The circumference of a circle is 704 cm,find its area

2 answers:

5 0

The circumferince of the circle is 2πR ;
The area of the circle is π $R^{2}$ ;
Then, 2πR = 704 ;
R = 352 / π ;
π $R^{2}$ = π × ( 352 / π )^2 = ( 352^2) / π = 123904 / π ≈ 39459.87 ≈ 39460 cm^2 ;

Anna007 [38]3 years ago

3 0

If the circumference of a circle is 704 cm, then the area is: 39439.87 cm.

The formula looks like this: A = π r 2 and C = 2 π r.

So, C = 704 cm and A = 39439.87 cm.

Hope I helped!

- Amber

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I'm guessing the series is supposed to be

$\displaystyle\sum_{n=1}^\infty\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}$

By the ratio test, the series converges if the following limit is less than 1.

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The first $n$ terms in the numerator's denominator cancel with the denominator's denominator:

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7(n+1)}}{n^2x^n}\right|$

$|x^n|$ also cancels out and the remaining factor of $|x|$ can be pulled out of the limit (as it doesn't depend on $n$ ).

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which means the series converges everywhere (independently of $x$ ), and so the radius of convergence is infinite.