Question

if r varies directly as s and inversely as the square of u, and r = 2 when s = 18 and u = 2​

Answer 1

SOLUTION

TO DETERMINE

The equation if r varies directly as s and inversely as the square of u, and r = 2 when s = 18 and u = 2

EVALUATION

Here it is given that r varies directly as s and inversely as the square of u

$\displaystyle \sf{r \propto \: \frac{s}{ {u}^{2} } }$

$\displaystyle \sf{ \implies \: r = \: \frac{ks}{ {u}^{2} } }$

Where k is variation constant

Now r = 2 , s = 18 , u = 2 gives

$\displaystyle \sf{ \implies \: 2= \: \frac{k \times 18}{ {2}^{2} } }$

$\displaystyle \sf{ \implies \: k = \frac{8}{18} }$

$\displaystyle \sf{ \implies \: k = \frac{4}{9} }$

Hence the required equation is

$\displaystyle \sf{ \: r = \: \frac{4s}{ 9{u}^{2} } }$

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