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Thread: Pre-calc problem: Minimizing distance

  1. February 6th 2009, 12:12 PM #1
    Juice08
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    Pre-calc problem: Minimizing distance

    At 2:00 PM bike A is 4km north of point C and traveling south at 16km/h. At the same time, bike B is 2km east of C and traveling east at 12km/h.

    a. Show that t hours after 2:00 PM the distance between the bikes is:
    square root of 400t^2 - 80t + 20

    b. At what time is the distance between the bikes the least?


    Help would really be appreciated!
    Thanks!!!
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  2. February 6th 2009, 12:23 PM #2
    skeeter
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    Quote Originally Posted by Juice08 View Post
    At 2:00 PM bike A is 4km north of point C and traveling south at 16km/h. At the same time, bike B is 2km east of C and traveling east at 12km/h.

    a. Show that t hours after 2:00 PM the distance between the bikes is:
    square root of 400t^2 - 80t + 20

    b. At what time is the distance between the bikes the least?


    Help would really be appreciated!
    Thanks!!!
    bike A's distance from C ...

    d_A = 4 - 16t

    bike B's distance from point C ...

    d_B = 2 + 12t

    distance between the two bikes at any time t ...

    D = \sqrt{d_A^2 + d_B^2}

    how were you taught to minimize ... with or w/o calculus?
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  3. February 6th 2009, 12:28 PM #3
    Jhevon
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by skeeter View Post
    how were you taught to minimize ... with or w/o calculus?
    the title indicates that this is for a precalculus class, so i guess w/o calculus is the way to go
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  4. February 6th 2009, 12:58 PM #4
    Juice08
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    Thanks!

    With a calculator....i can take it from here...thank you so much guys!!!
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  5. February 6th 2009, 04:24 PM #5
    HallsofIvy
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    Quote Originally Posted by Juice08 View Post
    With a calculator....i can take it from here...thank you so much guys!!!
    ?? How do you use a calculator to find a minimum value?
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  6. February 6th 2009, 04:26 PM #6
    skeeter
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    Quote Originally Posted by HallsofIvy View Post
    ?? How do you use a calculator to find a minimum value?
    graph the function and find the min ... it's really amazing what graphing calculators can do these days.
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