Question

A norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular norman window is to be 12 ft. What should its dimensions be in order to allow the maximum amount of light to enter through the window?

Answer 1

The question requires the application of calculus to optimize the dimensions of a Norman window, given a fixed perimeter, to allow maximum light to enter.

Step-by-step explanation:

The question is about a Norman window, which is a geometric figure combining a rectangle and a semicircle. Given that the perimeter of the window is 12 feet, the goal is to determine the dimensions that would allow maximum light to enter, which is an application of calculus involving optimization. The answer involves setting up an equation for the perimeter that includes the semicircle and rectangle components, differentiating the area function, finding critical points, and testing these points to find the maximum area.