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lesya [120]
2 years ago
7

Can somebody solve this

Mathematics
1 answer:
Gemiola [76]2 years ago
4 0
The answer is 36
lmk if you need steps
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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
1 year ago
Me wit filtersssssssssssssss
N76 [4]

Answer:

Your cute. Keep being you!

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
A recipe for banana bread requires 3 cups of bananas for every 1 1/2 cups of sugar used. At this rate how many cups of sugar sho
mr Goodwill [35]

Answer:

The answer is 1 cup of sugar

Step-by-step explanation:

x = 2 x 1.5/3

x = 3/3

x = 1 cup of sugar

hope it helps!

4 0
3 years ago
Find the angles a, b, c and d.
Alborosie

A=180-79= 101°

B=75°

C=83°

D=101°

6 0
3 years ago
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Fill in the table using this function rule. y= -6x+1
Eddi Din [679]
Take a picture of the table
6 0
3 years ago
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