Calculus/maths

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Expert: Alon Mandes - 9/14/2008


Question

kite
We know area of BCD = 200 sin 2x.   Can we find an expression for BD^2  and can we use this to show that the area of triangle BAD is 200 - 200cos2x and hence show that area of kite is  A(x) = 200(1 - cos2x + sin2x)"


Answer
First of all , yes we can express BD^2 as function of x, for that we can use 2 methods :
1. Cosine rule : BD^2=20^2+20^2-2*20*20cos(2x)
2. Sine rule   : BD^2/sin(2x) = 20/sin(60-x)
  //the triangle has 2 equal angles & the sum of both
    & 2x gives 180 degrees//
As for the Area of the triangle BAD, we might have difficulties, because AD is not equal to AD !! So we will have to use a different approach.
Consider the angle ADB is α & the angle of ABD is 90-α, then we
might set up these equations :
1. AB/sinα = AD/sin(90-α)=BD
2. BD^2=AB^2+AD^2
From there we can find AD,AB & α. & then we can express the area.

Alon.
    Questioner's Rating
    Rating(1-10)Knowledgeability = 10Clarity of Response = 10Politeness = 10
    CommentAn excellent explanation. Well presented and understandable. Fantastic response time. A Million Thanks


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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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