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Related rates need help calculus

Related rates need help calculus-example-1
User Void Void
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1 Answer

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Answer:

0.1468 ohms per second

Explanation:

You want the rate of change of R when ...

  • 1/R = 1/r1 +1/r2
  • r1 = 70 Ω
  • r2 = 120 Ω
  • r1' = 0.3 Ω/s
  • r2' = 0.2 Ω/s

Derivative

The desired rate of change is the derivative of R with respect to time. Implicitly differentiating the given relation with respect to time, we have ...

-R'/R² = -r1'/r1² -r2'/r2²

R' = R²(r1'/r1² +r2'/r2²)

Using the given relation and values, we have ...

1/R = 1/70 +1/120 = 190/(70·120)

R = (840/19)

R' = (840/19)(0.3/70² +0.2/120²) = 53/361 ≈ 0.1468

The rate of change of R is about 0.1468 ohms per second.

Additional comment

Most graphing calculators can figure this value for you.

Related rates need help calculus-example-1
User Shawn Chen
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