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formula manipulation/simplification

sbrews

New member
Joined
Dec 24, 2009
Messages
3
1 - this is not homework.
2 - I havent thought about this stuff since high school and that was approx. 30 years ago.

I have a problem that I would like to solve - not numerically, but in simplification.

Problem - find area of a circle with a given radius. I know the area formula is A=PI(r)^2. The radius is: 1/(2 * sqrt (PI)). the overall formula is:

A = PI * (1/(2 * sqrt(PI) ) )^2

Since the radius portion is squared, I recall that it can be simplified, but dont recall the rules for doing so. I am not looking for a final answer for A, just how to simplify the r^2 portion.

Note: ^ = raised to the power, sqrt - square root
 

galactus

Super Moderator
Staff member
Joined
Sep 28, 2005
Messages
7,216
The area of a circle with given radius, r, is \(\displaystyle A={\pi}r^{2}\).

That's it.

If you solve the above for r and sub back into the same equation, you will just end right back where you started.

Back to \(\displaystyle A={\pi}r^{2}\)
 

sbrews

New member
Joined
Dec 24, 2009
Messages
3
I dont think you understood what I was asking.

The radius is defined as

1
-----------------
(2 * sqrt (pi) )

That whole thing is then squared. I believe the sqrt(pi) portion somehow drops out. What I want to know is what are the steps to the simplication.
 

galactus

Super Moderator
Staff member
Joined
Sep 28, 2005
Messages
7,216
Oh, I am sorry. The radius is defined as \(\displaystyle r=\frac{1}{2\sqrt{\pi}}\)

To find the area, we sub this into the area formula:

\(\displaystyle A={\pi}\left(\frac{1}{2\sqrt{\pi}}\right)^{2}\)

Square everything in the parentheses.

\(\displaystyle A={\pi}\left(\frac{1}{4\pi}\right)\)

The Pi's cancel and we are left with \(\displaystyle \frac{1}{4}\)
 

sbrews

New member
Joined
Dec 24, 2009
Messages
3
Aha! Now I see what I was missing. So simple yet I missed it completely.

Thankyou for the help.
 

freshkaa

New member
Joined
Mar 6, 2010
Messages
1
If you could have any superpower what would it be? Well it cant be some overpowered crap, mine would be ice manipulation.
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