Each of the following linear system has complex eigenvalues. For eachsystem, (a) find the eigenvalues; (b) determine if the origin is a spiral sink, a spiral source, or a center; (c) determine the natural period and natural frequency of the oscillations; (d) determine the direction of the oscillations in the phase plane; and (e)using HPGSystemSolver, sketch thexy-phase portrait and thex(t)- andy(t)-graphsfor the solutions with the indicated initial conditions:

step-by-step explanation:

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

step-by-step explanation:

given perimeter: 28cm

length: 9cm

atp,

2(l+w)=p of the reactangle

2(9+x)=28

18+2x=28

2x=28-18

x=10/2

x=5

therefore width is 5 cm

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.