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About 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.
Education/Credentials
M.A in Mathematics & Bs.c in Electronics.
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You are here: Experts > Teens > Homework/Study Tips > Calculus > calculus
Expert: Alon Mandes - 11/3/2009
Question
i have a question about a ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2ft./sec, how fast is the angle between the top of the ladder and the wall changing when the angle is pi/4 radians?
Answer
According to Pythagoras : sin(θ)=(x+2t)/10 . Where x is the distance between the bottom of
the ladder %26 the wall . So, d/dt { sin(θ) } = d/dt { (x+2t)/10 } . This means :
cos(θ)* (dθ/dt) = 1/5 --> At θ=π/4 we get : cos(π/4)* (dθ/dt) = 1/5 --> (1/√2)(dθ/dt)=1/5 -->
(dθ/dt)=θ'(t)=(√2)/5 .
Alon.
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