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goldenfox [79]
3 years ago
7

Using The graph below identify the axis of symmetry for the parabola below 

Mathematics
1 answer:
11111nata11111 [884]3 years ago
4 0

Answer:

x=-3

Step-by-step explanation:

The axis of symmetry is the line that separates a parabola directly in half. It is measure on x axis because it is being split in terms of that number. Next, you identify the origin and find exactly where the parabola is in half and that is your answer. Another way to do this would be to identify the vertex of the parabola. The answer is the x coordinate of the location of the vertex. (The highest point of a parabola.)

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I am Lyosha [343]
Take the homogeneous part and find the roots to the characteristic equation:

y''+4y=0\implies r^2+4=0\implies r=\pm2i

This means the characteristic solution is y_c=C_1\cos2x+C_2\sin2x.

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form y_p=ax\cos2x+bx\sin2x. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With y_1=\cos2x and y_2=\sin2x, you're looking for a particular solution of the form y_p=u_1y_1+u_2y_2. The functions u_i satisfy

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W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2

So you have

u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx
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u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx
u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x

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u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x

but since \cos2x is already accounted for in the characteristic solution, the particular solution is then

y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x

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y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x
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kolbaska11 [484]
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8 0
4 years ago
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Tanya [424]

Answer:

a - 8

b - 20

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8 0
3 years ago
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Answer:

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Step-by-step explanation:

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