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Calculus/application of integration problem

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Expert: Alon Mandes - 12/15/2009


Question
Good evening!

I'm stuck on this problem.. I hope you can explain it step by step for me. :)

Find b such that the line y=b divides the region bounded by the graphs of the two equations into two regions of equal area.

Here are the equations: y= 9-|x|, y=0

Thanks very much!

Answer

drawing
Hello, I attached a drawing to illustrate the problem .
From the drawing we can easily see that :
S1=C(9-b)/2 . Let's find C :
The intersect point of the two lines : y=9-x %26 y=b will give us :
b=9-x --> x=9-b. Therefore C=9-b .
The area of the whole right triangle is : 9*9/2 = 81/2 .
We demand that : 81/2=S1/2 --> S1=81 . That means (9-b)^2/2=81 . That will give us 9-b=9*1.414
-->b=9*(1-1.414)=3.72

Alon.

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".

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

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M.A in Mathematics & Bs.c in Electronics.

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