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Andrews [41]
2 years ago
13

Question is attached below

Mathematics
1 answer:
Katarina [22]2 years ago
8 0
<span>x y
-3 1
1 3
3 4
5 5

is your answer
</span>
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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
Priya bought x grams of flour. Clare bought 3/8 more than that.
iris [78.8K]

Answer:

D

Step-by-step explanation:

y=x+3/8x

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3 years ago
The members of a cooking club are making cakes, which they will sell at a street fair for $14 apiece. It cost $22 for a booth at
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Is the amount of cakes estimated or rounded??
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The anwser is either 2.88 or 3, But others are saying it is 3.
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The formula for volume is length multiplied by width multiplied by height
I hope this helps sorry if it doesn't :)
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