Yes, you may substitute for , as an increase in implies a corresponding decrease in , and the area function may therefore be written in terms of alone.
A Norman Window has the perimeter of 30ft, find the dimentions of the window so that the greatest possible amount of light is admitted.
I did:
Perimeter of half circle = pi*r
Perimeter of the rectangle (3sides) 2r + 2y
Perimeter of the window
30 = pi*r + 2y + 2r
Solve for y
y = 15 - r - (pi*r)/2
I understand out of the text that I need the max area of the window:
Area half circle = (pi*r^2)/2
Area of rectangle = 2r * y
Area of the window A= (pi*r^2)/2 + 2r*y
Now I plug in y
A= (pi*r^2)/2 + 2r* [15 - r - (pi*r)/2]
My question:
Can I write y = 15 - r - (pi*r)/2 so that I can combine the two terms with r in one term?
Please, including the way you did that.
And what is the derivative then? A'(r)?
Please, do not give me any links of similar problems, I looked at them but this did not help me with my problem.
Thanks.