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2 years ago

What is the distance between the points (-1, 7) and (5, 7) in the coordinate plane?

Mathematics

2 answers:

zaharov [31]2 years ago

6 0

Answer:

The distance between the two points is 6 units

Step-by-step explanation:

With this one it is very easy to tell because x points change

Irina18 [472]2 years ago

4 0

Answer:

6 units

Step-by-step explanation:

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goldfiish [28.3K]

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3 years ago

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

Find the slope in fraction form

nlexa [21]

Answer:

-1/3

Step-by-step explanation:

Taking two points on the graph (I took (0,9) and (6,7)

Slope=(y2-y1)/(x2-x1)

(7-9)/(6-0)=-2/6

=-1/3

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3 years ago

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Which of the following is a description of the data with a correlation coefficient of 0.9?

aksik [14]

High positive correlation<span>
</span>

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3 years ago

4.25 rounded to the nearest tenths place

musickatia [10]

4.3

5 or more raise the score

4 or less let it rest

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2 years ago

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