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2 years ago

A certain bamboo plant grows 1.2 feet in one day. At that rate, how many feet could the plant grow in 0.5 day?

Mathematics

1 answer:

Rainbow [258]2 years ago

5 0

Answer:

0.6 feet in half a day

Step-by-step explanation:

If it grows 1.2 feet in 1 full day, then half of that 1.2÷2=0.6

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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

Help! In parallelogram LMNO below, find the length of MO

pashok25 [27]

Answer:

Step-by-step explanation:

The diagonals of a parallelogram bisect each other.

5y - 8 = 3y + 1 Add 8 to both sides

5y = 3y + 1 + 8 Subtract 3y from both sides

5y - 3y = 9 Combine

2y = 9 Divide by 2

2y/2 =9/2

y = 4. 5

5y - 8 =

5(4.5) - 8 =

22.5 - 8 =

14.5

That represents 1/2 of MO

MO = 2 * 14.5

MO = 29

5 0

2 years ago

5x=15 y 2x=6 <br> Son ecuaciones equivalentes?<br><br> PORFAVOR AYÚDENME ES EMERGENCIA

mihalych1998 [28]

Si, los dos son iguales

Cuando haces 5x=15, la división dice que x = 3. Para 2x=6 puedes usar el resultado de x=3 de la problema de antes, y cuando te usas esto va a ver que 2 de x cuando x=3 es igual a 6, y por eso 5x=15 y 2x=6 son equivalentes.

5 0

3 years ago

What is the answer and how did you work it out

Anna71 [15]

Answer: b

Step-by-step explanation:

10 x 10= 100

15 x 10= 150

100+150= 250

8 0

3 years ago

Who c is the value of the expression [(10^4)(5^2)/10^3)(5^3)]^3 1 2 8 10

Olegator [25]

Answer:

10 divided by 5 is 2, and 2 cubed is 8

6 0

3 years ago