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2 years ago

X∞n=0 (2 n + 1) x 2 n

Mathematics

1 answer:

Black_prince [1.1K]2 years ago

6 0

Answer:3

If x=0 or x=1 it is trivial, so 0<x<1. Define a=1−x2, then 0<a<1.

Step-by-step explanation:

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The circle with center O has a minor arc BSA with a length of

tangare [24]

Answer:

D. $\frac{27\pi}{2}$ inches.

Step-by-step explanation:

We have been given that the circle with center O has a minor arc BSA with a length of $3\pi^{2}$ inches. The central angle is 40°.

To find the circumference of circle we will use formula:

$\frac{\text{Central angle}}{2\pi}=\frac{\text{Arc length}}{2\pi r}$ , where $2\pi$ = measure of 360 degrees in radians and $2\pi r$ = circumference of circle.

Let us convert measure of central angle into radians.

$40^{o}=\frac{40*\pi}{180} =\frac{2\pi}{9}$

Upon substituting our given value in the formula we will get,

$\frac{\frac{2\pi}{9}}{2\pi}=\frac{\frac{3\pi}{2}}{2\pi r}$

$\frac{2\pi}{18\pi}=\frac{3\pi}{4\pi r}$

$\frac{1}{9}=\frac{3}{4r}$

Cross multiplying we will get,

$4r=27$

$r=\frac{27}{4}$

Hence, the radius of our circle is 27/4 inches.

Since the circumference of circle is $2\pi r$ . Upon substituting $r=\frac{27}{4}$ we will get,

$2\pi r=2\pi* \frac{27}{4}=\frac{27\pi}{2}$

Therefore, circumference of our given circle will be $\frac{27\pi}{2}$ inches and option D is the correct choice.

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2 years ago

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