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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?
You're not doing derivatives, are you?
I am @theEric , I am really bad at optimizing
Do you know what derivatives are? I just want to know what level you're at.
yes sir i do know the derivatives!:) at least supposed to
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...
https://answers.yahoo.com/question/index?qid=20080928213121AAXVcNK i got this one. thankyou for helping me!
so how would i take the derivative considering so many variables, that part confuse me!:(
That post on Yahoo! Answers actually mentions that! Look for all of the relationships between the variables. That way you can substitute! |dw:1398212518200:dw| 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.
So, what is the perimeter?
You can use \(h\) for height, \(w\) for width, \(r\) for radius, \(p\) for perimeter, and \(A\) for area. So many variables!
haha right!, so i would figure equations for permeter and area. solve to h,w,r then plug them in the area equation and take the derivative?
Yeah! You have constant \(p\), so you don't have to worry about taking a derivative with respect to it. You want to solve for the area \(A\), so you won't be taking the derivative with respect to it. You'll be taking the derivative of it with respect to something else. Your problem lies within having three variables in your formulas, but you only know how to take the derivative with respect to one. So you see if you can find some variables to be "in terms of" the other. For example. You have \(w\) and \(r\), right? Well, looking at the picture, \(w=2r\). So now you have \(w\) "in terms of" \(r\). And you can put \(2r\) in the place of any \(w\). And so all the \(w\)'s are gone and you're left with 2 of 3 variables: \(r\) and \(h\).
Does that sound okay with you?
Yess sir, so i go perimeter equaling P^2/(8+2pi), and i got it right!, Thankyou so much!! big help
Haha, I didn't do a whole lot! If you got it right, I guess you're good! :)
haha thankyou !! @theEric
You're welcome! :) Take care!