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3 years ago

Find the slope of a line that passes through (3, 4) and (-2, 4).

1 answer:

7 0

The answer is 0 because the formula to finding a slope from two different points are y1-y2/x1-x2 (meaning as a fraction) in this case, the answer is 0/5, which is equivalent to 0

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A quadrilateral is shown. One pair of opposite sides have lengths of 10 inches and (x + 2) inches. The other pair of opposite si

ziro4ka [17]

Step-by-step explanation:

Yes, one pair of opposite sides could measure 10 inches. and the other pair could measure 13 inches

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3 years ago

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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

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

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3 years ago

1. The graph shows the cost to rent a jetski for different

Shkiper50 [21]

Answer:

Step-by-step explanation:

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3 years ago

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Consider the recursively defined function below

Zinaida [17]

Answer:

So, the first five terms of the sequence defined by the given recursive function are shown below.

F(1) 0.75 f(2) 1.1 F(3) 1.45 F(4) 1.8 f(5) 2.15

written on plato

Step-by-step explanation:

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3 years ago

(11x + 8) + (8x + 12) =27

Tju [1.3M]

Answer:

11x + 8 +8x +12 =27 (drop the parenthesis, there's no actual need for them)

19x +20 =27 (i combined like terms and then subtracted 20 from both sides)

19x = 7 (divide both sides by 19 to get x alone)

x= 7/19 or 0.36842105 (the answer)

Step-by-step explanation:

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3 years ago

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