Please take a look at the picture

Take the Laplace transform of both sides:

L[y'' - 4y' + 8y] = L[δ(t - 1)]

I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :

(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]

s²Y - 4sY + 8Y = exp(-s)

(s² - 4s + 8) Y = exp(-s)

Y = exp(-s) / (s² - 4s + 8)

and complete the square in the denominator,

Y = exp(-s) / ((s - 2)^2 + 4)

Recall that

L⁻¹[F(s - c)] = exp(ct) f(t)

In order to apply this property, we multiply Y by exp(2)/exp(2), so that

Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)

Then taking the inverse transform, we have

L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]

L⁻¹[Y] = exp(-2) exp(2t) L⁻¹[exp(-s) / (s² + 4)]

L⁻¹[Y] = exp(2t - 2) L⁻¹[exp(-s) / (s² + 4)]

Next, we recall another property,

L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)

where F is the Laplace transform of f, and u(t) is the unit step function

[tex]u(t) = \begin{cases}1 & \text{if }t \ge 0 \\ 0 & \text{if }t < 0\end{cases}[/tex]

To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is

L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)

Then we find

L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))

and so we end up with

y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)

A variable is a letter in the equation that can be replaced by a number.

In the equation shown the variable is the letter z.

Answer: A) z

[tex] \huge \bf༆ Answer ༄[/tex]

The domain of given function is All real numbers

[tex] \sf \: f(x) = { \bigg( \dfrac{1}{4} \bigg) }^{x} [/tex]

For each value of x the function is defined.

Example -

The value is [tex] \sf\frac{1}{4}[/tex]

The value is 4

[tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]

Answer:

a. P(male) = 0.4

b. P(no sport and male) = 0.1

c. Unclear question (isn't it the same as b.?)

Step-by-step explanation:

The data below is what I've worked according to, which isn't very clear from the question so the answers are only correct if this is the correct table of data;

[tex]\left[\begin{array}{ccc}&No \ Sports&Sports\\Female&10&32\\Male&7&21\end {array}\right][/tex]

a.

[tex]P(male) = \frac{7 + 21}{70} \\\\ = \frac{28}{70} \\\\ = \frac{2}{5}[/tex]

b.

Using the tree diagram in the picture;

[tex]P(no \ sport \ and \ male) = \frac{2}{5} * \frac{1}{4} \\\\ = \frac{1}{10}[/tex]

Answer:

Q (-4, -2); 2 units; Q' will be above the x-axis; 2 unites; no; yes, the y coordinates are multiplied by -1; Q' (-4, 2); R' (-2, 2), S' (1, 5), T' (-2, 5);

Step-by-step explanation:

even after a reflection over the x-axis, each points distance from the x-axis will stay the same

the x-coordinates don't change because the distance from the y-axis stays the same

the picture below shows points of Q'R'S'T', just connect the vertices

Answer: Yes

Step-by-step explanation:

A: 12 minutesAnswer to B: 36 minutesAnswer to C:

Answer:

y=4x-17

Step-by-step explanation: Distribute the 4(x-5)

4x-20

Then add three to both sides

y=4x-17

Answer:

2.25

Step-by-step explanation:

m = 9 / 4 = 2.25

points belong to an increasing, linear function.

Equation: y = 2.25x + 2.75.

BRAINLIEST?

Hello! :)

√99=9.95...

π²=9.9

9.8888...

So I think the numbers should be written like this:

9.8888, √99, π²

Hope it helps!

~Just a determined gal

[tex]MysteriousNature[/tex]

Answer:

Step-by-step explanation:

x = 127

y = 5

z = 31

Answer:

51/12 - 23/4

find the LCM of 12 and 4

51-69/12= -18/12= -9/6 = -3/2 = -1.5

Answer:

The slope is:

[tex] \binom{1}{2} [/tex]

In slope-intercept form the equation is:

[tex]y = \binom{1}{2} x - 3[/tex]

Answer:

14 sections

Step-by-step explanation:

2 1/3=7/3

7/3 divided by 1/6 is nothing but 7/3*6, which is just 14

Answer:

b=114°

.....................

c=43°

Answer:

A) 87 degrees

B) 114 degrees

C) 43 degrees

Answer:

14 - (-10) = 24Step-by-step explanation: 14 - (-10) (-10)= 10    14 + 10 = 4

Answer:

is he a business man or something

Answer:

The correct answer is (c) 30°

Hope it helps

Reduce the expression, if possible, by cancelling the common factors.

Exact Form: [tex] \:- \frac{3}{10} \\ [/tex]

Decimal form[tex] \: \:- 0.3[/tex]

Answer:

7/8

Step-by-step explanation:

7/16×2=7/16×2/1

          =14/16

          =7/8

Answer: C

Step-by-step explanation: Brainliest please

Answer:

rude customers and complaints

Answer:

Ignorant managers.

Step-by-step explanation:

Ignore them

Find somewhere else to move.

Answer:

509.6 calories

Step-by-step explanation:

196+196=392 calories

10g of bacon=19.6 calories

60g of bacon=19.6×6=117.6 calories

392+117.6=509.6 calories

Answer:

Step-by-step explanation:

$760(1.023) = $777.48

Answer:

I will what is the question?

Answer:

What is the question lol

Step-by-step explanation:

I can try to help!

Answer:

4/12 > simplified to > 1/3

Step-by-step explanation:

hope it helps

Answer:−0.6

Step-by-step explanation:

(-1).3/5=−0.6

F(3) occurs when x =3. So lets plug 3 into our equation.

[tex]f(3) = -4(3)^2 + 4(3)-4\\f(3) = -4(9) + 12- 4\\f(3) = -36 + 12- 4\\f(3)= -28[/tex]

F(3) = -28

I hope this helps! :)

Answer:

8/25.

Step-by-step explanation:

As a fraction it is 32/100 but simplified is 8/25 :)