Answer:
A
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
24/8 = 3
18/6= 3
10x3 = 30
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I am not familiar with Laplace transforms, so my explanation probably won't help, but given that for two Laplace transform
![F(s)](https://tex.z-dn.net/?f=F%28s%29)
and
![G(s)](https://tex.z-dn.net/?f=G%28s%29)
, then
![\mathcal{L}^{-1}\{aF(s)+bG(s)\} = a\mathcal{L}^{-1}\{F(s)\}+b\mathcal{L}^{-1}\{G(s)\}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5C%7BaF%28s%29%2BbG%28s%29%5C%7D%20%3D%20a%5Cmathcal%7BL%7D%5E%7B-1%7D%5C%7BF%28s%29%5C%7D%2Bb%5Cmathcal%7BL%7D%5E%7B-1%7D%5C%7BG%28s%29%5C%7D)
Given that
![\dfrac{1}{s^2} = \dfrac{1!}{s^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7Bs%5E2%7D%20%3D%20%5Cdfrac%7B1%21%7D%7Bs%5E2%7D)
and
![-\dfrac{48}{s^5} = -2\cdot\dfrac{4!}{s^5}](https://tex.z-dn.net/?f=-%5Cdfrac%7B48%7D%7Bs%5E5%7D%20%3D%20-2%5Ccdot%5Cdfrac%7B4%21%7D%7Bs%5E5%7D)
So you have
![\mathcal{L}^{-1}\left\{\dfrac{1}{s^2} - 2\cdot\dfrac{4!}{s^5}\right\} = \mathcal{L}^{-1}\left\{\dfrac{1}{s^2}\right\} - 2\mathcal{L}^{-1}\left\{\dfrac{4!}{s^5}\right\}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5Cleft%5C%7B%5Cdfrac%7B1%7D%7Bs%5E2%7D%20-%202%5Ccdot%5Cdfrac%7B4%21%7D%7Bs%5E5%7D%5Cright%5C%7D%20%3D%20%5Cmathcal%7BL%7D%5E%7B-1%7D%5Cleft%5C%7B%5Cdfrac%7B1%7D%7Bs%5E2%7D%5Cright%5C%7D%20-%202%5Cmathcal%7BL%7D%5E%7B-1%7D%5Cleft%5C%7B%5Cdfrac%7B4%21%7D%7Bs%5E5%7D%5Cright%5C%7D)
From Table of Laplace Transform, you have
![\mathcal{L}\{t^n\} = \dfrac{n!}{s^{n+1}}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5C%7Bt%5En%5C%7D%20%3D%20%5Cdfrac%7Bn%21%7D%7Bs%5E%7Bn%2B1%7D%7D)
and hence
![\mathcal{L}^{-1}\left\{\dfrac{n!}{s^{n+1}}\right\} = t^n](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5Cleft%5C%7B%5Cdfrac%7Bn%21%7D%7Bs%5E%7Bn%2B1%7D%7D%5Cright%5C%7D%20%3D%20t%5En)
So you have
![\mathcal{L}^{-1}\left\{\dfrac{1}{s^2}\right\} - 2\mathcal{L}^{-1}\left\{\dfrac{4!}{s^5}\right\} = \boxed{t-2t^4}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5Cleft%5C%7B%5Cdfrac%7B1%7D%7Bs%5E2%7D%5Cright%5C%7D%20-%202%5Cmathcal%7BL%7D%5E%7B-1%7D%5Cleft%5C%7B%5Cdfrac%7B4%21%7D%7Bs%5E5%7D%5Cright%5C%7D%20%3D%20%5Cboxed%7Bt-2t%5E4%7D)
.
Hope this helps...
Answer:
A
Step-by-step explanation: