Answer
(a) 
(b) 
Step-by-step explanation:
(a)
δ(t)
where δ(t) = unit impulse function
The Laplace transform of function f(t) is given as:

where a = ∞
=> 
where d(t) = δ(t)
=> 
Integrating, we have:
=> 
Inputting the boundary conditions t = a = ∞, t = 0:

(b) 
The Laplace transform of function f(t) is given as:



Integrating, we have:
![F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.](https://tex.z-dn.net/?f=F%28s%29%20%3D%20%5B%5Cfrac%7B-e%5E%7B-%28s%20%2B%201%29t%7D%7D%20%7Bs%20%2B%201%7D%20-%20%5Cfrac%7B4e%5E%7B-%28s%20%2B%204%29%7D%7D%7Bs%20%2B%204%7D%20-%20%5Cfrac%7B%283%28s%20%2B%201%29t%20%2B%201%29e%5E%7B-3%28s%20%2B%201%29t%7D%29%7D%7B9%28s%20%2B%201%29%5E2%7D%5D%20%5Cleft%20%5C%7B%20%7B%7Ba%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
Inputting the boundary condition, t = a = ∞, t = 0:

9514 1404 393
Answer:
17/99
Step-by-step explanation:
Replace the digits 23 in your example with the digits 17 and you have your answer:

_____
In general, a 2-digit repeat will have 99 as its denominator. If the digits are a multiple of 3 or 11, then the fraction can be reduced. 17 is prime, so the fraction cannot be reduced.
Answer:
First question: Choice A
second question:Choice D
Third question: Choice c
Fourth question: Choise b
5th Question: choice b
Given:
The coordinates of point K' are (6,5).
K' is the image of K after a reflection in the line y=2.
To find:
The coordinates of point K.
Solution:
Let the coordinates of point K are (a,b).
If a figure is reflected over the line y=2, then
Using this formula, the coordinates of image of K are

The coordinates of point K' are (6,5).

On comparing both sides, we get




Therefore, the coordinates of point K are (6,-1).
Answer
The answer is A, y=-1/2x +2