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3 years ago

The measured length of an arc as a distance is the definition of what?

Mathematics

1 answer:

igomit [66]3 years ago

7 0

Answer:

The arc length is the measure of the distance along the curved line making up the arc. It is longer than the straight line distance between its endpoints (which would be a chord)

Step-by-step explanation:

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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

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

7 0

3 years ago

Find the 79th term of the following arithmetic sequence. 5,11, 17, 23...

NikAS [45]

Answer:

the answer is 479.

Step-by-step explanation:

to make it simpler, pretend you start from 1. 1,7,so on. multiply six by 79, to get 474. but because you are starting from 5 and not 1, you have to add 5 on.

sorry im super bad at math so this might be wrong

4 0

3 years ago

Read 2 more answers

Which of the following systems describes the graph ?

Gnoma [55]

Answer:

x > -3 and y ≥ 1/2x - 2

Step-by-step explanation:

blue line = x > -3

red line = pass (0, -2) (4, 0)

y = 1/2x - 2

HOPE THIS HELPS AND HAVE A NICE DAY <3

7 0

2 years ago

Can you help me find the B plzzz

UNO [17]

Answer:

B=80

Step-by-step explanation:

B is the same answer as the number on the other side

8 0

3 years ago

Read 2 more answers

6th grade math i mark as brainliest

VLD [36.1K]

step (1) 32+23*4 =124 step (2) 9+23*4= 101 step (3) 9+9*4=45 step 4 9+35=44

Step-by-step explanation:

4 0

3 years ago