Question

OPTIMIZING--Please help


A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of p feet?

Answer 1

You're not doing derivatives, are you?

Answer 2

I am @theEric , I am really bad at optimizing

Answer 3

Do you know what derivatives are? I just want to know what level you're at.

Answer 4

yes sir i do know the derivatives!:) at least supposed to

Answer 5

Okay! I'm not sure if that's what we need for this or not. I remember this from high school advanced math, but I need to find an example on the internet...

Answer 6

https://answers.yahoo.com/question/index?qid=20080928213121AAXVcNK

i got this one. thankyou for helping me!

Answer 7

so how would i take the derivative considering so many variables, that part confuse me!:(

Answer 8

That post on Yahoo! Answers actually mentions that! Look for all of the relationships between the variables. That way you can substitute!



So, you have the perimeter. That doesn't change.

You are concerned with the height; that can change. But it's related to the perimeter.

You are concerned with the width of the rectangle, which can change. But it's related to other things as well.

And you are concerned with the radius of the semicircle atop the rectangle, which also changes.

See, the width is always going to be two times the radius. It will be the same as the diameter.

The height is still limited by the known perimeter.