An object lifted with a rope or wire should not weigh more than the [i]safe working load[/i] for the rope or wire. The safe working load [i]S[/i] (in pounds) for a natural fiber rope is a function of [i]C[/i], the circumference of the rope in inches.[br][br] [b]Safe working load model[/b]: [math]150\cdot C^2=S[/math][br][br]You are setting up a block and tackle to lift a 1350-pound safe. What size natural fiber rope do you need to have a safe working load?

Use the model to find a safe rope size. Substitute 1350 for [i]S[/i].[br][br]   [math]150C^2=S[/math]     [color=#0000ff]Write model.[br][br][/color]   [math]150C^2=1350[/math]      [color=#0000ff]Substitute.[br][br][/color]   [math]150C^2-1350=0[/math]    [color=#0000ff]Subtract 1350 from each side.[br][/color][br]   [math]150\left(C^2-9\right)=0[/math]   [color=#0000ff]Factor out common factor.[br][/color][br] [math]150\left(C-3\right)\left(C+3\right)[/math]   [color=#0000ff]Factor.[br][/color][br] [math]\left(C-3\right)=0[/math] or [math]\left(C+3\right)=0[/math] [color=#0000ff]Use zero-product property.[/color][br][br] [math]C-3=0[/math]     [color=#0000ff]Set first factor equal to 0.olve for [i]C[/i].[br][br][/color] [math]C=3[/math]      [color=#0000ff]Solve for [i]C[/i].[/color][br]     [br] [math]C+3=0[/math]     [color=#0000ff]Set second factor equal to 0.[br][/color][color=#0000ff][br][/color] [math]C=-3[/math]      Solve for [i]C[/i].[br][color=#0000ff][br][/color]The negative solution makes no sense. You need a rope with a circumference of at least [b][i][color=#ff0000]3 inches.[br][/color][/i][/b]