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Thread: Related rates: urgent

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    Exclamation Related rates: urgent

    2) The combined electrical resistance R of R1 and R2, connected in parallel, is
    1/R= 1/R1 + 1/R2
    where R, R1 and R2 are measured in ohms. R1 and R2 are increasing at rates of 1 and 1.5 ohms per second, respectively. At what rate is R changing when R1= 50 ohms and R2= 75 ohms?

    3) Cars on a certain roadway travel on a circular arc of radius r. In order not to rely on friction alone to overcome the centrifugal force, the road is banked at an angle of magnitude Q (theta) from the horizontal. The banking angle must satisfy the equation
    rg tanQ= v^2
    where v is the velocity of the cars and g= 32 ft/sec^2 is the acceleration due to gravity. Find the relationship between the related rates dv/dt and dQ/dt.

    4) A fishing line is reeled in at a rate of 1 foot per second from a bridge 15 feet above the water. At what rate is the angle between the line and the water changing when 25 feet of line is out?
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    Quote Originally Posted by ml_2007 View Post
    2) The combined electrical resistance R of R1 and R2, connected in parallel, is
    1/R= 1/R1 + 1/R2
    where R, R1 and R2 are measured in ohms. R1 and R2 are increasing at rates of 1 and 1.5 ohms per second, respectively. At what rate is R changing when R1= 50 ohms and R2= 75 ohms?
    \frac{dR}{dt} = \frac{\partial R}{\partial R_1} \cdot \frac{\partial R_1}{\partial t} + \frac{\partial R}{\partial R_2} \cdot \frac{\partial R_2}{\partial t}

    So:
    R = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}} = \frac{R_1R_2}{R_1 + R_2}

    \frac{\partial R}{\partial R_1} = \frac{R_2^2}{(R_1 + R_2)^2}

    \frac{\partial R}{\partial R_2} = \frac{R_1^2}{(R_1 + R_2)^2}

    So given your numbers:
    \frac{dR}{dt} = \frac{(75 \, \Omega)^2}{(50 \, \Omega + 75 \, \Omega)^2} \cdot \frac{1 \, \Omega}{s} + \frac{(50 \, \Omega)^2}{(50 \, \Omega + 75 \, \Omega)^2} \cdot \frac{1.5 \, \Omega}{s} = 0.6 \, \Omega/s

    -Dan
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