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docker41 [41]
3 years ago
6

Solve. 4 + x 7 = 2 A) -14 B) 10 C) 12 D) 42

Mathematics
1 answer:
Dima020 [189]3 years ago
7 0

Answer:

Step-by-step explanation:

c

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Rachel has developed a plan to start paying off her credit card debt, and has stopped making purchases with her credit card. She
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(with steps please) Find the inverse Laplace transform, f(t), of the function: 16/(s-4)^3
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Answer:  The required inverse transform of the given function is

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We have the following Laplace formula :

L\{t^ne^{at}\}=\dfrac{n!}{(s-a)^{n+1}}\\\\\\\Rightarrow L^{-1}\{\dfrac{1}{(s-a)^{n+1}}\}=\dfrac{t^ne^{at}}{n!}.

Therefore, we get

f(t)\\\\=L^{-1}\{\dfrac{16}{(s-4)^3}\}\\\\\\=16\times\dfrac{t^{3-1e^{4t}}}{(3-1)!}\\\\\\=\dfrac{16}{2}t^2e^{4t}\\\\\\=8t^2e^{4t}.

Thus, the required inverse transform of the given function is

f(t)=8t^2e^{4t}.

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Hope this helps......... :)

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