What can you conclude about the intersection of a chord and the radius that bisects it

Mathematics

1 answer:

IRINA_888 [86]2 years ago

4 0

Answer: The radius and the cord must be perpendicular to each other.

Step-by-step explanation:

A cord is a line from a point of circumference of a circle to another point of the circumference of the circle without passing through the centre.

A radius is a line from the centre of a circle to the circumference of the circle.

When the radius line intersect and bisects a cord of a circle, the radius and the cord must be perpendicular to each other.

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defon

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 $n$ ).

$\displaystyle|x|\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2}{7(n+1)}}{n^2}\right|=|x|\lim_{n\to\infty}\frac{|n+1|}{7n^2}=0$

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

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ICE Princess25 [194]

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Alex17521 [72]

Answer:

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