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Calculus/WORD PROBLEMS WITH DERIVITIVES!

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Expert: Alon Mandes - 5/12/2009


Question
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 26 feet?


A fence 3 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?


How do I do these with derivatives??

Answer
Area of the window        A  :2xr+πr²
perimeter of the window   M  :πr+2x+2r=2x+(π+2)r
1st Eq : M=26 -> 2x+(π+2)r=26 -> x=½[26-r(π+2)] .
2nd Eq : A(r)=πr²+2r*½[26-r(π+2)]=πr²+26r-(π+2)r² .
To find maximum we derive A(r) & solve A'(r)=0 :
A'(r) = 2πr+26-2(π+2)r = 2πr+26-2πr-4r = 26-4r .
A'(r)=0 : 26-4r=0 -> 26=4r -> r=6.5 & therefore ,
A(6.5) = π(6.5)²+26(6.5)-(π+2)(6.5)² = 84.5

Alon.

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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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