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2 years ago

Using the math panel write the distance from 20 to zero as an absolute value

Mathematics

1 answer:

Ronch [10]2 years ago

8 0

There a app called photo math

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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

2 years ago

5. An investment doubles in value every 9 years. What was the starting value of the investment if

arlik [135]

Answer:

16,00

Step-by-step explanation:

9 years is the (time)

divide the 27 years by 9 to see how many times it doubles

the ans is 3

now simply divide the value which is $4,800 by the 3

this gives you 1,600

7 0

2 years ago

Hey I hope this helps many people but how do you do this problem <br><br> 5x=0.4

Scrat [10]

X=0.08 hope it helps love

4 0

2 years ago

Read 2 more answers

Solve the system of equations using the elimination method and enter the value of y.

Viktor [21]

I think it is y= 9/5 + 4x/5

7 0

2 years ago

4. True or False: The solution to 4g +7=5g-1-g is Infinitely Many Solutions.

Nitella [24]

Answer:

False

Step-by-step explanation:

4g + 7 = 5g - 1 - g

Simplify:

4g + 7 = 4g - 1

Subtract both sides by 4g:

7 = -1

There are no solutions to this equation.

7 0

2 years ago