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3 years ago

8. Find the slope of the line that passes through the points: (7, 1/2) and (-2,1/2)

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

4 0

Answer:

m=0

Step-by-step explanation:

m=y2-y1/x2-x1

m=1/2-1/2/-2-7

m=0/-9

m=0

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5137

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3 years ago

Why is graphing not always the best option for solving systems?

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Step-by-step explanation:

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3 years ago

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3 years ago

5. Find the general solution to y'''-y''+4y'-4y = 0

CaHeK987 [17]

For any equation,

$a_ny^(n)+\dots+a_1y'+a_0y=0$

assume solution of a form, $e^{yt}$

Which leads to,

$(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0$

Simplify to,

$e^{yt}(y^3-y^2+4y-4)=0$

Then find solutions,

$\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}$

For non repeated real root y, we have a form of,

$y_1=c_1e^t$

Following up,

For two non repeated complex roots $y_2\neq y_3$ where,

$y_2=a+bi$

and,

$y_3=a-bi$

the general solution has a form of,

$y=e^{at}(c_2\cos(bt)+c_3\sin(bt))$

Or in this case,

$y=e^0(c_2\cos(2t)+c_3\sin(2t))$

Now we just refine and get,

$\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}$

Hope this helps.

r3t40

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3 years ago