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:

Answer:
Common ratio is 3
The three terms are 162, 486, 1458
Step-by-step explanation:
Given: The first 4 terms of a sequence are 
To find:
A. the common ratio
B. the next 3 values in the geometric sequence
Solution:
Geometric sequence is a sequence in which each of the terms is obtained by multiplying the previous term by a fixed number.
A.

So, the common ratio is 
B.
The next three values are as follows:

To find the cost of labor for one worker, you multiply the wage by the number of hours worked.
40 * 8 = 320
Because there are two workers, now you double it.
320 * 2 = 640
To find the percentage of the revenue that this is, you do the labor cost divided by the revenue.
640 / 2000 = 0.32
Move the decimal two places to the right to get the percentage.
0.32 = 32%
The labor cost is 32% of the revenue.
D
The reason is because well first of the plotted dot is filled in with means that x needs to be less then or equal too so to represent that you put the line under the less then symbol and none of the other options have that exact symbol
The arrow is going to the left this is stating that x needs to be less than -2
If it’s wrong then I apologize because I don’t really remember this
Answer:
The cost of 250 g carrots is €0.45.
Step-by-step explanation:
Given that,
Cost of carrots is €1.80 per kg
We need to find the cost of 250 g of carrots.
1 kg cost = €1.80
We know that, 250 gram = 0.25 kg
0.25 kg cost = €1.80 × 0.25
= €0.45
So, the cost of 250 g carrots is €0.45.