Given 1-f - 1-v - 1-u- find v- if u - 3f and f - 10cm

Given 1f= 1v+1u Multiply #160;both sides by fuv Then vu=fu+fv Or #160; vu fv=fu Or #160; v(u f)=fu Or #160; v= fuu f # ...

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Mathematics

Area of a Sector of a Circle

Given 1/f =...

Question

Given $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ ; find $v$ , if $u = 3 f$ and $f = 10 c m$

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Solution

Given $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
Multiply both sides by $f u v$
Then $v u = f u + f v$
Or $v u - f v = f u$
Or $v (u - f) = f u$
Or $v = \frac{f u}{u - f}$ Given $u = 3 f$
Then $v = \frac{f \times 3 f}{3 f - f}$
given $f = 10 c m$
So $v = \frac{3 f^{2}}{2 f}$
Or $v = \frac{3 \times 100}{2 \times 10} = \frac{300}{20} = 15 c m$

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Given 1f=1v+1u; find v, if u=3f and f=10cm

Given 1f=1v+1uMultiply both sides by fuvThen vu=fu+fvOr vu−fv=fuOr v(u−f)=fuOr v=fuu−f Given u=3fThen v=f×3f3f−f given f=10cmSo v=3f22fOr v=3×1002×10=30020=15cm

Given $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ ; find $v$ , if $u = 3 f$ and $f = 10 c m$