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.
Step-by-step explanation:
70:100 (They're related because 7 x 10 = 70 and 10 x 10 = 100)
14:20 (They're related because 7 x 2 = 14 and 10 x 2 = 20)
Answer:
$40
Step-by-step explanation:
$4 times $19 is $76 then $116 minus $76 is $40
Answer:
23.49 in.
Step-by-step explanation:
Formula for area of triangle: 1/2 * b * h
1/2 * 16.2 = 8.1
8.1 * 2.9 =23.49 in.
