Answer:
Step-by-step explanation:
1)
y is 3 times more than x.
X=0 Y=0 3x0=0
X=1 Y=3
X=2 Y=6
X=3 Y=9
X=4 Y=12
Then just plot it as co-ordinates (x,y)
2)
Y is 1/4 of x. Divide by 4
X=0 Y=0
X=4 Y=1
X=8 Y=2
X=12 Y=3
X=16 Y=4
Then just plot it as co-ordinates (x,y)
Answer:
116.4545454545455
Step-by-step explanation:
One way of determining the answer is by substituting the values to the equation. It is done as follows:
A. (4,1)
<span>y = 3x - 1
</span>1 = 3(4) - 1 = 11 -------> not equal
B. (2,5)
<span>y = 3x - 1
</span>5 = 3(2) - 1 = 5 --------> equal
C. (4,3)
<span>y = 3x - 1
</span>3 = 3(4) -1 --------------> not equal
D. (0, -3)
<span>y = 3x - 1
-3 = 3(0) -1 = -1 ---------> not equal</span>
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:
