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Math Help - word problems

  1. #1
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    word problems

    I actually have three but i put them up one at a time.
    The first:
    A truck is 250 mi due east of a sports car and is traveling west at a constant speed of 60mi/h. Meanwhile, the sports car is going north at 80mi/h. When will the truck and the car be closest to each other? what is the minimum distance between them? Hint: Minimize the square of the distance. The answer says The minimum distance is 200 mi.

    I figure this is a Pythag. theorem problem. the adjacent(the truck) is heading left at 60mi/h. The opposite(the car) is going up at 80mi/h. and hypot. is 250mi. I tried deriving to get x or y, but that did not work. Please help.
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  2. #2
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    By Pythagoras:

    D^2=(250-60t)^{2}+(80t)^{2}

    D^2=t^{2}-3t+\frac{25}{4}

    Now, minimize.
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  3. #3
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    Now, I am lost, do I try to find the derivitive next?
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  4. #4
    Eater of Worlds
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    Yes, find the derivative, set to 0 and solve for t. Plug it back into the original equation. You will get the answer you
    seek.

    You can just differentiate t^{2}-3t+\frac{25}{4}
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  5. #5
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    I did what u said and got the right answer. Thanks. I am just a little bit confused on how (250-60t)^2+(80t)^2 is (or at least simplified to)t^2-3t+25/4? Other than that, i'm good on this problem.
    Last edited by driver327; July 30th 2007 at 02:06 PM.
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  6. #6
    Eater of Worlds
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    All I did was expand and divide through by 10000.

    See, when you expand you get 10000t^{2}-30000t+62500

    I divided by 10000 to simplify.
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  7. #7
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    I expanded and, and i got 3600t^2-30000t+68900. I exactly pressed the equation right and it gave that. I am not sure what is happening here.
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  8. #8
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    Quote Originally Posted by driver327 View Post
    I did what u said and got the right answer. Thanks. I am just a little bit confused on how (250-60t)^2+(80t)^2 is (or at least simplified to)t^2-3t+25/4? Other than that, i'm good on this problem.
    Quote Originally Posted by driver327 View Post
    I expanded and, and i got 3600t^2-30000t+68900. I exactly pressed the equation right and it gave that. I am not sure what is happening here.
    (250-60t)^2+(80t)^2

    = 3600t^2 - 30000t +62500 + 6400t^2

    = 10000t^2 - 30000t +62500

    -Dan
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