nice cal question 2

[pudder]

A church window is to be built in the form of a rectangle topped by two equal semicircles across the top. The window needs to be decorated with paper boarders along the edges. The boarder to go along the edge of the semicircle cost $20/m. The boarder to go along the edge of the rectangular part cost $10/m. The window must have an area of 32m2(squared). Find the window that minimizes the cost of decorating the edges.

[pudder]

can anyone help solve this problem
thanks

[OfficeShredder]

To start, what equations give us the total area of the window? You should be able to write this using only two independent variables. Then, the cost can be written out based on the perimeter, calculable by these variables (hint: the rectangles can be any width and height, except must fulfill the area requirement). Then to minimize the cost, you take the derivative (make sure the cost is written out in terms of one variable at this point)

[pudder]

up to here is it correct
P=10(2y+x)+20(2pie(x/4))

[Epsilon=One]

To start, what equations give us the total area of the window? You should be able to write this using only two independent variables. Then, the cost can be written out based on the perimeter, calculable by these variables (hint: the rectangles can be any width and height, except must fulfill the area requirement). Then to minimize the cost, you take the derivative (make sure the cost is written out in terms of one variable at this point)I greatly admire, in many of your posts, your ability to coax a solution. If only all teachers had this ability.