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:
Formula for trapezoid area is A=b1+b2 x heightx 1/2 so your answer would be 161m squared
Answer: x < 4
Step-by-step explanation: When solving the inequality 3x - 3 < 9, just like an equation our first step is to isolate the <em>x</em> term which is 3x by adding 3 to both sides of the inequality.
On the left, -3 + 3 cancels and we have 3x.
Make sure to bring down the < sign.
On the right, 9 + 3 simplifies to 12.
So we have 3x < 12.
Now, divide both sides of the inequality by 3 to isolate <em>x</em>.
When we do that we get <em>x < 4</em>
So our answer is x < 4.
Answer:
Riding 2 miles = $6.50
Riding m miles: C = 1.25m + 4
Step-by-step explanation:
(1.25)*(2) + 4 = $6.50
