Answer:
3rd option
Step-by-step explanation:
Under a rotation about the origin of 270°
a point (x, y ) → (y, - x ) , then
A (- 3, 4 ) → (4, - 3 )
B (4, - 5 ) → (- 5, - 4 )
C (1, 6 ) → (6, - 1 )
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: 10. Answer is -3
Step-by-step explanation:
I'm ASSUMING that we're talking about Three Ordered Ordered Pair Solutions.
If so, the answer is (0,−1),(1,2),(2,5).
Answer:
<em>The options are not visible enough (See Explanation)</em>
Step-by-step explanation:
Given
x:- 1 || 2 || 3 || 4 || 5
y:- 13 || 22 || 37 || 58 || 85
Required
Determine if the function is quadratic
Calculate the difference between the values of y




<em>The resulting difference are: 9 || 15 || 21 || 27</em>
Next; Calculate the difference between the difference of values of y



<em>The resulting difference are: 6 || 6 || 6</em>
<em>For the function to be quadratic, the above difference must be the same and since they are the same (6), then the function represents a quadratic function.</em>