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3 years ago

Use the graph to answer the question. Find the slope

Mathematics

1 answer:

Liula [17]3 years ago

8 0

We can take the two points given and plug them into the slope formula.

$\sf~m=\dfrac{y_2-y_1}{x_2-x_1}$

(-3, 3), (1, -5)
x1 y1 x2 y2

$\sf~m=\dfrac{-5-3}{1-(-3)}$

Subtract:

$\sf~m=\dfrac{-8}{4}$

Divide:

$\sf~m=-2$

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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

Models can be helpful in scientific investigations because

Ksenya-84 [330]

Answer:

the answer is d

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Divide using long division.<br><br> <img src="https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20-5%29" id="TexFormula1" title="(x^{2} -5)

Morgarella [4.7K]

Answer:

The quotient = x + 5 and the remainder = 20

Step-by-step explanation:

$\frac{x^{2}+0-5 }{x-5}=x+\frac{5x-5}{x-5}$

$\frac{5x-5}{x-5}=5+\frac{20}{x-5}$

The quotient = x + 5 and the remainder = 20

4 0

3 years ago

Express 3 objects as a percentage of 1 dozen<br>show working.

user100 [1]

Answer:

25%

Step-by-step explanation:

1 dozen = 12

3 out of 12

3/12

Simplify

1/4

Multiply top and bottom by 25 to get a denominator of 100

25/100

25%

3 0

3 years ago

rashid is paid by the hour he earned 50 for a 4 hour workday how much does he earn for a 5 1/2 hour workday

gregori [183]

Rashid is paid by the hour. He earned $50 for 4 hour workday. How much does he earn for a 5 1/2 hour workday?

-----------------

Use a proportion:

x/(5 1/2) = 50/4

--------

x = (11/2)(50/4)

--------

x = 550/8

----

x = $68.75

================

7 0

3 years ago