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3 years ago

Can someone solve this? The answer needs to be in fraction form so can't be done by a calculator.

Mathematics

1 answer:

Lesechka [4]3 years ago

7 0

Answer:

9 1/6

You may use a fraction calulator for this question by the way!

Hope this helps!

Sorry if its wrong!

Have a nice day!

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Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x2/(x4 +

ella [17]

Answer:

Given the function: $f(x) =\frac{x^2}{x^4+16}$

A geometric series is of the form of :

$\sum_{n=0}^{\infty} ar^n$

Now, rewrite the given function in the form of $\frac{a}{1-r}$ so that we can express the representation as a geometric series.

$\frac{x^2}{x^4+16}$

Now, divide numerator and denominator by $x^4$ we get;

$\frac{\frac{1}{x^2}}{1+\frac{16}{x^4}}$ = $\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2}$

Therefore, we now depend on the geometric series which is;

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

let $x \rightarrow x^2$ then,

$\frac{1}{1+x^2} =\sum_{n=0}^{\infty} (-1)^n x^{2n}$

to get the power series let $x \rightarrow \frac{4}{x^2}$

so,

$\frac{1}{1+(\frac{4}{x^2})^2} =\sum_{n=0}^{\infty} (-1)^n (\frac{4}{x^2})^{2n}$

Multiply both side by $\frac{1}{x^2}$ we get;

$\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2} =\frac{1}{x^2} \cdot \sum_{n=0}^{\infty} (-1)^n (\frac{4}{x^2})^{2n}$

$\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2} =x^{-2} \cdot \sum_{n=0}^{\infty} (-1)^n (16)^n (x^{-2})^{2n}$

$\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2} =\sum_{n=0}^{\infty} (-1)^n (16)^n x^{-4n} \cdot x^{-2}$

Using $x^n \cdot x^m = x^{n+m}$

we have,

$\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2} =\sum_{n=0}^{\infty} (-1)^n (16)^n x^{-4n-2}$

therefore, the power series representation centered at x =0 for the given function is: $\sum_{n=0}^{\infty} (-1)^n (16)^n x^{-4n-2}$

6 0

3 years ago

Help me please i need answer

marishachu [46]

Answer: 57.75 m

Explanation: First do 5 times 0.25. (The 0.25 is the same as 1/4.) Now take that answer and multiply it by 11. Your equation should look like this: 11*(5 1/4).

* = times

I hope this helps! :)

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3 years ago

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Which factor do 64x2 + 48x + 9 and 64x2 – 9 have in common?

nikklg [1K]

Answer: Start with the second expression. That factors easily into (8x-3)(8x+3).

Since 64x^2 + 48x + 9 has no negative signs, I'd bet that the common factor is (8x+3). Divide 64x^2 + 48x + 9 by that to verify.

hope this helps <3

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2 years ago

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Solve the equation.<br> 1/3p + 7 = 25

Helga [31]

P=6
You minus the 7 from 25 and you get 18 then you divide 18 from 1/3

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Find out by using binomial theory<br> (2y-3x)^3

AveGali [126]

Binomial theory : ( a - b ) ^3 = a^3 - 3a^2b + 3ab^2 - b^3 ;
Then, ( 2y - 3x ) ^3 = 8y^3 - 36y^2x + 54yx^2 - 27x^3

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3 years ago