A circle's radius is 25 inches.

Use theorem 7. 4. 2 to evaluate the given laplace transform. do not evaluate the convolution integral before transforming. (writ

irga5000 [103]

With convolution theorem the equation is proved.

According to the statement

we have given that the equation and we have to evaluate with the convolution theorem.

Then for this purpose, we know that the

A convolution integral is an integral that expresses the amount of overlap of one function as it is shifted over another function.

And the given equation is solved with this given integral.

So, According to this theorem the equation becomes the

$\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{ \mathscr{L} (e^{-\tau} \cos \tau ) }{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{\frac{s+1}{(s+1)^2+1}}{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{1}{s}\left (\frac{s+1}{(s+1)^2+1} \right).$

Then after solving, it become and with theorem it says that the

$\mathscr{L} \left( \int_{0}^{t} f(\tau) d\tau \right) = \frac{\mathscr{L} ( f(\tau))}{s} .$

Hence by this way the given equation with convolution theorem is proved.

So, With convolution theorem the equation is proved.

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3 0

2 years ago

I need HELPPPPPPPPPPPPPPPPPPP

alex41 [277]

The Simplification of the following expression is;

m = -30/7
v = -8.8
x = 3
u = -2.49
a = -3/70

<h3>Simplification</h3>

7/8m - 4/7 - 5/6m = - 3/4

7/8m - 5/6m = -3/4 + 4/7

21m-20m/24 = -21+16/28

1/24m = -5/28

m = -5/28 ÷ 1/24

= -5/28 × 24/1

= -120/28

m = -30/7

4.3v + 10.75 - 4v = 8.11

0.3v = 8.11 - 10.75

0.3v = -2.64

v = -2.64/0.3

v = -8.8

9/7 + 9/7x - 6/7x =0

9/7x - 6/7x = - 9/7

(9-6)x /7 = 9/7

3/7x = 9/7

x = 9/7 ÷ 3/7

= 9/7 × 7/3

= 9/3

x = 3

6.9u - 2 - 3.2u - 10 = 2.8

3.7u = 2.8 - 12

3.7u = -9.2

u = -9.2/3.7

u = -2.49

8/5 = - 4a + 7/5 - 2/3a

8/5 - 7/5 = -4a - 2/3a

8-7/5 = -12a-2a/3

1/5 = -14/3a

a = 1/5 ÷ -14/3

= 1/5 × -3/14

a = -3/70

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7 0

2 years ago

Find the perimeter of the figure to the nearest hundredth.

ArbitrLikvidat [17]

Answer:
50.274in

Explanation:

Half circle perimeter
9/2 = 4.5
2 * pi * 4.5 = 28.27433388230814

28.27433388230814 + 5 + 12 + 5 = 50.27433388230814

Answer = 50.27433388230814
Rounded to nearest hundredth = 50.274

I hope I helped. Brainliest would be appreciated

5 0

3 years ago

A culture started with 5000 bacteria after three hours it grew 6500 bacteria predict how many bacteria will be present after 13

charle [14.2K]

Answer:

15595 bacteria will be present after 13 hours.

Step-by-step explanation:

Continuous population growth:

The continuous population growth model, for the population after t hours, is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial population and r is the growth rate.

Started with 5000 bacteria

This means that $P(0) = 5000$

So

$P(t) = 5000e^{rt}$

After three hours it grew 6500 bacteria:

This means that $P(3) = 6500$ . We use this to find r.

$P(t) = 5000e^{rt}$

$6500 = 5000e^{3r}$

$e^{3r} = \frac{65}{50}$

$\ln{e^{3r}} = \ln{\frac{65}{50}}$

$3r = \ln{\frac{65}{50}}$

$r = \frac{\ln{\frac{65}{50}}}{3}$

$r = 0.0875$

So

$P(t) = 5000e^{0.0875t}$

How many bacteria will be present after 13 hours?

This is P(13). So

$P(13) = 5000e^{0.0875*13} = 15594.8$

Rounding to the nearest whole number

15595 bacteria will be present after 13 hours.

7 0

3 years ago

A recycling plant recycled 4.9 kg of paper and cardboard the first hour and 7.8 kg/h

Daniel [21]

Answer: R = {0kg, 59.5kg}

Step-by-step explanation:

When we have a function f(x) = y.

The set of the possible values of x is called the domain of the function, and the set of the possible values of y is called the range of the function,

In this case, we have that:

the plant recycled 4.9kg the first hour, and 7.8 kg per hour after.

So this function can be written as piecewise function, with one part for the first hour, and another part for the time after the first hour.

F(x) = 4.9kg*x if 0h < x ≤ 1h

F(x) = 4.9kg + 7.8kg/h*(x -1) if x ≥ 1h

We use (x - 1) for the second part because if x = 1 h, we must have the same result in both parts of the function.

Where x is the number of hours.

And we know that the domain is (0hours, 8 hours)

Then the minimum value of y will be:

F(0h) = 4.9kg*0h = 0kg.

And the maximum value in the range will be:

F(8h) = 4.9kg + 7.8kg*7 = 59.5kg

Then the range is:

R = {0kg, 59.5kg}

7 0

3 years ago