Step 1 :The question is asking for the maximum safe speed a car can travel on a curved road with a radius of curvature of 710 feet. The formula given is \(v=\sqrt{23 r}\), where \(v\) is the speed and \(r\) is the radius of curvature.
Step 2 :We need to substitute \(r\) with 710 and solve for \(v\).
Step 3 :After finding \(v\), we need to round down to the nearest whole number because it's safer to drive at a lower speed than the calculated maximum safe speed.
Step 4 :Substituting \(r\) with 710 in the formula \(v=\sqrt{23 r}\), we get \(v=\sqrt{23*710}\).
Step 5 :Solving this, we get \(v=127\).
Step 6 :Final Answer: The maximum safe speed is \(\boxed{127}\) miles per hour.