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:
The measure of the smallest angle of the triangle is 40.
Step-by-step explanation:
A right triangle adds up to 180
x+15+2x+90=180
Combine like terms
3x+105=180
Subtract both sides by 105
3x+105=180
-105=-105
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3x=75 Divide by 3
x=25
Plug in 25 for x for equation expression
90=90
25+15=40
2(25)=50
Therefore for the smallest angle is 40
Hope this helps
If the one factor of the function is (x - 4). Then the other two factor of the function will be (2x + 1) and (x + 1).
<h3>What is a factorization?</h3>
It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
(x - 4) is the factor of the function.
f(x) = 2x³ - 5x² - 11x - 4
Then the factor of the function will be
f(x) = 2x³ - 5x² - 11x - 4
f(x) = 2x³ + x² - 6x² - 3x - 8x - 4
f(x) = x²(2x + 1) - 3x (2x + 1) - 4(2x + 1)
f(x) = (2x + 1)(x² - 3x - 4)
f(x) = (2x + 1)(x² - 4x + x - 4)
f(x) = (2x + 1)[x(x - 4) + 1 (x - 4)]
f(x) = (2x + 1)(x + 1)(x - 4)
More about the factorization link is given below.
brainly.com/question/6810544
#SPJ1
Explanation
As you can see all the possible answers have the same form:
By looking at the picture you'll notice that the graph of g(x) has to pass through the point (2,1). Remember that the points in the graph of g(x) have the form (x,g(x)). Since (2,1) is part of the graph of g(x) then we have the following:
So let's evaluate the expression for g(x) that we wrote before at x=2. This way we'll obtain an equation for the number a:
Then we can divide both sides by 4:
Then we get:
Answer
Then the answer is option A.
