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Math Help - Related Rate Again..

  1. #1
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    Related Rate Again..

    1. Let be the area of a circle with radius . If , find when .

    2. The radius of a right circular cone is increasing at a rate of 4 inches per second and its height is decreasing at a rate of 3 inches per second. At what rate is the volume of the cone changing when the radius is 50 inches and the height is 20 inches?

    3. At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 22 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

    4. The top of a 28 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 7 feet away from the base of the wall?
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  2. #2
    Member Mentia's Avatar
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    Dec 2008
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    Bellingham, WA
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    134
    Lets take a look at #1 and #2

    1)

    Area of a circle:

    A = \pi r^{2}

    Then, by implicit differentiation,

     \frac{dA }{dt } = 2 \pi r  \frac{dr }{dt }

    And we know  \frac{ dr}{dt } = 4 and r = 1, so we can get \frac{dA }{dt }


    2)

    Volume of a right circular cone:

    V = \frac{ \pi }{3 }r^{2}h

    Then, again by implicit differentiation,

    \frac{dV }{dt } = \frac{2 \pi }{3 }rh\frac{dr }{dt } + \frac{ \pi }{3 }r^{2}\frac{dh }{dt }

    and this time we know \frac{dr }{dt } = 4, \frac{dh }{dt } = -3, r = 50, h = 20
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  3. #3
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    Sorry but just dont do number 4..i got the answer already
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