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2 years ago

What quantity will correctly complete the formula? arc length = ?/360circumference

Mathematics

1 answer:

jeka57 [31]2 years ago

8 0

? should be the angle measure of the arc.

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Now, lets evaluate the same integral using power series. first, find the power series for the function f(x = \frac{32}{x^2+4}. t

BlackZzzverrR [31]

No idea what the previous part of the problem is, but you have

$f(x)=\dfrac{32}{x^2+4}=\dfrac8{1-\left(-\frac{x^2}4\right)}=\displaystyle8\sum_{n\ge0}\left(-\frac{x^2}4\right)^n$
$f(x)=\displaystyle8\sum_{n\ge0}\left(-\dfrac14\right)^nx^{2n}$

which is valid for $\left|-\dfrac{x^2}4\right|$ , or $|x|$ . So the integral from 0 to 2 is

$\displaystyle\int_0^2f(x)\,\mathrm dx=\int_0^28\sum_{n\ge0}\left(-\frac14\right)^nx^{2n}\,\mathrm dx$
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\int_0^2x^{2n}\,\mathrm dx$

Note that since the power series only converges on the interval if $x$ is strictly less than 2, which means we have to treat this as an improper integral.

$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\int_0^tx^{2n}\,\mathrm dx$ [/tex]
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\frac{x^{2n+1}}{2n+1}\bigg|_{x=0}^{x=t}$
$=\displaystyle8\sum_{n\ge0}\frac{(-1)^n}{2^{2n}(2n+1)}\lim_{t\to2^-}t^{2n+1}$
$=\displaystyle16\sum_{n\ge0}\frac{(-1)^n}{2n+1}$
$=16-\dfrac{16}3+\dfrac{16}5-\dfrac{16}7+\dfrac{16}9+\cdots$

6 0

2 years ago

What is the answer for this express

kotykmax [81]

12, 2, 4, and 7. The coefficients in the expression 12xy³+2x⁵y+4x⁵y²+7x⁵y are 12, 2, 4, and 7.

In order to solve this problem we have to know that the coefficients is a factor linked to a monomial. For example, the first monomial of the equation is 12xy³ the coeffcient of xy³ is 12.

8 0

2 years ago

Read 2 more answers

Sara uses 7.6 pints of blue paint and white paint to paint her bedroom walls. 3 4 of this amount is blue paint, and the rest is

labwork [276]

Answer:

1.9

Step-by-step explanation:

7.6/4= 1.9

1.9*1= 1.9

ans is 1.9 pints

4 0

2 years ago

Write an algebraic expression to represent each scenario.<br><br> Part A: “the sum of 6 and y”

Nostrana [21]

Answer:

6 + y

Step-by-step explanation:

Here, we want to write an algebraic expression to represent the situation

Mathematically, we want to add 6 and y

The algebraic expression will be;

6 + y

3 0

2 years ago

Does the graph represent a function?

stiv31 [10]

No it does not. Any function that has any of the same X vaules (The line going up left to right) is not a function.

6 0

2 years ago

Read 2 more answers