Is one ounce greater than one gram

P(x) --->p(x+6)+3 ? what would the graph look like?

Setler79 [48]

<span>given that P(x) --->p(x+6)+3
</span>
∴ x will become x+6
and P(x+6) will become P(x+6)+3
<span />
So, The graph of [p(x+6)+3] will be the same as the graph of [p(x)] but shifted 6 units to the left then shifted 3 units up
OR by another words, we need to make axis translations from (0,0) to (-6,3)

5 0

3 years ago

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

How many seconds equal 3.6 hours?

MAXImum [283]

12960 seconds equals 3.6 hours.

since its 3.6 hours we need to calculate it so one minute = 60 seconds and 60 minutes = a hour so those are the basics to solve this. now u have add 1 minute of 60 minutes to equal just one hour which gets u 3 if u do it 3 times.

5 0

3 years ago

G(x) = (two-thirds) Superscript x – 2?

snow_tiger [21]

Answer:

-1 1/3

Step-by-step explanation:

7 0

2 years ago

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The scale model of a rectangular garden is 1.5 ft by 4 ft. The scale model is enlarged by a scale factor of 7 to create the actu

LenaWriter [7]

It is given that the scale model of a rectangular garden is 1.5 ft by 4 ft. The scale model is enlarged by a scale factor of 7 to create the actual garden.

Therefore, we can see clearly that the width of the scale model is 1.5 feet. Hence, the width of the actual garden which has been enlarged by a scale factor of 7 will be 7 times the width of the scale model.

Thus the width of the actual garden will be: $1.5\times 7=10.5$ feet

In a similar fashion the length of the actual garden will be $4\times 7=28$ feet

Thus, the area of the actual garden will be:

$Area=Length\times width=10.5\times 28=294$ $ft^2$

As we can see, out of the given options, the last option is the correct one.

6 0

2 years ago

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