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:
Yes
Step-by-step explanation:
To determine if (1, 2 ) is a solution of the inequality, substitute the coordinates into the inequality and if satisfied then they are a solution, that is
(6 × 1) - 2 = 6 - 2 = 4 > 3
Since 4 > 3 then (1, 2 ) is a solution
Answer: B
Step-by-step explanation:
Plug in <em>x</em> for 3. Then solve.
4*(1/3)^3
4*1/9
4/9
<span> When area is equal 1120. We can write an equation
(x+4)(-x+64)=1120
-x²-4x+64x+256=1120
-x²+60x+256-1120=0
-x²+60x-864=0
D=b² - 4ac= 3600-4*864=144, √D=12
x= (-b+/-√D)/2a
x=(-60+/-12)/(-2)
x=24, x=36
For x=24
(x+4)=24+4=28
(-x+64)=(-24+64)=40
For x=36
(x+4)=36+4=40
(x-64) =(-36+64)=28
So sides should be 28 and 40 in.
We did not get any extraneous solutions. They could be if we get negative length side, for example. They can come because a quadratic equation can
give positive and negative numbers because a^2 and (-a)^2 give the same positive number.
We chose to solve this equation using formula for quadratic equations, because this equation has too big numbers to solve it using other methods.
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