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COMEDK2024Morning ShiftMathematicsApplication of DerivativesActual

The side of an equilateral triangle expands at the rate of 3 ~cm / sec . When the side is 12 ~cm , the rate of increase of its area is

Options

  1. A3 3 ~cm ^2 / sec
  2. B18 ~cm ^2 / sec
  3. C12 ~cm ^2 / sec
  4. D10 ~cm ^2 / sec

Correct answer

B. 18 ~cm ^2 / sec

Step-by-step solution

A = 3 4 a^2 dA dt = 3 2 a da dt Substituting a = 12 cm and da dt = 3 cm/sec: dA dt = 3 2 12 3 = 3 12 3 2 = 36 2 = 18 cm ^2 /sec

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