Search:
Home Math Games Word Games Strategy Reference Junior Games Daily Puzzles Printables Problems Members

Find the rate at which the area defined by the poles is changing
 

How fast does it change?

A particular dance is performed with four moving poles. At any one instant in time, these poles form a rectangle. The poles forming each pair of opposite sides move closer together and farther apart throughout the course of the dance. The dancer is to step into this rectangle and out again in such a way that he or she never gets pinched by the poles. In the diagram shown, assume that the Length of the rectangle varies according to the equation L = 4 + 3cos t, and the Width of the rectangle varies according to the equation W = 3 + 3sin t, where t is in seconds, and the dimensions are in feet. The area, A, then varies as a function of time.

Find the rate at which the area is changing at time t = 5 seconds. Be sure to indicate whether the area is increasing or decreasing.



Problem Moderated by: MrT

  
 
 
 

Problem Solution

Since A = LW, an application of the chain rule and product rule give us the equation A' = LW' + WL'. Substituting the equations provided give us:

A' = (4 + 3cos t)(3cos t) + (3 + 3sin t)(-3sin t).

After being sure your calculator is in radian mode, simply substitute the value t = 5, and you get a decimal value of 4.483 square feet per second (accurate to three decimal places). Since this value is positive, the area is currently increasing.

2002 Archive

  
 
 



 
Search For More Resources Search For More Educational Resources

 

Top Games On This Site

 
Adders!
Scramble
Entrapment
Secret Word
Trio Match 		 

Just a few of the educational game resources available on The Problem Site!

  
 






Home       All Games       Problems       Contact       Site History       Privacy Policy       Member Page