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Question
A boat is pulled toward a dock by means of a rope wound on a drum that is located
4 ft above the bow of the boat. If the rope is being pulled in at the rate of 3 ft/sec, how fast
is the boat approaching the dock when it is 25 ft from the dock?
Thanks
If we set the length of the rope pulled as y , & the distance traveled by the boat as x ,
then according to Phytaguras : y=√(4²+x²). Let's derive :
dy/dt = [2x(dx/dt)]/[2√(4²+x²)] . We know that at x=25 dy/dt=3 . Thus ,
3=25(dx/dt)/√(4²+25²)
dx/dt = (3/25)√(4²+25²)
Alon.
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Answers by Expert:
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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