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Expert: Alon Mandes - 3/28/2010


Question
A piece of wire 12 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (Give your answers correct to two decimal places.)
(a) How much wire should be used for the circle in order to maximize the total area?
 m

(b) How much wire should be used for the circle in order to minimize the total area?

Answer
One piece will be with length x, & the other length is y=12-x .

The square : x=4L --> L=x/4 . Area of the square : S=L²=x²/16 .

The circle : y=2πr . --> r=y/2π . The area of the circle is :
S=πr²=π(y/2π)²=πy²/4π²=y²/2π=(12-x)²/2π .

The Total Area is A=[x²/16]+[(12-x)²/2π] .

We derive with respect to x, & solve the equation A'=0 . We get 2 possible solutions ,
1 for max & 2nd for min .
I will leave it to you from here to proceed .

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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