Math

Two parallel resistors have resistances R1 and R2. If the total resistance is R, then 1/R = 1/R1 + 1/R2. R1 is increasing at 0.04 ohm/sec,and R2 is decreasing at 0.03 ohm/sec. How fast is the total resistance changing at the
moment that R1 is 3 ohms and R2 is 4 ohms?

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  1. 1/R = 1/R1 + 1/R2

    -1/R^2 dR/dt = -1/R1^2 dR1/dt - 1/R2^2 dR2/dt

    using the two given resistances,
    1/R = 1/3 + 1/4 = 7/12

    (7/12)^2 dR/dt = (1/3)^2(.04) + (1/4)^2(-.03)

    dR/dt = 37/4900 = 0.0076

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