
optimization prob.
Hey all, struggling with this greatly, I understand the gist but finding the formulas is proving difficult;
An evaporative cooler design uses a rotating wheel that is placed upright (vertical) and is partially submerged in water. The center of the circle is above the waterline. Let R be the radius of the wheel and x be the distance from the center to the waterline. As the wheel turns, the portion that was submerged remains we after it rotates above the waterline. The efficiency of the cooler is maximized when the wet area of the wheel above the waterline is the largest possible.
a. Find the exact value of x which does this, in terms of R.
b. What percent of the circle's diameter should be submerged?