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andrew-mc [135]
3 years ago
8

Plz somebody help me i’ll give you 40 points

Mathematics
1 answer:
elena55 [62]3 years ago
6 0

Answer:

-3+-2

Step-by-step explanation:

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Please help me with the below question.
Snezhnost [94]

6a. By the convolution theorem,

L\{t^3\star e^{5t}\} = L\{t^3\} \times L\{e^{5t}\} = \dfrac6{s^4} \times \dfrac1{s-5} = \boxed{\dfrac5{s^4(s-5)}}

6b. Similarly,

L\{e^{3t}\star \cos(t)\} = L\{e^{3t}\} \times L\{\cos(t)\} = \dfrac1{s-3} \times \dfrac s{1+s^2} = \boxed{\dfrac s{(s-3)(s^2+1)}}

7. Take the Laplace transform of both sides, noting that the integral is the convolution of e^t and f(t).

\displaystyle f(t) = 3 - 4 \int_0^t e^\tau f(t - \tau) \, d\tau

\implies \displaystyle F(s) = \dfrac3s - 4 F(s) G(s)

where g(t) = e^t. Then G(s) = \frac1{s-1}, and

F(s) = \dfrac3s - \dfrac4{s-1} F(s) \implies F(s) = \dfrac{\frac3s}{\frac{s+3}{s-1}} = 3\dfrac{s-1}{s(s+3)}

We have the partial fraction decomposition,

\dfrac{s-1}{s(s+3)} = \dfrac13 \left(-\dfrac1s + \dfrac4{s+3}\right)

Then we can easily compute the inverse transform to solve for f(t) :

F(s) = -\dfrac1s + \dfrac4{s+3}

\implies \boxed{f(t) = -1 + 4e^{-3t}}

6 0
2 years ago
Write a decimal to show how much of the grids are shaded.<br><br><br><br>plz help me​
NikAS [45]

Answer:

1a. 1.5

1b. 0.38

Step-by-step explanation:

a.

one full grid is full (1) and half a grid is full (0.5)

b.

there are 100 squares and 38 of them are filled in,so you divide 38 by 100 which is 0.38

4 0
3 years ago
An example of exponential growth is y=2(1/3)^x<br> True<br> False
Lemur [1.5K]

Answer:

False

Step-by-step explanation:

Since the b value (the value inside the parentheses) is less than 1, it represents exponential decay.

8 0
3 years ago
Chloe received 86% on her first test, a 47/50 in her next test, and a 0.89 on her third test. List her percentages in order from
Mumz [18]

Answer:

  84%, 86%, 89%

Step-by-step explanation:

The three numbers, expressed as percentages, are ...

  • 86%
  • (47/50)×100% = 84%
  • 0.89×100% = 89%

Smallest to largest, they are 84%, 86%, and 89%. In the original form, they are 47/50, 86%, and 0.89.

7 0
4 years ago
How many toys were stuffed animals
Umnica [9.8K]

Answer:

It would be the first one.

Step-by-step explanation:

The way you figure it out is that it said that there was a total of 80 stuffed animals, so model B is out. Then, you change the percent into a decimal by moving the decimal point over to the right 2 times and you get 0.30. Finally, you multiply 80 by 0.30 and you get 24 stuffed animals.

4 0
3 years ago
Read 2 more answers
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