Answer:
See below
Step-by-step explanation:
-4 (1/3)^(n-1)
Part A
<em><u>For n = 1</u></em>
-4(1/3)^(1 - 1)
-4(1/3)^0 Anything to the 0 power (except 0) is 1
-4 (1)
-4
<em><u>n = 2</u></em>
-4(1/3)^(2 - 1)
-4*(1/3)^1
-4/3
<em><u>n = 3</u></em>
- 4(1/3)^2
-4/9
<em><u>n = 4</u></em>
-4/(1/3)^3
-4 / 27
Part B
The series converges.
1/3 is between -1 <= 1/3 <= 1
Part C
<em><u>Formula</u></em>
Sum = a/(1 - r)
a = - 4
r = 1/3
Sum = -4/(1 - 1/3) = -4//2/3 = - 4/(0.666666666...) = -6
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
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Answer:
Solution
Step-by-step explanation:
If im wrong let me know okay!
If im wrong Im sorry Im only 15 and im working here to help
The path of the ball is the diagonal of the rectangle.
You can use the Pythagorean theorem.
a^2 + b^2 = c^2
64^2 + 48^2 = c^2
4096 + 2304 = c^3
6400 = c^2
c = 80
Answer: 80 meters
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