Question

tell the answer with proof

Answer 1

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( 9 )
$\sqrt{ \tan(x) + \: \: \sqrt{ \tan(x) + \sqrt{ \tan(x) + ... + \infty } } } = 3$
$= > {3}^{2} - \tan(x) = 3$
$= > \tan(x) = {3}^{2} - 3 \\ = > \tan(x) = 6 \\ = > { \tan(x) }^{2} = 36 \\ = > 1 + { \tan(x) }^{2} = 37 \\ = > { \sec(x) }^{2} = 37 \\ = > \sec(x) = \sqrt{37}$
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( 10 )
✓✓ Assume the ratio as [ k : 1 ]
∆ By Section Formula ->
$- > \frac{10k}{k + 1} = 7 \\ = > 3k = 7 \\ = > k = \frac{7}{3}$
∆ Verifying for y- coordinate :
$- > \frac{ - k + 9}{k + 1} = 2 \\ = > 3k = 7 \\ = > k = \frac{7}{3}$
∆ Hence, k : 1 = ( 7 / 3 ) : 1
=> The Desired Ratio = 7 : 3
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Hence, the correct options are : ( b ) and ( 7 : 3 ) respectively