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vera_ewing
 one year ago
Math question
vera_ewing
 one year ago
Math question

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1since: \[  1 \leqslant \cos \left( {4x + \pi } \right) \leqslant 1\] then we can write: \[3 \leqslant  3\cos \left( {4x + \pi } \right) + 6 \leqslant 9\] so the requested amplitude is \[A = \frac{{9  3}}{2} = 3\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1for period T, we can write this: \[\begin{gathered} \cos \left( {4x + \pi } \right) = \cos \left( {4x} \right)\cos \pi  \sin \left( {4x} \right)\sin \pi = \hfill \\ \hfill \\ =  \cos \left( {4x} \right) \hfill \\ \end{gathered} \] so our function becomes: \[f\left( x \right) = 3\cos \left( {4x} \right) + 6\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, if we make this change of variable: \[y = 4x\] then our function becomes: \[f\left( y \right) = 3\cos \left( y \right) + 6\] As you can know, the period of that function is \[T = 2\pi \] So what can you conclude?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1oops..as you well know...

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the amplitude of a periodic function, has to be always positive

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1since the cos(x) function is such that: 1 </ cos(x) </ 1, here </ stands for "less or equal to" then we can write: 3</ f(x) </ 9 so the amplitude is: A=(93)/2=...?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1furthermore, if we make this change of variable: 4x=y, then we can rewrite your fuunction as follows: f(x)=3*cos(4x)+6, and therefore: f(y) = 3 cos(y)+6 the period of that function is T= 2*pi, so what can you conclude?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I'm sorry, I can not give the direct answer, since I have to respect the Code of Conduct

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think that option D is a wrong answer!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the period can not be 2*pi, since as I wrote before, if we use this substitution: y=4x then your function as a function of y has period = 2*pi, whereas as function of x has the period equal to: (2*pi)/4=...?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now using the same substitution, we have these correspondences: x>y/4 and therefore: pi> pi/4 so what can you conclude about the phase shift?

vera_ewing
 one year ago
Best ResponseYou've already chosen the best response.0The phase shift is x=pi/4 ?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the phase shift is a relative quantity, so we can assume taht it is  pi/4

vera_ewing
 one year ago
Best ResponseYou've already chosen the best response.0Oh so the answer is A!

vera_ewing
 one year ago
Best ResponseYou've already chosen the best response.0Michele thank you so much! :)
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