Answer:
1) -15/32
2) 2/15
3) -203.5
4) -3/2 = -1.5
5) 10/3 = 3 1/3
Step-by-step explanation:
For 1, you just multiply the numerators and denominators together (3 by 5, 4 by 8) and then because it is negative, add the negative sign.
For 2, you multiply again, but because there are 2 negative signs, it becomes positive.
For 3, you divide 81.4 by 0.4, you could also divide 814 by 4.
For 4, you keep change flip, so the equation would become -9/4 (-2 1/4=-9/4) and 3/2 would become 2/3. The equation would be (-9/4 * 2/3). Then, you would get -18/12 which is -3/2.
For 5, you just multiply 4/3 by 5/2 which is 20/6 and because 2 negatives, it becomes positive.
For the given function f(t) = (2t + 1) using definition of Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
As given in the question,
Given function is equal to :
f(t) = 2t + 1
Simplify the given function using definition of Laplace transform we have,
L(f(t))s = 
= ![\int\limits^\infty_0[2t +1] e^{-st} dt](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Cinfty_0%5B2t%20%2B1%5D%20e%5E%7B-st%7D%20dt)
= 
= 2 L(t) + L(1)
L(1) = 
= (-1/s) ( 0 -1 )
= 1/s , ( s > 0)
2L ( t ) = 
= ![2[t\int\limits^\infty_0 e^{-st} - \int\limits^\infty_0 ({(d/dt)(t) \int\limits^\infty_0e^{-st} \, dt )dt]](https://tex.z-dn.net/?f=2%5Bt%5Cint%5Climits%5E%5Cinfty_0%20e%5E%7B-st%7D%20-%20%5Cint%5Climits%5E%5Cinfty_0%20%28%7B%28d%2Fdt%29%28t%29%20%5Cint%5Climits%5E%5Cinfty_0e%5E%7B-st%7D%20%5C%2C%20dt%20%29dt%5D)
= 2/ s²
Now ,
L(f(t))s = 2 L(t) + L(1)
= 2/ s² + 1/s
Therefore, the solution of the given function using Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
Learn more about Laplace transform here
brainly.com/question/14487937
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-10 -10y = 10
+10 +10
-10y = 20
20/-10 = -2
Y = -2
Answer:
n = 144
Step-by-step explanation:
6 / n = 5/120
6 * 120 = 5*n
5n = 6*120
5n = 720
n = 720/5
n = 144
It's 96%
816/850 = 0.96, which is 96%
Hope I helped! ( Smiles )
