Y=2/3x
The y-intercept is zero, and the slope is 2/3
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.
Here in the second term I am considering 2 as power of x .
So rewriting both the terms here:
First term: 12x²y³z
Second term: -45zy³x²
Let us now find out whether they are like terms or not.
"Like terms" are terms whose variables (and their exponents such as the 2 in x²) are the same.
In the given two terms let us find exponents of each variable and compare them for both terms.
z : first and second term both have exponent 1
x: first and second term both have exponent 2
y: first and second term both have exponent 3
Since we have all the exponents equal for both first and second terms variables, so we can say that the two terms are like terms.
