The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics »

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Trigonometric area optimization
Replies: 13   Last Post: Dec 20, 2012 3:29 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Peter Scales

Posts: 192
From: Australia
Registered: 4/3/05
Re: Trigonometric area optimization
Posted: Dec 11, 2012 12:25 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Hi Adam,
> The lines y=10-2x, y=mx and y=(-1/m)x, where m > 1/2,
> form a right triangle. Find an m, so that the area
> measurement of the triangle is as small as possible.

Let line y=m.x be OA, line y=(-1/m).x be OB
and line y=10-2.x be AB

Then Area =1/2 .OA .OB

A is 10/(m+2),m.10/(m+2)
B is 10/(2-1/m),10/(1-2.m)


Area=1/2 .OA .OB =50.(1+m^2)/(2.m^2+3.m-2)
Find dArea/dm and set it to = 0
and select the option with m>1/2

Sketch the result and check Area for m=0 and
a few other values of m, including both solutions
of the quadratic dArea/dm=0.

Regards, Peter Scales.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.