Monday

April 21, 2014

April 21, 2014

Posted by **Danny** on Friday, June 19, 2009 at 6:17am.

I have already done the first part of the question, i only don't know how to do the "hence...". Please help, Thanks!

- How do i do this maths question?? -
**Reiny**, Friday, June 19, 2009 at 1:46pmarc length = a = rѲ

Then P = 2r + rѲ

7 = 2r + rѲ

Ѳ = (7-2r)/r

Let the area of the sector be A

by ratios

A/(pir^2) = Ѳ/(2pi)

A = (r^2)Ѳ/2

or

Ѳ = 2A/r^2

then 2A/r^2 = (7-2r)/r

solving for A after cross-multiplying and simplifying

A = (7r-2r^2)/2 or r/2(7-r) as required

second part:

A = (7/2)r - r^2 from above

dA/dr = 7/2 - 2r

= 0 for a max/min of A

2r - 7/2 = 0

r = 7/4

so Ѳ = (7 - 2(7/4))/(7/4)

Ѳ = 2 (how nice)

so max area = (r^2)(Ѳ)/2

= (49/16)(2)/(7/4)

= 7/2

**Related Questions**

trigonometry - A sector AOB of a circle, centre O, radius r cm, where the acute ...

maths - please can some one help me..? Part a - O is the centre of the circle, ...

Trig - Find the area of a sector with the given central angle θ in a circle...

trig - In a circle of radius 12 inches, a sector is formed by a central angle of...

pre-calc - Find an angle between 0 and 2ð that is coterminal with the given ...

trigonometry - please check my answers. 1.Find the area of the sector of a ...

maths - ABC is the segment of a circle with center O. This segment is enclosed ...

Calc - Consider a circle of radius 2 and a point P rotating around it. The angle...

Precalculus - The figure shows part of a curve traced by a point on the ...

Geometry - The measure of the central angle of a sector of a circle is ...