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Gnesinka [82]
3 years ago
5

Plz answer the question step by step​

Mathematics
1 answer:
Alenkinab [10]3 years ago
5 0

Answer: <em>x = 59°, y = 114°.</em>

Step-by-step explanation:

<em>The sum of the opposite angles of a quadrilateral in a circle is 180°.</em>

<em>y = 180° - 121° = 59°</em>

<em>The two angles being adjacent makes a total angle of 180° on the straight line.</em>

<em>x = 180° - (180°-114°) = 180° - 66° = 114°</em>

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1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING
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If

y=\displaystyle\sum_{n=0}^\infty a_nx^n

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y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n

The ODE in terms of these series is

\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0

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\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}

We can solve the recurrence exactly by substitution:

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\boxed{y(x)=a_0e^{-2x}}

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