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Evgen [1.6K]
3 years ago
9

Which following options represents the graph of F(x)= 2cos(4x - pi)?

Mathematics
1 answer:
wlad13 [49]3 years ago
3 0

Answer:C

Step-by-step explanation:

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Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(
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The particular quadratic solution to the ODE is found as follows:

x=at^2+bt+c
x'=2at+b

(2at+b)+2(at^2+bt+c)=t^2+4t+7
2at^2+(2a+2b)t+(b+2c)=t^2+4t+7

\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

x'+2x=0\implies r+2=0\implies r=-2

so that x_c=Ce^{-2t} is a characteristic solution to the ODE, and the general solution would be

x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4
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4 years ago
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
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Factoring 12m^2n^2-8mn+1=
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12m^2n^2-8mn+1=12m^2n^2-2mn-6mn+1=\\\\=2mn\cdot6mn-2mn\cdot1-1\cdot6mn-1\cdot1=\\\\=2mn(6mn-1)-1(6mn-1)=(6mn-1)(2mn-1)
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3 years ago
Read 2 more answers
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