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Lady bird [3.3K]

3 years ago

10

TRUE or FALSE? When plotting a point on a coordinate plane, the first number in a coordinate pair tells you the number of spaces

to move across the x-axis, while the second number tells you the number of spaces to move across the y-axis. (yes i am dumb)

1 answer:

Luda [366]3 years ago

7 0

Answer:

True

Step-by-step explanation:

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Solve the equation:<br><br> -17-2x=6-x<br><br> Solve for x.

irinina [24]

<span>-17-2x=6-x
-2x + x = 6 + 17
-x = 23
x = -23</span>

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hoa [83]

Answer:

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finlep [7]

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ben drives from a 36- foot platform. The equation h= -16t^2+14t+36 models the dive. How long will it take Ben to reach the water

Valentin [98]

So you want to plug in the height for h and solve for t

36 = -16t^2+14t+36
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Hope this helped!

6 0

3 years ago

If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

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3 years ago