15 = a + b

⇒ sin60 = perpendicular/hypotenuse = z/15

⇒ z = 15sin60 = (15√3)/2

⇒ cos30 = base/hypotenuse = b/z

⇒ b = zcos30 = (15√3)/2 * √3/2 = 45/4

⇒ a + b = 15

Substitute the value of b in the above equation,

⇒ a = 15-b = 15-45/4 = 15/4

Hence, the value of a is 15/4.

Learn more about the right triangle here:

brainly.com/question/6322314

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What is 3x+8x=13+31?

Answers

Answer:

x = 4

Step-by-step explanation:

3x+8x=13+31

Combine like terms

11x =44

Divide by 11

11x/11 = 44/11

x = 4

The answer you are looking for is x=4.

Solution:

3x+8x=13+31

Combining and adding similar terms,

11x=44

Dividing both sides by 11,

So, therefore,

The final answer is x=4.

Which graph matches the exponential function f(x) = (3)x?

Answers

It is C if you plug in any x value into the equation

Find the value of x in each case:

Answers

<FIG=2x(Opposite angles)<FGI=x(Interior angles)

We know

Sum of two interior angles =exterior angle

[tex]\\ \sf\longmapsto 2x+x=3x[/tex]

[tex]\\ \sf\longmapsto 3x=3x[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

A factory used 99.19 kilograms of tomatoes to make 7 batches of pasta sauce. What quantity of tomatoes did the factory put in each batch?

Answers

Answer:

14.17 kilograms

Step-by-step explanation:

Find what quantity of tomatoes was in each batch by dividing the total amount of tomatoes by the number of batches:

99.19/7

= 14.17

So, the factory put 14.17 kilograms of tomatoes in each batch.

What is 3.24 ( 4 repeating) as a fraction?

Answers

Answer:

81/25

Step-by-step explanation:

change 3.24 into faction

324 over 100 because there are two decimal points .

simplfy into the smallest fraction

the answer is 81 over 25

a shopkeeper gains #1.75 by selling an article for #6.25. what is the percentage gain.​

Answers

Answer:

≈ 38.89%

Step-by-step explanation:

The cost is:

6.25 - 1.75 = 4.50

Percentage gain:

1.75/4.50*100% ≈ 38.89%

The number of hearing aids that needs to be produced and sold is??

Answers

Answer:

14.36 AND 9.89 ===> 14 or 10

Step-by-step explanation:

Y =  Ax2 Bx C

Enter coefficients here >>>  -4 97 -568

   

Standard Form: y = -4x²+97x-568    

-24.25 -12.125 147.015625 -588.0625 20.0625

Grouped  Form: No valid Grouping      

   

Graphing Form: y = -4(x-12.13)²+20.06    

     

Factored Form: PRIME    

   

Solution/X-Intercepts: 14.36 AND 9.89    

   

Discriminate =321 is positive, two real solutions    

   

VERTEX: (12.13,20.06)     Directrix: Y=20.13    

Helpp me plzzz im being timed

Answers

Above question
Slope = change in y / change in x
(2 different random point on the line)
Let’s point out 2 points: (0,3) and (6,0)
So slope = (3 - 0) / (0 - 6) = 3/(-6) = -1/2

Y-intercept is when x = 0, the line cross the y-axis at y = ?
So y = 3
Below question is farmiliar:
Slope = (30-50) / (0-6) = -20/(-6) = 10/3
Y-intercept = 30

17 x 35=56 over 76 hope it helps s

Which function describes this graph

Answers

Answer:

C.

Step-by-step explanation:

A P E X

A study of the effects of color on easing anxiety compared anxiety test scores of participants who completed the test printed on either soft yellow paper or on harsh green paper. The scores for five participants who completed the test printed on the yellow paper were 17, 19, 28, 21, and 1 8. The scores for four participants who completed the test on the green paper were 20, 26, 17, and 24. Using the .05 level, test the researcher's prediction that participants should have lower anxiety scores when taking the test on the yellow paper than when taking the test on the green paper. What is the research hypothesis

Answers

Answer:

H0 : μYellow = μGreen

H1 : μYellow < μGreen

Step-by-step explanation:

Let :

Yellow paper = μYellow

Green paper = μGreen

To test the hypothesis :

The null hypothesis is will state that there is no difference in mean of anxiety scores obtained for test taken of yellow and green papers

H0 : μYellow = μGreen.

The alternative hypothesis is the opposite of the null and it is to the left, where we want to test if the anxiety score is lower when take on a yellow paper

H1 : μYellow < μGreen

The 3rd and 6th term of a geometric progression are 9/2 and 243/16 respectively find the first term, common ratio, seventh term​

Answers

Answer:

Hello,

Step-by-step explanation:

[tex]Let\ (u_n)\ the\ geometric\ progression.\\\\r\ is\ the\ common\ ratio.\\\\u_3=u_0*r^3\\u_6=u_0*r^6\\\\\dfrac{u_6}{u_3} =r^3=\dfrac{\frac{243}{16} }{\frac{9}{2} } =\dfrac{27}{8} =(\frac{3}{2} )^3\\\\\boxed{r=\dfrac{3}{2} }\\\\\\u_3=u_1*r^2 \Longrightarrow\ u_1=\dfrac{u_3}{r^2} =\dfrac{\frac{9}{2} }{(\frac{3}{2^2}) } =2\\\\\\u_7=u_6*\dfrac{3}{2} =\dfrac{729}{32}[/tex]

The object of a popular carnival game is to roll a ball up an incline into regions with different
values. The probability that Angus will get 100 points in a roll is 40%, 200 points is 35%, and
300 points is 25%. Find the expected value, E(X), of a roll.
O 185
O 200
O 400
O 150

Answers

The expected value, E(x) of the given observation is 185

The expected value is the mean of the overall observed value or random value. In other words, it is the average of the observed values.

The given parameters can be represented as:

[tex]\begin{array}{cccc}x & {100} & {200} & {300} \ \\ P(x) & {40\%} & {35\%} & {25\%} \ \end{array}[/tex]

The following formula calculates the expected value:

[tex]E(x) =\sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 100 * 40\% + 200 * 35\% + 300 * 25\%[/tex]

[tex]E(x) = 40 + 70 + 75[/tex]

[tex]E(x) = 185[/tex]

Learn more about expected values at:

https://brainly.com/question/16726343

90units needed 8 units per case what's the #of cases & # of additional units

Answers

Answer:

# of cases: 11

Additional units: 2

Step-by-step explanation:

If each case can hold 8 units, and we want to find the total # number of cases, we have to divide the # of units (8) for one case by the total # units (90).

As you can see, after dividing by 8, we have a total of 11 cases and a remainder of 2 units. The remainder will be the # of additional units because we cannot have another case filled with 8 units.

Start with the number 2380.
Divide by 10,
The 8 will end up in the _____ place.

Answers

Answer:

The 8 will end up in the ones place.

Step-by-step explanation:

If you want to divide 2380 by 10… sry gtg

The 8 will end up in the "ones place".

How can we interpret the division?

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to find the 8 will end up in which place

A negative divided by a negative is positive, then;

2380/ 10 = 238

Therefore, The 8 will end up in the _ ones_ place.

Learn more about division here:

brainly.com/question/26411682

#SPJ2

The total number of branches in a tree diagram will be which of the following values?

the probability of an event occurring
the denominator of a probability
the numerator of a probability

Answers

Answer:

The total number of branches = total possibilities = the denominator of a probability.

So the second choice is correct.

Let me know if this helps!

Answer:

Step-by-step explanation: answer B (the denominator of a probability)

A right pyramid with a square base has
volume of 252 cubic centimeters. The
length of one of the sides of its base is 6
centimeters. Rounded to the nearest
centimeter, what is the vertical height of
the pyramid?

Answers

Hey there!

A right pyramid with a square base just means that it isn't slanted all funny. If you create a triangle with a point on one of the edges of the base, the center of the base, and the top of the pyramid, it would be a right triangle.

To find the volume of a right pyramid, you just take the base area, multiply it by the height, and then divide by three.

However, we are looking for the height. We have been given, so we will just go backwards.

252×3=756 (multiply instead of divide)

6×6=36 (base is a square, so you just square 6. This is our base area)

756/36=21

So, the vertical height of the pyramid is 21 cubic centimeters.

Have a wonderful day! :D

1. Find the 4th term for the sequence with formula tn= n² + 1

Answers

Answer:

17

Step-by-step explanation:

T4 = 4² + 1

T4 = 4² + 1 = 17

Yip yip that's all

i need help on 8-9 plss :))

Answers

Answer:

8. SU = 24

9. TU = 16√3

Step-by-step explanation:

Recall: SOH CAH TOA

8. Reference angle (θ) = 30°

Opposite = 8√3

Adjacent = SU

Apply TOA,

Tan θ = Opp/Adj

Substitute

Tan 30° = 8√3/SU

Tan 30° × SU = 8√3

SU = 8√3/Tan 30°

SU = 8√3/(1/√3) (tan 30° = 1/√3)

SU = 8√3*√3/1

SU = 8*3

SU = 24

9. Reference angle (θ) = 30°

Opposite = 8√3

Hypotenuse = TU

Apply SOH,

Sin θ = Opp/Hyp

Substitute

Sin 30° = 8√3/TU

Sin 30° × TU = 8√3

TU = 8√3/sin 30°

TU = 8√3/(½) (sin 30° = ½)

TU = 8√3 × 2/1

TU = 16√3

The gcf of two numbers is 3 and their lcm is 180, if one of the numbers is 45 then found the second number

Answers

Answer:

answer is 12

Step-by-step explanation:

gcf = 3

lcm = 180

let 45 be y

let unknown be X

to get x

X=( lcm * gcf) / y

X=(180*3)/45

X=(540)/45

X=12

the other number is 12

In GeoGebra, display the slope of AB and the slope of the perpendicular line passing through C. Use this to verify your responses in parts B and C. Then move points A, B, and C on the grid to several different locations, and record the slopes of the two lines and the coordinates of A, B, and C.

Answers

Answer:

plato screenshot!

Step-by-step explanation:

I don't personally know *how* to find the answers, but here's the screenshot of the suggested answer on Plato

Answer:

A B Slope of  C Slope of Line Through C

(−5,4) (−1,−1) −1.25 (1,2) 0.8

(−5,4) (−3, 5) 0.5 (−2, 1) −2

(−4, 1) (−3, 5) 4 (−2, −2) −0.25

(−5, −2) (−1, 1) 0.75 (−4, 3) −1.33

(−5, −2) (1, −1) 0.17 (−3, 1) −6

Step-by-step explanation:

that way you can copy and paste each one but Plato

Change the word phrase to an algebraic expression. Use x as the variable to represent the number.
16 subtracted from a number

Let x = the number.


16 subtracted from a number can be written as…

Answers

Answer:

I think the answer is

x-16

since 16 is subtracted from x.

I hope this helps

What is the probability of rolling a 2 and 3 with 2 die

Answers

1/6 * 1/6 = 1:36
the probability of rolling a 2 is 1/6 and the probability of rolling a 3 is 1:6 to find the final probability you need to multiply the two
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