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3 years ago

Construct a truth table for the given statement.

Mathematics

1 answer:

Anna11 [10]3 years ago

3 0

Answer:

I'm going by lines

TTFFTT
TFTTFT
FTFFFF
FFTFFF

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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

iogann1982 [59]

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

then

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

The ODE in terms of these series is

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

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

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

We can solve the recurrence exactly by substitution:

$a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0$

$\implies a_n=\dfrac{(-2)^n}{n!}a_0$

So the ODE has solution

$y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}$

which you may recognize as the power series of the exponential function. Then

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

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3 years ago

The following steps are used to rewrite the polynomial expression, 3(x + 4y) + 5(2x - y).

ololo11 [35]

Answer:

step1 - distributive property

step2 - associative property

step3 - cumulative property

step4 - associative property

Step-by-step explanation:

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3 years ago

Which comparison is not correct? -8<1-41 1-21 <1-91 1-7]>-9 |81 > 1-91

Savatey [412]

Answer:

I'm pretty sure it is C

Step-by-step explanation:

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2 years ago

Rewrite as a simplified fraction 1.6 <-- repeating=?

Norma-Jean [14]

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3 years ago

Evaluate the following expression: 62 - 7(8 + 6 – 3²) ANSWER STAT!!

Anna11 [10]

Answer:

Step-by-step explanation:

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