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Marina CMI [18]

3 years ago

11

In Mr. Sheldon’s physical education class, each student plays at most 1 sport.

1 answer:

Maslowich3 years ago

8 0

20 students play soccer or basketball and <span>8 students play basketball, then 20-8=12 students play soccer. </span>
<span>
</span><span>Given that 1/3 of the students play soccer you can conclude that 1\3 is equal 12 student, then in class totally are 12*3=36 students.
</span>
36-20=16 students <span>play neither soccer nor basketball
</span>
Answer: Correct choice is B.
<span />

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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]

If

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

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

What is the slope intercept form of the equation 4x-8y=72

Masteriza [31]

Answer:

y = 1/2x - 9

General Formulas and Concepts:

<u>Alg I</u>

Standard Form: Ax + By = C

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step-by-step explanation:

<u>Step 1: Define</u>

Standard Form: 4x - 8y = 72

<u>Step 2: Find slope-intercept form</u>

Subtract 4x on both sides: -8y = 72 - 4x
Divide both sides by -8: y = -9 + 1/2x
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6 0

3 years ago