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3 years ago

What quotient is equal to 3 3/4

Mathematics

2 answers:

otez555 [7]3 years ago

8 0

Hello.

C would be your answer.

Hope it helps :)

Sever21 [200]3 years ago

7 0

15 divided by 4!!!!!!

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

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3 years ago

Which equation represents a line that has a slope of – 2/3 and a y-intercept of 4?

katrin2010 [14]

Answer:

Step-by-step explanation:

Slope-intercept form: y=mx+b

2x+3y = 12

3y = 12-2x

y = (12-2x)/3

y = 4-2/3x

Here we can see that the slope is -2/3 and y-intercept 4. We already got the answer so we dont need to try the other options.

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A shopping channel shipped 467,023 packages last year. What is a reasonable estimate of number of packages shipped?Explain.

kirza4 [7]

470,000 because when you round the number up, you get 470,000. it is reasonable

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640 divided by 5 is 128, therefore it’s 128 calories

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Solve for d. Show each step: d(e-f)=g

Fofino [41]

Hey there!!

Given equation :

d(e-f) = g

Solve for d :

Dividing by ( e - f ) on both sides :

d = g / e - f which is $d=\frac{g}{e-f}$

Hope my answer helps!

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3 years ago