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What is the length of an arc of a circle that substends 2\(\frac{1}{2}\) radians...


Question

What is the length of an arc of a circle that substends 2\(\frac{1}{2}\) radians at the centre when the raduis of the circle = \(\frac{k}{k + 1}\) + \(\frac{k + 1}{k}\) then

Options

A) p< 0

B) p\(\geq\) 0

C) p \(\leq\) 0

D) p < 1

E) p > 0

The correct answer is E.

Explanation:

\(\frac{k}{k + 1}\) + \(\frac{k + 1}{k}\)
= \(\frac{k^2 + (k + 1)^2}{k(k + 10}\)
= \(\frac{2k^2 + 2k + 1}{k(k + 1}\)
let k = \(\frac{1}{2}\)
p = \(\frac{10}{3}\)
p > 0

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Dicussion (1)

  • \(\frac{k}{k + 1}\) + \(\frac{k + 1}{k}\)
    = \(\frac{k^2 + (k + 1)^2}{k(k + 10}\)
    = \(\frac{2k^2 + 2k + 1}{k(k + 1}\)
    let k = \(\frac{1}{2}\)
    p = \(\frac{10}{3}\)
    p > 0

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