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Hi, I've tried to figure this one out but I keep getting stuck, help please.
Q. A farmer plans to fence his rectangular pasture adjacent to a river. The pasture must contain 180,000 square meters in order to provide enough grass for the herd. If no fencing is needed along the river, what dimensions would require the least amount of fencing?
Let's set x to be the length of the rectangle of the fence %26 y is the width . Thus,
xy=180000 --> y=180000/y .
The perimeter is M=x+2y . M=180000/y + 2y .
Let's derive M with respect to y :
M'=-180000/y^2 +2 . To obtain minimum we solve M'=0 :
-180000/y^2 +2 = 0
180000/y^2=2
y^2/180000=(1/2)
y^2=90000
y=300 .
If y=300 then x=180000/300=600 . %26 these are the optimal dimensions .
Alon.
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Answers by Expert:
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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