So as x increases, y increases until halfway through, before decreasing at a proportional rate to how it increased (looking like an upside-down x^2 graph?). This would make sense, because, you would want to essentially minimize the lengths urm hold on
I think I got it! Remember, you said that the sides should be equal length for max area. So set the two terms (9 * x^2 / pi^2 and sqrt(4pi^2 - x^2)) equal to each other. Solve for x
This is coming from the 2019 handbook for AP physics btw
"A police car of mass m moves with constant speed around a curve of radius R. (The car is, from your point of view, coming out of the page and is in the process of turning towards the left side of the page.) The car is moving as fast as it can without sliding out of control on the flat roadway to respond to an emergency. This maximum safe speed isv 0 . The coefficient of static friction between the car’s tires and the roadway is μ s ."
"Derive an expression for the maximum safe speed that the car can take the turn in terms of μ and R."