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If y varies directly as x and if x = 2 when y = 8 then k = 4.

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X varies directly with y and inversely with z. x 5 when y 10 and z 5. Find x when y 20 and z 10x varies directly with y and inversely with z. x 5 when y 10 and z 5. Find x when y 20 and z 10x varies d?

Since ( x ) varies directly with ( y ) and inversely with ( z ), we can express this relationship as ( x = k \frac{y}{z} ), where ( k ) is a constant. Given that ( x = 5 ) when ( y = 10 ) and ( z = 5 ), we can find ( k ): [ 5 = k \frac{10}{5} \implies k = 2. ] Now, to find ( x ) when ( y = 20 ) and ( z = 10 ): [ x = 2 \frac{20}{10} = 4. ] Thus, ( x ) equals 4.