Mathematics College

Chapter 8 Practice:

Compute the inverse Laplace transform of
[tex]F(s) = \frac{s² +1}{(s-1)(s+1)(s - 2)} [/tex]

(​Cover up method)

Chapter 8 Practice: Compute The Inverse Laplace Transform Of [tex]F(s) = \frac{s +1}{(s-1)(s+1)(s - 2)}

Answers

Answer 1

Continue the given solution and solve for B and C :

[tex](s+1)\dfrac{s^2+1}{(s-1)(s+1)(s-2)} = (s+1)\left(-\dfrac1{s-1} + \dfrac B{s+1} + \dfrac C{s-2}\right)[/tex]

[tex]\dfrac{s^2+1}{(s-1)(s-2)} = -\dfrac{s+1}{s-1} + B + \dfrac{C(s+1)}{s-2}[/tex]

[tex]s=-1 \implies B = \dfrac13[/tex]

Similar steps lead to C = 5/3, and so

[tex]\dfrac{s^2+1}{(s-1)(s+1)(s-2)} = -\dfrac1{s-1} + \dfrac13\times\dfrac1{s+1} + \dfrac53\times\dfrac1{s-2}[/tex]

Now take the inverse transform of each term.

[tex]Y(s) = -\dfrac1{s-1} \implies y(t) = -e^t L^{-1}\left\{\dfrac1s\right\} = -e^t[/tex]

[tex]Y(s) = \dfrac13\times\dfrac1{s+1} \implies y(t) = \dfrac{e^{-t}}3 L^{-1}\left\{\dfrac1s\right\} = \dfrac{e^{-t}}3[/tex]

[tex]Y(s) = \dfrac53\times\dfrac1{s-2} \implies y(t) = \dfrac53e^{2t} L^{-1}\left\{\dfrac1s\right\} = \dfrac{5e^{2t}}3[/tex]

Then the inverse transform of F(s) is

[tex]F(s) = \dfrac{s^2+1}{(s-1)(s+1)(s-2)} \implies f(t) = -e^t + \dfrac{e^{-t}+5e^{2t}}3[/tex]

[tex]\implies f(t) = \boxed{\dfrac{5e^{3t} - 3e^{2t} + 1}{3e^t}}[/tex]

Related Questions

A circular table has a radius 56cm. A tablecloth covers the table. The edge of the cloth is 10cm below the tabletop. What is the area of the tablecloth?

Answers

Answer:

13,363.84 square cm

Step-by-step explanation:

For this question,

The circle table has a radius of 56 cm and the height of the edge of the cloth is 10cm(height) below the tabletop, which is a rectangle

We need to find out the area of a circle, Then the area of the rectangle.

Area of circle FORMULA= πr^2 | Area of rectangle FORMULA = l * h

πr^2

3.14 * 56 * 56 = area of circle = 9,847.04

[(2*3.14*56)Perimeter of circle which is also length of rectangle] * 10 = area of rectangle = 3516.8

9,847.04 + 3516.8 = 13,363.84

he slope of the line that contains the points (1, -1) and (2, 3) is 4. What is the y-intercept? A. 5 B. 4 C. -4 D. -5

Answers

Answer:

D

Step-by-step explanation:

Equation of a line given by the two-point form is:

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

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

(y+1)/(x-1) = -4 / -1

y+1 = 4(x-1)

y = 4x-4-1

y = 4x - 5

y-intercept at x=0 is -5

Answer is D.

Solution:

We know that:

Given points: (1, -1) and (2, 3)Slope = 4

Picking any point:

=> (1, -1)

Using point slope form:

y - y₁ = m(x - x₁)y - (-1) = 4(x - 1)y + 1 = 4x - 4y = 4x - 4 - 1y = 4x - 5

Comparing the equation with the formula:

y = (m)x + (b) and y = (4)x + (-5)

⇒ m = slope = 4

⇒ b = y-intercept = -5

model each two step operation by drawing algebra tiles.
3m + 5 = 8

Answers

The answer for 3m+5=8 is m=5

Help Me On This Plss!!​

Answers

Step-by-step explanation:

Hello, first you have to substitute x=-3 in 12-3x which is 12-3(-3)= 12+9=21. So number 1 is 21. You continue like that till you finish.

2. You substitute x=-3 in y=x^2 +3x - 2. So that would be y= - 3^2+3(-3)-2. Which is 9+(-9)-2 which will be 9-9-2=-2. So the first blank space for number 2 is - 2.

What is the volume of the figure below?

30ft^3 60 ft^3 90ft ^3

Answers

Answer:

60 ft^3

Step-by-step explanation:

assuming the entire height is nine

4.5 * 4 * 5 /3=30

30*2=60

A local screen-printing company sells T-shirts at various prices, in dollars, depending upon how many T-shirts are bought at the time. The piecewise function below represents their pricing structure, where n is the number of T-shirts purchased. The school volleyball team purchased 20 shirts.
How much did the volleyball team spend on shirts?
$480
$180
$220
$260

Answers

Answer:

i think it’s 260 too^^

Step-by-step explanation:

The total Amount Spent by the volleyball team spend on shirts from the given piecewise function is; $260

How to work with Piecewise Function?

From the given piecewise function, we see that;

y = {13n, 0 < n ≤ 20

y = {11n, 20 < n ≤ 50

y = {9n, n > 50

We are told that the volleyball team purchased 20 shirts.

From the first piecewise function, we can deduce that;

Amount Spent = 13n = 13 * 20

Amount Spent = $260

Read more about Piecewise function at; https://brainly.com/question/4494373

- x + 3y = 11
x - 5y = -17




Ans. (x.y) = ( . )

Answers

Answer:

(x,y)=(-2,3)

Step-by-step explanation:

please help i have 20 min

Answers

Answer:

12, 20, 28

Step-by-step explanation:

The equation s=r+4 shows that no matter the value of r, s will always be 4 more. This means that whatever number is in the r-value of the table, you need to add 4 to it to get your s-value. So when r=8, s=12 and so on.

What is 88 x 9 - 60- 80+ 200

A: 792
B: 800
C: 852
D: 300

Answers

Answer:

852

Step-by-step explanation:

Answer:

852

Step-by-step explanation:

Using PEMDAS:

Multiply the numbers

88 × 9 - 60 - 80 + 200

792 - 60 - 80 + 200

Subtract the numbers

792 - 60 - 80 + 200

652 + 200

Add the numbers

652 + 200

= 852

[RevyBreeze]

i messed up on last picture pls help 5 star rating

Answers

Answer:

5b + 4 = 89

b = 17

Step-by-step explanation:

Work shown in picture! Hope this helped.

you and 4 friends go to a restaurant to eat. the bill comes to a total of $110 before tax and tip. you want to leave a 20% tip for the $110 bill. you must also pay an 8.25% tax on the $110 bill. after you include the tax and tip, what is the price of the bill?

Answers

First,

To find Value for tip=20/100×110=$22To find value for tax=8.25/100×110 = 825/100×110=$907.5Add value of tip to tax=$907.5+$22=$929.5Add to original billFinal answer=$1039.5

A circular garden has a diameter of 4 m. What is the area of the garden? Use 3.14 for TT.

Answers

Answer:

12 56 m²

Step-by-step explanation:

Radius r = 4/2 = 2 m

Area = π(2)² = 3.14 * 4 = 12 56 m²

A school wants to buy a chalkboard that measures 4 feet by 6 feet. The chalkboard costs $7.21 per square foot. How much will the chalkboard cost?

Answers

Area of chalkboard = 4 feet x 6 feet = 24 square feet.


Total cost = 24 square feet x $7.21 per square foot = $173.04


Answer: $173.04

A local card store marks up the price of all the items they sell by 15%. If the store buys photo albums for $7.00 each, at what price will they sell them?

Answers

Answer:

$8.05

Step-by-step explanation:

This answer is found by making an equation that represents this word problem which uses the formula %(decimal form)(original price).

Using this formula, the equation representing this word problem is 0.15(7).

When evaluated, gives us $1.05 (the mark up).

Then, this must be added to the original price using the formula (original price+mark up);

1.05+7.00

Answer= $8.05

A right triangle has legs of length 121 cm and 134 cm.

What is the length of the hypotenuse of the right triangle?

Enter the answer, rounded to the nearest tenth.

Answers

Answer: 180.5

Step-by-step explanation:

[tex]\sqrt{121^{2}+134^{2}} \approx 180.5[/tex]

QUESTION ON PIC THANK YOU FOR ANSWERING

Answers

Answer:

Step-by-step explanation:

Rhombus: All sides are congruent,  2 pairs of parallel sides,

Parallelogram: 2 pairs of parallel sides,

Square: All sides are congruent,  2 pairs of parallel sides, four right angles

Help I’m willing to give out extra point for the help that I need for these ?

Answers

1/3 because 4 to 12 can be written as 4/12 which can be simplified to 1/3
And 1/3 of 6 is two and if you reverse the process you would 4 into 12 three times and then find what goes into 6 three times with is 2

A TV can be purchased from the manufacturer for $250. An online retailer has a markup of 30%, and a superstore has a standard markup of 40%.

(a) What is the price of the TV when purchased online?

(b) What is the price of the TV when purchased at the superstore?

(c) Which has the better deal – the online retailer or the superstore?

Answers

Answer:

(a)  325

(b)  350

(c) The online retailer has a better deal.

Step-by-step explanation:

250 * 130% = 325

25- * 140% = 350

325 is less than 350, so its the better deal.


A line passes through the point (-10,-7) and has a slope of
2 Write an equation in slope-intercept form for this line.

Answers

Answer:

y-(-7) = 2(x-(-10))

Step-by-step explanation:

Point slope form: y-y1 = m(x-x1)

yx-9 that is the answer for the equation

Blank - 3/10 = 1/5 What is the blank number

Answers

Answer:

1/2

Step-by-step explanation:

Let's consider the number we want is x

x-3/10=1/5

On both sides of the equation, if we substract (or add) a certain number, say 3/10, the equality relation still exists.

That is x-3/10+3/10=1/5+3/10

Then x=1/5+3/10

You see 1/5+3/10=2/10+3/10=1/2

So x=1/2

is f(x)=3x-2 and g(x)=-x+1 what is f(f(x))

Answers

Answer:

if f(x)=3×-2and g(x)=-x+1then so f=3×andx=-2 so the answer is 3×3×-2

Yeah..I got another one but please hurry :’)

Answers

Answer:

6root2

Step-by-step explanation:

3-1,5-1. (2,4)

R=root(4+16). =6root 2

inequality shown by the graph.! please help me

Answers

Answer: y ≥ -1/3x + 2

Step-by-step explanation:

y - intercept = 2

To find the slope, subtract the given points:

2 - 4

_____ = -2/6

0 - (-6)

Simplify:

-2/6 = -1/3

The line is solid, which means solutions are included on the boundary line.

y ≥ -1/3x + 2

If the first common multiple of two numbers is
6, find the fourth common multiple

Answers


24

6 x 4 = 24


And to check it is safe to assume the two numbers are 2 and 3

2 4 6 8 10 12 14 16 18 20 22 24

3 6 9 12 15 18 21 24


6 is the first common multiple, 12 is second, 18 third and 24 fourth.

A brainliest would be appreciated!!

Hope this helped!

Answer:

The first common number are 2 and 3

their comnon multiple is 6

So, the fourth number will be 24 because

multiple means we should multiply 4*6 it will be 24.

Please solve no c and 7 a . ​

Answers

c) 12 / 4 = 3 (scale factor)
2 x 3= 6cm

7) no figures are given but the two small lines on the triangle represents the fact that the triangle is an isosceles, this means that abc will equal to abd

square root of 0.0645 divided by 0.0082

Answers

Answer:

30.9717685346

Step-by-step explanation:

16. If you have $60, for how many hours can you rent a canoe?​

Answers

Well how much many is it per hour

Solve the inequality 7y-35<2(x-5)

Answers

Answer:

x < 5

Explanation:

 7*x-35-(2*(x-5))<0

 (7x - 35) -  2 • (x - 5)  < 0

Pull out like factors :

  5x - 25  =   5 • (x - 5)

 5 • (x - 5)  < 0

Divide both sides by  5

Add  5  to both sides

x < 5

Cate randomly samples the out-of-state tuition and fees for 25 public universities and found a mean of $20,340 with a standard deviation of $2,494. Using the alternative hypothesis that µ < $21,706, Cate found a z test statistic of -2.74. Given the data provided, what is the p-value of the z-test statistic?

Answers

Answer:

0.003

Step-by-step explanation:

Recall for a p-value, it must be a value that is as extreme and more extreme than the test statistics. If we go to the chart for the z-score and go to the row of -2.7 and to the column 0.04, we can see the value is 0.0031 or 0.003. Since the test is a one-tailed test (note that  is less than, "<"), this is the p-value.

NO LINKS!!! Please help me with this problem. Part 10​

Answers

Answer:

h = 1053 ft (to the nearest foot)

Step-by-step explanation:

The sum of the interior angles of a triangle is 180°

Therefore, the angle at the bottom vertex of the triangle is:

180 - 69.2 - 65.5 = 45.3°

Sine rule:

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

where A, B and C are the angles in a triangle, and a, b and c are the sides opposite those angles (e.g. side a is opposite angle A).

Now we can use the sine rule to calculate the length of the diagonal sides of the triangle.

Let a = the length of the right diagonal (the side with unknown length adjacent to angle 65.5°)

[tex]\dfrac{a}{\sin(69.2)}=\dfrac{880}{\sin(45.3)}[/tex]

[tex]\implies a=1157.353973...[/tex]

Now we can use the sine trig ratio to determine h:

[tex]\sin(65.5)=\dfrac{h}{1157.353973...}[/tex]

[tex]\implies h=1053.147292...[/tex]

Therefore, h = 1053 ft (to the nearest foot)

Answer:

  1053 feet

Step-by-step explanation:

We choose to solve this problem using the tangent relation. It relates an acute angle to the adjacent and opposite legs of a right triangle.

  Tan = Opposite/Adjacent

  Opposite = Adjacent × Tan

__

For this to be useful here, we need to know the angles at the bottom of the figure. The left-side angle is 90° -69.2° = 20.8°. The right-side angle is 90°-65.5° = 24.5°. The tangent relation tells us ...

  bridge left side + bridge right side = 880 ft

  h×tan(20.8°) +h×tan(24.5°) = 880 ft

  h = (880 ft)/(tan(20.8°) +tan(24.5°)) = (880 ft)/(0.37986 +0.45573)

  h ≈ 1053.147 ft

The bridge is about 1053 feet high.

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