Answer:
i dont know i just want points
Step-by-step explanation:
>;)
Answer: She had 200 cards to start with
Step-by-step explanation:
Let x = the amount of cards she had initially. This means she had x cards to start with.
She gave half of the cards she had to a friend. This means she gave her friend x/2 cards. She is left with with (x-x/2) = x/2 cards.
She also gave 1/4 of the remaining cards to her brother. This means that she gave (1/4 × x/2) = x/8 cards to her brother.
Remaining number of cards will be x/2 - x/8 = (4x-x)/8 = 3x/8
She still has 75 cards left. This means
3x/8 = 75
Cross multiplying with 8, it becomes
3x = 75×8 = 600
x = 600/3 = 200
She had 200 cards to start with.
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:
