Track

[joey123]

You're designing a track that is to be comprised of a rectangular section and two semicircles, one on each end. Find the radius that maximizes the area enclosed by the track if the perimeter must be 500 meters.

 

[mammothrob]

You can make an equation that describes your perimeter
You can make an equation that describes your Area.

One equation will give you substitutions, the other you can use to differentiate and find a max...

 

[joey123]

but how exactly?

 

[stapel]

Start by drawing a picture. Label dimensions. Figure out how to relate the radius to the width. Work with the area formulas for rectangles and circles.

If you get stuck, please reply showing what you have tried. Thank you.

Eliz.

 

[mammothrob]

P = 2(lenth of rectangle) + Circmference of Circle

use that, youll only have to variables.... isolate the one. p is your given constant.

A= what?

when you get the formula for A, what does the graph of that formula look like? cann you visualize a max/min...

A'=?