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:
Step-by-step explanation:
6/10
divided by 2
3/10
divided by 1/2
3/5
Take the common denominator and divide by 3
Answer:
Answer: Using the proportions between the segments, the area of the triangles are:
1. Area of triangle ADC is 25 in^2.
2. Area of triangle BDC is 15 in^2.
3. Area of triangle CDE is 12 in^2.
Step-by-step explanation:
Answer:
187.5
Step-by-step explanation:
17 × 5 = 85
100 - 85 = 15% = 0.15
1250 × 0.15 = 157.5
