Performing laplace transform of the equation.
sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)
Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)
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Answer:
Step-by-step explanation:
<u>Given Second-Order Homogenous Differential Equation</u>
<u>Use Auxiliary Equation</u>
<u />
<u>General Solution</u>
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Note that the DE has two distinct complex solutions 
where 
and 
are arbitrary constants.
Answer:
f(x) = -4x + 20
Refer attachment for graph.
Step-by-step explanation:
Given: when Zane was 20 meters below the edge of a volcano. He heard some rumbling, so he decided to climb up out of there as quickly as he could. He managed to climb up 4 meters each second and get out of the volcano safely.
We have to graph Zane's elevation relative to the edge of the volcano (in meters) as a function of time (in seconds).
Let he takes x seconds to get out of the volcano.
and y be the distance covered by the volcano to reach Zane.
Then, to reach the edge of volcano,
Thus, The equation that represent Zane's elevation relative to the edge of the volcano (in meters) as a function of time (in seconds). is given by
f(x) = -4x + 20
At x = 0 the Zane will be at f(0) = 20 that is 20 meter below the volcano.
Thus points are (0,20)
and when x = 5 Zane will be escaped from volcano.
Thus points are (5,0)
Plot this and obtained the graph for the given equation as attached below.
Answer:
y=3/4x-3
Step-by-step explanation:
Okay so to be parallel to an equation of another line, the line must have the same slope but a different y-intercept. First, you need to find the slope of the equation -3x+4y=4. The equation must be in y=mx+b format, so you first move -3x to the right by adding it on both sides, leaving you with 4y=3x+4. Next, you divide 4y by 4 in order to isolate y and do that on the other side. Now, you have y=3/4x+1.
To find the equation of the new line, you must put the point and slope into point slope form: y-y1=m(x-x1). In the point (4, 0), 4 would be x1 and 0 would be y1. so, the new equation is y-0=3/4 (x-4). now, distrubute the 3/4, leaving you with y=3/4x-3. This is correct since the slope remains the same in both equations with a different y-intercept. To check deeper, you could place point (4, 0) on a graph and then rise 3, run 4 until you get the line :) hope this helps
