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#1 2007-11-01 08:29:09

Daniel123
Member
Registered: 2007-05-23
Posts: 663

radian measure

A minor sector OMN of a circle centre O and radius R has a perimeter of 100cm and an area of Acm².

a) Show that A = 50r - r² [I have done this]

b) Given that r varies, find the value of r for which A is a maximum and show that A is a maximum


The main problem is that I don't really understand what the question wants me to do. I tried completing the square from part a, but I get the wrong answer. How do you do it?

Thanks.

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#2 2007-11-01 10:13:41

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: radian measure

The way I'd do it would be to differentiate 50r-r² and equate to 0.
That'll get you a critical point, and you can prove that it's a maximum by showing that the second derivative is negative.

However, completing the square does work.

50r - r²
= 50r - r² - 625 + 625
= -(r-25)² + 625.

Clearly, this is a maximum when r = 25, since the left term can never be positive and the right term is a constant.


Why did the vector cross the road?
It wanted to be normal.

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#3 2007-11-01 20:27:49

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: radian measure

Well I haven't done differentiation yet...

and that is the nswer I got, but it disagrees with the back of the book.

Thanks smile

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