Add. (f + 3) + (2f + 8)

I suppose you're asking about the inverse Laplace transform of

[tex]F(s)=\dfrac4{(s-3)(s-2)}[/tex]

by way of the convolution theorem.

The theorem itself says that

[tex]\mathscr L^{-1}\{A(s)B(s)\}=(a*b)(t)[/tex]

where [tex]A(s)[/tex] and [tex]B(s)[/tex] are the Laplace transforms of [tex]a(t)[/tex] and [tex]b(t)[/tex], respectively.

Let [tex]A(s)=\frac1{s-3}[/tex] and [tex]B(s)=\frac1{s-2}[/tex]. Then

[tex]a(t)=\mathscr L^{-1}\left\{\dfrac1{s-3}\right\}=e^{3t}[/tex]

[tex]b(t)=\mathscr L^{-1}\left\{\dfrac1{s-2}\right\}=e^{2t}[/tex]

So we have

[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=e^{3t}*e^{2t}[/tex]

Convolution is defined as

[tex](a*b)(t)=\displaystyle\int_0^t a(t-\tau)b(\tau)\,\mathrm d\tau[/tex]

The convolution of [tex]e^{3t}[/tex] and [tex]e^{2t}[/tex] is

[tex]e^{3t}*e^{2t}=\displaystyle\int_0^t e^{3(t-\tau)}e^{2\tau}\,\mathrm d\tau[/tex]

[tex]=\displaystyle e^{3t} \int_0^t e^{-\tau}\,\mathrm d\tau[/tex]

[tex]=e^{3t}(1-e^{-t})=e^{3t}-e^{2t}[/tex]

We end up with

[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=\boxed{4(e^{3t}-e^{2t})}[/tex]

Answer:

x = -3 + 2 i or x = -3 - 2 i

Step-by-step explanation:

Solve for x:

x^2 + 6 x + 13 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 13 from both sides:

x^2 + 6 x = -13

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 9 to both sides:

x^2 + 6 x + 9 = -4

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x + 3)^2 = -4

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x + 3 = 2 i or x + 3 = -2 i

Hint: | Look at the first equation: Solve for x.

Subtract 3 from both sides:

x = -3 + 2 i or x + 3 = -2 i

Hint: | Look at the second equation: Solve for x.

Subtract 3 from both sides:

Answer: x = -3 + 2 i or x = -3 - 2 i

Answer:

620000000

Step-by-step explanation: 6.2 10^8

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form,62*10^5 is the scientific notation of 6,200,000 kilograms

We need to express 6,200,000 kilograms using scientific notation in kilograms.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

We need to express 6,200,000 kilograms into scientific notation

The format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10.

Now 62*10^5 is the required scientific notation.

Therefore 62*10^5 is scientific notation of 6,200,000 kilograms.

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Answer:

Step-by-step explanation: 14 11/12 rounds up to 15 and 3 1/6 is closer to 3 so the answer would be 18

Answer: 0.44

Step-by-step explanation:

Answer:

For me I think 216 diapers for 39.98 is the best option

Step-by-step explanation:

Get the price of one diaper in each offer

216 = $39.98

1= ?

1×39.98÷216=0.19

Option 2

88=24.99

1 =?

1×24.99÷88=0.28

So I prefer buying 1 diaper for$0.19 and get 216 of them for $39.98 rather than buying 1 diaper for $0.28 and get 88 of them for $24.99

Answer:

f(-3) = 10

Step-by-step explanation:

Simply plug in x as -3 to find f(-3):

f(-3) = -6(-3) - 8

f(-3) = 18 - 8

f(-3) = 10

Answer:

274

Step-by-step explanation:

113+88+73

Answer:

a

Step-by-step explanation:

just did it

Answer:the 2nd one is the answer it's easy I just did it :

Answer:

Step-by-step explanation:

[tex]r=\frac{-28}{56}=-\frac{1}{2}\\a_{n}=\frac{-1}{2}a_{n-1}[/tex]

The recursive formula for the sequence is aₙ = (-1/2) * aₙ₋₁

A sequence of numbers such that the consecutive term is increasing or decreasing by a fixed ratio is called a geometric series.

The standard equation for geometric series is

Tₙ = a₁ rⁿ⁻¹

The formula above represents the explicit formula to determine the nth term of the sequence.

The recursive formula is used to determine the nth term when (n-1) th term is given.

The geometric sequence is,

56, -28, 14, -7,.................

The first term of the sequence is 56

The common ratio is determined by taking the ratio of the second term to the first term.

r = -28/56 = -1/2

The recursive formula is represented by,

aₙ = r * aₙ₋₁

aₙ = (-1/2) * aₙ₋₁

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The correct answer is B. $ 19.25

Explanation:

To calculate the hourly rate of pay, first, let's calculate the total number of hours Kai worked, and then divide the total earned into the number of hours.

6 hours x 4 days = 24 hours

8 hours x 1 day = 8 hours

24 hours + 8 hours = 32 hours

This shows Kai worked a total of 32 hours. Now to find the hourly rate of pay, follow this procedure:

$616 (total earned) ÷ 32 hours = $19.25 each hour

This means Kai earns $19.25 for each hour of work and therefore the hourly rate of pay is $19.25.

Answer:

B

Step-by-step explanation:

Answer:

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Step-by-step explanation:

Step-by-step explanation:

10x2-10x+2

20-10x+2

22-10x

8x2+7-7

16+0

16

I'm confused so I add together cuz why not?

16+22-10x

28-10x

Answer: undefined; vertical line

Step-by-step explanation:

To find the slope, you use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

[tex]m=\frac{1-(-7)}{6-6} =\frac{8}{0}[/tex]

The slope is undefined because you cannot divide anything by 0.

The graph of the line is a vertical line at x=6. We know this because the points are both at x=6, with different y-values.

Answer:

Domain:

-∞<x<∞, or (-∞,∞) in interval notation

Range:

-∞<f(x)<∞, or (-∞,∞) in interval notation

Step-by-step explanation:

It’s infinite both ways, so:

Domain:

-∞<x<∞, or (-∞,∞) in interval notation

Range:

-∞<f(x)<∞, or (-∞,∞) in interval notation

Answer: the product is always positive.

Step-by-step explanation: Rule 1: The product of a negative integer and a positive integer is a negative integer. Rule 2: The product of two positive integers or two negative integers is a positive integer. That means if you multiply two OF the same sign numbers, the product is always positive.

Answer: No because the product of a positive integer and a negative integer is always negative.

Answer:

8.9%

Step-by-step explanation:

sales tax rate (in percentage) = 409.40÷4600*100=8.9%

Answer: 85 units

Step-by-step explanation:

x^2 +35x + 35 = 10235

-10235 on both sides

x^2 + 35x -10200

Now Factor

( x - 85 ) ( x + 120 )

Now plug in for x using 85 or -120

(85)^2 + 35(85) + 35

7225 + 2975 + 35 = 10235

So 85 is the right answer

Answer:

12/37

Step-by-step explanation:

Answer:

3840

Step-by-step explanation:

Hope this helps you out

Answer:

The numerical length of UW is 27

Step-by-step explanation:

Answer:She will count the cookies by 2's

Step-by-step explanation:

the answers 16 if you need an explanation then ill comment one.....!

Answer:

16

Step-by-step explanation:

8 :2 ×(2 +2) =

4 ×4 =

16

Answer:

f(1)=5x-13=-8

Step-by-step explanation:

5-13=-8

or

f(1)=5x-13=-8

Answer:

y = 2x

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Find slope m

2x - y = -4

-y = -2x - 4

y = 2x + 4

Since the 2 lines are parallel, they have the same slope.

Step 2: Define variables

Slope m = 2

Origin (x-int and y-int) (0, 0)

Step 3: Write parallel linear equation

y = 2x + 0

y = 2x

Answer:

complement of set A={2,4,6}

hope it helps

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