42.0 ft.

Explanation

To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

\(R_{a} d_{a}=R_{b} d_{b}\)

where a represents the left side of the fulcrum and b the right, R is resistance (weight) and d is the distance from the fulcrum.Solving for da, our missing value, and plugging in our variables yields:

\(d_{a}=\frac{R_{b} d_{b}}{R_{a}}=\frac{30 l b . \times 7 f t .}{5 l b .}=\frac{210 f t . l b .}{5 l b .}=42.0 f t\)

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