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Math Help - A couple of optimization questions

  1. #1
    Junior Member NAPA55's Avatar
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    A couple of optimization questions

    I understand how to work with the extreme values and the like, but the problem with these questions is coming up with the function that models the problem.

    If someone could help me get started with the function or give me a hint on how to get it, I can handle the rest.

    Thanks!

    1. Train #1 departs the station at 10:00 and heads due south at 60km/h. Train #2 has been travelling due west at 45km/h and arrives at the same station at 11:00. When were the two trains closest together?

    2. A rectangle lies in the first quadrant with a vertex at (0,0) and two of the sides along the coordinate axes. If the fourth vertex lies on the line defined by x+2y-10=0, what is the maximum area of the rectangle?
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by NAPA55 View Post
    I understand how to work with the extreme values and the like, but the problem with these questions is coming up with the function that models the problem.

    If someone could help me get started with the function or give me a hint on how to get it, I can handle the rest.

    Thanks!

    1. Train #1 departs the station at 10:00 and heads due south at 60km/h. Train #2 has been travelling due west at 45km/h and arrives at the same station at 11:00. When were the two trains closest together?

    2. A rectangle lies in the first quadrant with a vertex at (0,0) and two of the sides along the coordinate axes. If the fourth vertex lies on the line defined by x+2y-10=0, what is the maximum area of the rectangle?

    The Best thing you can do is draw a picture

    A couple of optimization questions-capture.jpg
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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    I swear that questin was there before

    Here is the next one.
    A couple of optimization questions-capture.jpg

    so using the pythagorean theorem we get

    d=\sqrt{(60t)^2+(45-45t)^2}

    minimize this function
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  4. #4
    Junior Member NAPA55's Avatar
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    The first one was there but I figured it out and then erased it before you had a chance to post lol... book says 100 square cm and I got that too so I'm happy.

    Thanks for the help!

    I worked the second one out and got the right answer, but why do we use 45-45t? What does that mean?
    Last edited by NAPA55; April 2nd 2008 at 05:41 PM.
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