Answer:
Example 1 Find the inverse transform of each of the following.
F
(
s
)
=
6
s
−
1
s
−
8
+
4
s
−
3
H
(
s
)
=
19
s
+
2
−
1
3
s
−
5
+
7
s
5
F
(
s
)
=
6
s
s
2
+
25
+
3
s
2
+
25
G
(
s
)
=
8
3
s
2
+
12
+
3
s
2
−
49
Show All Solutions
Answer:
A=5257.76
Step-by-step explanation:
Or use a calculator online.
This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
<span>Multiplying both sides of the equation by the integrating factor: </span>
<span>(y')e^(6x) + 6ye^(6x) = e^(12x) </span>
<span>The left side is the derivative of ye^(6x), hence </span>
<span>d/dx[ye^(6x)] = e^(12x) </span>
<span>Integrating </span>
<span>ye^(6x) = (1/12)e^(12x) + c where c is a constant </span>
<span>y = (1/12)e^(6x) + ce^(-6x) </span>
<span>Use the initial condition y(0)=-8 to find c: </span>
<span>-8 = (1/12) + c </span>
<span>c=-97/12 </span>
<span>Hence </span>
<span>y = (1/12)e^(6x) - (97/12)e^(-6x)</span>
2x+3x=
X is simply a letter
Answer:
240units^2
Step-by-step explanation:
The formula for area on a triangle is 1/2 x b x h, so you do 4 x 10 x 1/2, giving you 20, there are two of these triangles so you double it to 40.
Then for the rectangle below you do l x w, or 10 x 20 giving 200.
You then add it all together, 200+20+20=240 units squared.
Hope this helps!
