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Calculus/Related rates?

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Expert: - 4/28/2008


Question
At noon ship A was 100 miles due east of ship B. Ship A is sailing west at 12 miles per hour and ship B is sailing south at 10 miles per hour. At what time will the ships be nearest to each other, and what will this distance be?

Answer
Put ship B at the origin.  Ship A has the equation -100+12t=x with y=0.  Ship B has the equation -10t=y with x=0.  From the Pythagorean Theorem, it is known that the distance between the two ships is
c^2=x^2+y^2.  Use the equation for A and B for x and y.  Note that since distance between the ships is always positive, we can differentiate f(t)=a^2+b^2 to find the extrreme points.  The value of f(t), however, will be the distance squared.

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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