Question

Find the mean proportional between
(i) 0.6 and 9.6
(ii) 1⁄4 and 1/16

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Answer 1

Hey mate here is ur solution,

(1) Let the mean proportional between 0.6 and 9.6 be x

Thn,

0.6,x and 9.6 are in continued proportional


$\frac{0.6}{x} = \frac{x}{9.6} \\ {x}^{2} =( 9.6)(0.6) \\ {x}^{2} = 5.76 \\ x = \sqrt{5.76} \\ x = 2.4$


(2)1/4 and 1/16
Let the mean proportional b/w them be x

Thn,

1/4,x and 1/16 are in continued proportional

$\frac{ \frac{1}{4} }{x} = \frac{ x }{ \frac{1}{16} } \\ x(x) = \frac{1}{4} \times \frac{1}{16} \\ {x}^{2} = \frac{1}{64} \\ x = \sqrt{ \frac{1}{64} } \\ x = \frac{1}{8}$



Hope it helps u

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