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Calculus/Math (related rates)

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Expert: Alon Mandes - 2/25/2009


Question
A rectangle is expanding so that its length is always twice its width. The perimeter of the rectangle is increasing at a rate of 6cm/min. Find the rate of increase of the area of the rectangle when the perimeter is 40cm.

Answer
Suppose that the dimensions of the rectangle are x(t) & y(t).
We know that the perimeter M is M=x+y -> M(t)=x(t)+2x(t)=3x(t).
M'(t)=6 -> 3x'(t)=6 -> x'(t)=2.
The area is S=x(t)*y(t)=x(t)*2x(t)=2x(t)². Thus, S'(t)=4x(t)x'(t)=
8x(t).
The perimeter is 40 when : 40=3x(t)->x(t)=40/3. Thus :
S'(M=40)=8*40/3=106.66

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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