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Math Help - Related rates

  1. #1
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    Mar 2009
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    Related rates

    No idea where to start and trying to find solutions to 3 problems, here we go.
    1) The trunk of a tree is approximately cylindrical in shape and has a diameter of 1m when the height is 15m. If the radius is increasing at mm/year and the height is increasing at 0.4m/year, find the rate of increase of the volume of the trunk?

    2) At 1:00 pm ship A was 80 km south of ship B. Ship A is sailing north at 30km/h and ship B us sailing east at 40 km/h. How fast is the distance between them changing at 3:00 pm?

    3) A man on a bridge 10m above the water reels in a fish line at the rate of 1m/s. Find the rate of change of the angle between the line and the water level when 20 m of the line is let out.

    Full solutions would be greatly appreciated with little side notes plz. Need to make sense of it all haha, thx for the help everyone.
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  2. #2
    Member
    Joined
    Dec 2008
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    130
    Quote Originally Posted by InAHole View Post
    No idea where to start and trying to find solutions to 3 problems, here we go.
    1) The trunk of a tree is approximately cylindrical in shape and has a diameter of 1m when the height is 15m. If the radius is increasing at mm/year and the height is increasing at 0.4m/year, find the rate of increase of the volume of the trunk?

    2) At 1:00 pm ship A was 80 km south of ship B. Ship A is sailing north at 30km/h and ship B us sailing east at 40 km/h. How fast is the distance between them changing at 3:00 pm?

    3) A man on a bridge 10m above the water reels in a fish line at the rate of 1m/s. Find the rate of change of the angle between the line and the water level when 20 m of the line is let out.

    Full solutions would be greatly appreciated with little side notes plz. Need to make sense of it all haha, thx for the help everyone.
    2) step 1, draw picture
    use pythagorean theorem
    differentiate pythagorean theorem with respect to time
    use given information
    solve for \frac{dz}{dt}|_{t=3 \text{hours}}
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  3. #3
    Member
    Joined
    Feb 2009
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    92
    heres a link to a thread i had with a similar problem
    http://www.mathhelpforum.com/math-he...same-time.html
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