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If two resistors R1 and R2 are connected in parallel, then the total resistance R measured in ohms is given by

1/R=1/R1+1/R2

If the resistance of R1 and R2 are increasing at 330 and 660 ohms per second respectively, then the rate of increase of R when R1=5000 and R2=5000 is how many ohms per second?

Just plug and chug

1/R = 1/R1 + 1/R2
1/R = 1/5000 + 1/5000 = 2/5000
R = 2500

-1/R^2 R' = -1/R1^2 R1' - 1/R2^2 R2'
-1/625E4 R' = -1/25E6 * 330 - 1/25E6 * 660
1/625E4 R' = 990/25E6
R' = 990*625E4/25E6 = 990*625/2500
R' = 247.5 ω/s

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