Answer:
(a) true
(b) true
(c) false; {y = x, t < 1; y = 2x, t ≥ 1}
(d) false; y = 200x for .005 < |x| < 1
Step-by-step explanation:
(a) "s(t) is periodic with period T" means s(t) = s(t+nT) for any integer n. Since values of n may be of the form n = 2m for any integer m, then this also means ...
s(t) = s(t +2mt) = s(t +m(2T)) . . . for any integer m
This equation matches the form of a function periodic with period 2T.
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(b) A system being linear means the output for the sum of two inputs is the sum of the outputs from the separate inputs:
s(a) +s(b) = s(a+b) . . . . definition of linear function
Then if a=b, you have
2s(a) = s(2a)
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(c) The output from a time-shifted input will only be the time-shifted output of the unshifted input if the system is time-invariant. The problem conditions here don't require that. A system can be "linear continuous time" and still be time-varying.
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(d) A restriction on an input magnitude does not mean the same restriction applies to the output magnitude. The system may have gain, for example.
Answer:
54,554.5
Step-by-step explanation:
Have you heard about this amazing thing called a calculator?
Answer:
uh the 2nd one
Step-by-step explanation:
cause im smart
Answer:
Period of the function is 4π
Step-by-step explanation:
Given is a graph:
It oscillates between -1 and +1
The graph shows angles on x axis and trig values on y axis.
The graph has value +1 when x=0 and reaches minimum -1 when x =2pi and again reaches y=1 when x =4 π
Thus we find that this is a periodic function with amplitude 1 and phase shift 0 and period 4π
So we get the period of the trignometric funciton is 4π
So option 1 is right
Verify:
Given function is y = cos
Since parent function y =cosx has a period of 2pi, we have
here period = 2pi/coefficient of x in cos
=2pi/(1/2)
=4pi
<span>arctan(2x) = -1 radian
</span>⇒ 2x = tan(-1)
⇒ 2x = -1.5574
⇒ x = -1.5574/2
⇒ x = - 0.7787<span>
</span>
