Word problem help

thetomps

Junior Member
Joined
Sep 26, 2005
Messages
59
I am trying to help my sister who is stuck on this problem for her alegbra class. Can someone show me how to do it so I know what I am talking about when I try to explain this to her. Thanks.

Kay Thompson

Problem reads:

A rancher has 20 miles of fencing to fence a rectangular piece of grazing land along a straight river. If no fence is required along the river and the sides perpendicular to the river are x miles long, find a formula for the area A(x) of the rectangle in terms of x. From practical considerations, what is the domain of the function A?


Thanks again!
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,789
What was inadequate about the response you got three days ago?
 

Gene

Senior Member
Joined
Oct 8, 2003
Messages
1,904
Since the blind are leading the blind, what Elizh said in
http://www.freemathhelp.com/forum/posti ... st&p=30067
was
20=w+2x
w=20-2x
'cause you have 20 mi and 2 x long pieces from the river.
A= wx
A=f(x) = (20-2x)*x =
20x-2x^2
We can't ask her what she knows about downward opening parabolas so I have to guess. The vertex of ax^2+bx is at
-b/2a = -20/(2*-2) = 5
so the maximum area is when x=5. If she uses some other way to find the vertex, it is still at x=5
w=20-2x=10
A=wx=50 sq miles.
w=20-2*5=10
Do not double post!!
 
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